It's nice to be back, second night. This time for a different topic, although it really does also, again, touch on, just as last night's talk was on, secession, which is a type of decentralization of political power. This is a related topic, which is the problem of decentralizing military power specifically within a confederation or a regime itself. And part of how I got on this topic was whenever I would write on the topic of gun rights, gun ownership rights in the United States, there was a lot of discussion about the Second Amendment. Second Amendment this, Second Amendment that. We don't need to talk about any of the details of what's behind gun ownership. We've got the Second Amendment, and that's good enough for me. But of course, it occurred to me, we have a very international audience that reads the Mises Institute website. And I thought, well, how do I explain why private ownership and decentralized ownership of weapons is a good thing without using the Second Amendment? Because if you're just talking about the US Bill of Rights, well, non-Americans will be like, OK, well, what does that have to do with me? You have to explain then what are the principles that work here that are behind the amendment? Why does the amendment exist and for what reason? And so I started looking then into the philosophical and ideological foundations behind the amendment and the idea of private ownership. And private ownership is simply a type of decentralizing. It's a way to decentralize the ownership of the means of coercion, right? So you'll remember if you studied Max Weber, state building, the history of the state, that sort of thing, the definition of the state is an organization that within a specific territory has a monopoly on the means of coercion. And it's the traditional definition of what a state is. Key important factor is there's this means of coercion. That is usually the use of weaponry and violence. How do we employ that? Either to protect ourselves or to enforce provisions, forcing other people to do things and force laws. And some organization has a monopoly on it.  So the question is, well, can we weaken a state's monopoly by weakening its or can we weaken a state's power by weakening its monopoly on the means of coercion? And that's precisely what the Second Amendment is supposed to do. It's supposed to weaken the power of the central state in the United States, that is the federal government, by prohibiting it from limiting and monopolizing for itself the complete control over the means of coercion. That is as expressed in the ownership of arms of a variety of different types. So I wanted to really look at the historical and ideological evolution here, so that I could really think more systematically and in terms of more universal concepts rather than just, well, there's this US constitution and it has a text in here and that should be sufficient for us. I'm going to try and examine for you the reasoning that this amendment exists and what the thinking was behind it and how we could potentially even recapture than the intended original purpose of the amendment which is to decentralize state power. So just as to start off, we can look at what the Second Amendment is. It's the Second Amendment specifically to the US Bill of Rights, which just means the first 10 amendments to the US Constitution. And so the second one that they're writing, this is after the adoption of the Constitution in 1787, 1788 and the current Constitution, not to be confused with the previous one, the Articles of Confederation, which we'll mention a little bit, the current Constitution and a couple of years later, they added some additional amendments. This was partly to placate some people who had opposed the adoption of the new Constitution which they felt was insufficiently protective of certain rights. And so the second one simply reads, a well-regulated militia being necessary to the security of a free state, the right of the people to keep and bear arms shall not be infringed. So normally when you talk about this with the public and people in terms of what modern public policy is, they tend to fixate just on the last couple of clauses there. The right of the people to keep and bear arms shall not be infringed. You hear much less about what the first couple of clauses here, which is a well-regulated militia being necessary to the security of a free state. That is, a militia is necessary to the security of the free state. What do they mean by that? Now people who are against gun ownership will argue that, well, what it means is that only gun ownership should be limited only to membership in these official militia groups. I would argue that is not the proper interpretation. However, we do need to note and grant here that they are speaking in specific terms of what a militia is. They are thinking of actual organized groups separate from the federal government that has access to weaponry, advanced weaponry even, and are organized along lines, in many cases, approved of by state and local governments. And there are two images of the militia that we'll look at. There's this idea of the unorganized militia, which are just people who own guns in their own homes and they can be called forth to join the militia in times of civil unrest. But it was also imagined that there would be some sort of locally controlled state or local militia that did not answer to the federal government, that there would be trained groups of people that had access to firearms and bigger weapons than that even, who would also just be, not just a loosely knit group of people who happen to have weapons but were a more institutional sort of organization. And they imagined both of those groups then existing. And the purpose then was to offer a counterbalance against the central government, which had a very large amount of control over a large number of weapons. The idea was, okay, we need some local people who could maybe protect us from the central government in case it becomes excessively powerful and aggressive. But that's the overall issue. Let's look then at where that comes from, where those ideas originally formed, just to get a sense of what's behind all of this. And I would note that if this is our vision for what the Second Amendment was, if this was their vision for what the Second Amendment should be, a large number of militia groups either institutionalized or more casually composed of private gun owners, then that vision has failed, that it has fallen out of usage, that it is no longer employed as a meaningful balance against federal control of the means of coercion. Now with so many things related to the Bill of Rights, to the American Revolution, to the American ideas of rights, you have to look beyond the revolution into the past. You have to look to the English Civil Wars of the 17th century because so much of what the American Revolutionaries thought in terms of what are their rights, how do they stand up for their rights? We can trace back directly to the English Civil Wars in the 1600s, in the mid 17th century. And this was a time where you had groups that started to advocate for amendments like what we now call the Fifth Amendment, which is the right to remain silent. Why was that an issue? Well, during the period of the English Civil Wars and the period leading up to it, they would torture people to get them to confess things and say things. But if you have a right to not say anything, then torture doesn't work within a legal setting nearly as well. So this all came to a head in the period leading up to the English Civil Wars, this period of when English kings attempted to become absolutist kings more on a French model and fancied themselves as absolute monarchs that the English didn't really go for nearly as much. So the Civil Wars resulted and you had some groups, the perhaps the most libertarian of which, the most classical liberal of which, and in one of the earliest examples of classical liberalism as a functioning group would be a group called the levelers. And these were radical liberals by today's standards for sure. And they themselves in the 1640s as absolutism is clearly an issue in England. And as the English Civil Wars are heating up, the levelers are calling for a decentralized militia system in England, the whole point of which was to lessen the power of the king in domestic affairs. And as one historian of the levelers writes, in May 1649, the levelers proposed that armed forces were to be raised strictly by local divisions and officers by men elected locally, only the general officers were to be appointed by parliament. John Wildman was to express similar views in more specifically Republican terms in the 1650s, opposing quote unquote mercenary armies in favor of the people being quote masters of their own arms. And militias weren't exactly favored under Oliver Cromwell who had a quasi dictatorship at the time when he had the protectorate that replaced the kings in this period. So they didn't want him being able to centralize power under the new model army either. So there was this ongoing efforts to get local civilly controlled militias that could help the locals stand up to the centralized power. And one of the great historians on this topic that I'll quote several times for this talk is a British historian named Marcus Cunliffe. And he has a book called Soldiers and Civilians. And it's a history of mostly the United States and the relationship between civilians and the military in the U.S. It's now out of print, but if you can find it, it's very interesting if you're interested in this topic. And we'll go into some of how he describes the views of Americans in terms of how they favored service in militias over service in the permanent federal military. And that early Americans made a very big distinction between people who served in the local militia and people who served in the national military. But he notes also that this goes back significantly farther than just the American revolution. And he notes that as the Cromwellian legacy died down at the end of the Civil Wars and as the Stuart Kings came back, who were now cured of their pretensions toward absolutism having been deposed and one of their heads cut off and all that, they were allowed to come back to the throne. And but the liberals, the levelers and their allies weren't going to allow this new king to have a monopoly on military force. And so they did allow, as Cunliffe notes, a small regular forces to be maintained for the military. This was the foundation of the modern British standing army. However, there was to be a nationwide militia composed of civilians who would, as in earlier days, be summoned in time of need. The militia, however, was to be under civil law and to be organized locally by the Lord Lieutenant in each county. It was thus decentralized and divorced from royal control. Unquote. And later American attitudes, Cunliffe explains, toward a standing army were adopted largely in this period, they inherited this thinking that to give the king or the executive power access to a permanent standing military force on land basically gave the executive the power to force the king's will on the local population. If any sort of group resisted, you would send in a military contingent and they would force the locals then to obey the executive power. And this, by the 18th century, had died down a little bit and the British had become a little more accepting of standing militaries at that time. But the Americans who were more in favor of, as we see just in general, had never quite abandoned the 17th century ideas that had come over with the earlier settlers had never quite been abandoned. So in many ways, the Americans were more conservative and more siding with, they were still more sympathetic to the old liberal, radical liberal ideas that had arisen during the English Civil War. So let's look at how this manifests itself then in the early years of the United States. The early years were marked not by the current constitution but by an earlier constitution. This was the so-called Articles of Confederation which came in and was approved in the 1770s. So more than a decade before 1787, the current constitution. And most of that document deals with arming in an army and a navy because it imagined the United States is basically this defense union that existed to defend it against European powers and such. The framers of the document were careful to allow states opportunities to veto federal actions. And according to the text, it notes and is very limiting upon how much the federal government can do in terms of waging war without agreement from the member states. So there are a variety of requirements in terms of buy-in from the member states in terms of waging any sort of war. However, it also goes on then to note that quote, every state shall always keep up a well-regulated and disciplined militia sufficiently armed and accoutred and shall provide and constantly have ready for use in public stores a due number of filed pieces and tents and a proper quantity of arms, ammunition and camp equipage. So of course you can start to see the beginnings of the text that later is incorporated into the Second Amendment here. And their concern again is making sure that the central government is not able to easily overwhelm the member states in terms of military power. And so by this time, it's noting what's also an existing reality. The member states already had many of their own provisions noting that the local population should be able to own arms. And they of course had a wide variety of local and member state militias. Why? Well they needed them for a variety of reasons, right? They had border disputes with say, the Spaniards in some cases, there were of course neighboring Indian tribes who might occasionally raid the whites communities as the whites pushed further and further into the frontier, this cultivated more trouble with the bordering tribes. And of course there was always some threat of some internal rebellion and disorder in general. And of course there was no police, right? Police, the idea of urban police is a 19th century innovation and certainly didn't exist in 18th century America. And so it's keep in mind that when people are debating something like the Second Amendment, it's assumed as a given that these villages, that these farmers, that they're pretty much on their own and they're gonna require some sort of arms in order to defend themselves from any sort of renegades, marauders, highwaymen, Indian tribes, et cetera. And it's not, and so the Second Amendment was not written to really address that issue because that was just assumed to already be a part and parcel of every state constitution. And we can see that in the text later. And so it's important that we don't look on the Second Amendment as something related to protecting yourself from crime or for hunting, right? Obviously has nothing to do with that. This is an attempt to balance military power and the monopolies, the potential monopolies on military power that existed. And you can see this in debates over the ratification of the US constitution. So as they're talking in 1787, 88 about should we adopt this new constitution, some of them got up and said, well, you don't have to worry about US centralized military power because you can assemble in Congress and then you can tell the federal government to stop abusing your rights. Just assemble the people. And Patrick Henry gets up at the Virginia discussion and debate over this and he's very sarcastic about it. He doesn't believe the idea that you can just assemble the people and solve the problem. He thinks you need guns. He says, sir, we should have fine times indeed if to punish tyrants it were only necessary to assemble the people. Your arms where with you could defend yourselves are now gone. Did you ever read of any revolution in any nation brought about by the punishment of those in power inflicted by those who had no power at all? A federally controlled standing army we shall have also to execute the extra bowl commands of tyranny and how are you to punish them? That is the tyrants. How will you order them to be punished and who shall obey these orders? So Henry is rejecting the idea that, well, we'll just call together Congress or we'll have some state legislatures meet and then we'll tell the tyrant to stop. What he's saying is if you want to actually oppose tyrannical behavior, you're gonna need to have guns to do so. And so this, of course, this attitude then feeds very much into then in the 1780s and 90s in terms of our idea of what is the purpose of the Bill of Rights and what came to be known as the Second Amendment. And this, of course, came to be just common among liberals in general. That is the group we call classical liberals today, 19th century liberals, historical liberalism. Generally the free markets people, Thomas Jefferson, John Locke, those sorts of people. And something that characterized those groups both in the United States and in the United Kingdom during this period throughout the 18th and 19th century was that the liberals opposed the idea of standing armies and hated the idea and generally considered anything more than just a token force of land troops was illegitimate and obviously a force for illiberal despotism. And this goes on into the mid-19th, even the late 19th century in Britain even among the radical liberals led by people like Richard Cobden who were very much against standing army in any form. And they favored of course the more local malicious system, the decentralized system that was being discussed here and was of course preserved much better in the United States. That idea is basically long gone in the modern United Kingdom. Some remnants remain in the United States. We see then expressed in some historians of the time. And we can see Leon or historian Leon Friedman states it right here, quote, the people organized in the state militias were regarded as a counter force against the threat that the regular army could be used as an instrument of oppression and service in the militia was a right of the citizen that could not be transgressed by the federal government. And that basically sums up the decentralized liberal view at the time. And at the time when the new constitution was adopted you ended up with a U.S. army around, let's see, Congress opposed any attempts to increase the size of the professional U.S. army much beyond a thousand men. That's of course stretched up and down the entire Eastern seaboard. And that didn't grow much over the next several decades. By the 1850s, they used the army for all sorts of weird stuff, the regular army. It was mostly the militia they used. But one instance where they did use the army in the mid-19th century was when the Mormons out in Utah refused to abandon a plural marriage, right? The multiple wives for one man. And for some reason everyone back in Washington was really freaked out about this and felt something had to be done. So they send in an army contingent to make them stop. Yet using the standing army for just what the liberals had said they shouldn't be using it for. So President Buchanan sent it in as many men as he could get together and they sent in about 2,500 men to Utah to do this. But that was a majority of the entire U.S. standing army at the time. So we're talking like 3,000 or 4,000 guys that make up this army for North America. So you can see just how small this force was by modern standards. Now that was the professional full-time U.S. military. And that was one thing. The balance of that was this unorganized and this localized militia and what does that mean? How did they imagine that? And they took many, many different forms. George Mason, one of the framers of the Constitutional Convention but one of the more libertarian ones, he was asked what is the militia? He says, they consist now of the whole people except for a few public officers. When the second Congress sought to exercise this constitutional authority to, quote, provide for organizing, arming and disciplining the militia, it directed each and every free able-bodied white male citizen of the respective states who is of the age of 18 and under the age of 45 to enroll in the militia of their states. Whereas Patrick Henley declared at the Virginia Ratifying Convention, the great object is that every man be armed. So is it just these guys who are hanging out? Is there any sort of more organized aspect of that? And that's not completely clear from the text, from the legal text we have, it's more clear from just historical experience that we get the clues about how people viewed this. From the text, it's quite clear that they had just some general idea that people should be able to own their own arms, either in case they're called out for the militia, just for general use. And this goes back to before the Bill of Rights and one of the clearest examples of this is the 1780 Massachusetts Declaration of Rights, which states that the people have a right to keep and bear arms for the common defense, quote, unquote. And it says it even goes on, in times of peace armies are dangerous to liberty, they ought not to be maintained without the consent of the legislature. And the military power shall always be held in exact subordination to the civil authority and be governed by it. So this is 1780, this is written years before the new constitution and the Bill of Rights is written and many state constitutions contain these sorts of provisions. And we see this sort of thing crop up then in other state constitutions decades later. For example, if we look at the original constitutions for say Montana and Colorado, so Colorado's constitution was 1876, Montana's was probably about 10 years later, I think maybe the 1880s. It's these constitutions have very similar language and they state that persons may keep and bear arms in defense of his home, person and property or in aid of the civil power, that is for this unorganized militia. Or you can find other clauses in Arkansas's text that says the citizens of this state shall have the right to keep and bear arms for their common defense. Maine's constitution says every citizen has a right to keep and bear arms for the common defense and this right shall never be questioned. Kansas says the people have the right to bear arms for their defense and security, but the standing armies in times of peace are dangerous to liberty and shall not be tolerated, et cetera. So you get the idea. They weren't relying on the US Federal Bill of Rights to set out the details of this. It was heavily ingrained into the state constitutions themselves and as is recognized by scholars today in many cases, the Federal Bill of Rights is based on state bills of rights, that these ideas pre-exist the text as written there. However, there was this other tradition that we see in actual practice, which you don't necessarily get from the earlier comments in the 1780s, but it's clear that the thinking on this by the early 19th century was that, okay, well we can also have these more institutionalized permanent militia groups controlled by state and local governments, or at least licensed by them in a sense. They were semi-private in many ways and they have a quite interesting history. Jeffrey Rogers Hummel has written a great journal article on a conscription in the militias in the United States. He says that there were certainly plenty of unorganized militia groups, but some of these militia groups made themselves permanent. They became essentially clubs and they met all the time and they trained and they became de facto private militias in many cases because they funded themselves with essentially a license from the state or local government, a charter of sorts. And it was unclear exactly what level of readiness was to be expected from these groups, but these people made themselves available and it was known to where you could go to get these militia guys to turn out in case of civil unrest, in case of attack from neighboring tribes, that sort of thing. And this was not to be confused with the idea of today's National Guard, which is a federally controlled and federally funded force, which is subordinate in times of emergency, federal officers and federal officials take control of the state National Guard groups and that's totally different. Now they did discuss that sort of thing at the time of the founders, but as one legal scholar notes, yes, the founders had a concept that approximates today's National Guard, but it was a concept of which they disapproved. This was the select militia, especially trained part of the citizenry. To the founders of select militia was a little better than an army. The Philadelphia Convention explicitly rejected a proposal to create a select militia for the federal government as did the third Congress. And also moreover this idea that the federal government would just quote unquote provide for training the militia was seen as totally unacceptable because they feared that okay, if the feds train and fund these state militias, they end up running these state militias and they end up working for the federal government. So that doesn't accomplish the end, which was to have militias totally separate from the federal government. Now this took the form of states funding their own militias and being jealous of their ability to control the use of those militias. And we can look to a variety of cases where the federal government attempted to quote unquote call forth the militia. That is the president declares there's some sort of emergency or a war and he tells the states to send us your militia troops and we'll fight the war with them. The idea of course was that if the executive power wanted to wage a war they were gonna have to ask nicely for the states to give them their militia men so that they could fight in the war. And that had a ingrained veto of sorts, right? Where the state government could potentially refuse to send those troops if the state government did not approve because the state essentially funded it and controlled these local groups. So he had to ask pretty please send us your militias so that we can fight this war. And it was early on in the war of 1812 that they already started to meet resistance from this. For example, Vermont, the governor of Vermont, Martin Chittenden, he very much opposed the use of Vermont troops in the war and what was essentially ended up being a campaign to invade Canada. He said that, look, our state troops are here to defend the state from incursion and invasion from foreigners. My troops are not here to invade Canada and to basically start wars with other countries. So he stood up to the feds and was very vehement about, you don't get to use my troops. The governor of Connecticut also refused to comply with a requisition from the secretary of war at the time. And on this, the state assembly backed him up saying that it is not only intolerably oppressive but subversive to the rights and liberties of the state and the freedom, sovereignty and independence of the same and inconsistent with the principles of the constitution of the United States. So they had these troops that were sitting there and they're like, these troops are for defending Connecticut. You don't get to use, so too bad. And during the Civil War, another case of this came up where Lincoln wanted to use troops out of Kentucky, which was a border state and had not actually seceded. And he'd attempted to call forth the troops from Kentucky and Kentucky refused, saying that, well, we don't want to secede and we're not favoring secession among the southern states, but we're also not going to participate in shooting our fellow citizens in these southern states. And so you don't get to use our troops. And as the governor claimed, we saved the union and frowned down secession was their idea that they could take this middle ground and they weren't going to let anyone use their troops for it. And one observer said, he said, a foreigner came to the country that he would be bewildered and he might well have concluded that the United States had become three countries, the Union, the Confederacy and Kentucky because Kentucky just refused to take sides in this. And part of refusing to help the federal government put down this rebellion was to refuse its use of the state troops. Now that ended in Lincoln's favor because eventually they had an election and a bunch of union people came into power in the Kentucky state government. And so that allowed Lincoln then to use those troops. But it did not establish any sort of legal precedent saying that, yes, the president gets to use these troops in any way he wants and you have to submit them. That was not established. He simply managed to win an election and at the state level and get the troops that way. So we can see then how that was working as intended then because of course during the Civil War, if Lincoln had not been able to call forth state troops in that way, he would have not been able to wage a war nearly to the degree that he had. Now in that case though, most of the state governors, most of the state legislatures were in agreement with the federal government's policy, at least in the North. And so they agreed to send their troops. Kentucky was the outlier. But that was a voluntary submission of troops. Later the fed started to use a federal conscription method and there were other methods used as the time as time went on. But early on the war relied heavily on states voluntarily sending in their troops. And they were able to do that because of agreement because there was a consensus in his favor among the Northern states. But he wasn't able to force or compel the states to send in their troops this way. So what did these local militias look like in many cases? Let's look at the 19th century and to get a sense of what was going on here. And first of all, it's very interesting to note how there were differences in views between federal troops, federal professional troops and these militia troops that were viewed as a good thing. But people took a very dim view of federal troops at this time. And this will be remarkable for younger people who've grown up in a time, although maybe the younger among you don't even remember these days during the Iraq war after 2003 and 9-11. People were everywhere putting magnets on their car saying, I support the troops and you're supposed to start saying, thank you for your service all the time. Which wasn't really a thing in the 80s or even really the 90s. It was kind of a post 9-11 thing. We thank the troops for everything all the time. And we announced it on our bumper stickers and that sort of thing. That would have not been your dominant attitude in regards to the federal government and their troops in the 19th century. And a lot of this is covered by Cunliffe in his book where he's got all sorts of great little anecdotes about it. And he takes a line from Ulysses S. Grand Union soldier talking about the first time he got his uniform and he went into town and he was very, very proud. He's a professional federal soldier. And so they see him in uniform and they know. And he says, I donned the uniform and set off for Cincinnati on horseback. Well, I was imagining that everyone was looking at and admiring him.  No sirree. This attitude, Richard Bruce Winders explains in his history of James A. Polk quote, illustrates the image of soldiers common in the 1840s as slackers on the public dole, unquote. Indeed, even as late as 1891, a speech published in the Christian Journal The Churchman recounted Grant's anecdote and concluded that quote, the national contempt for the army was based on the fact that quote, it is such a lazy life, unquote. Nor did the attitudes begin in the 1840s. In his biography of George Washington, historian Mason Weems notes the lack of concern over American casualties suffered under Anthony Wayne in a battle with the Shawnee in 1794, writing, however, after the first shock of the battle, the loss of these poor federal soldiers, these poor souls, was not much lamented. Tall young fellows who could easily get their half dollar a day at the healthful and glorious labor of the plow that these men would go and enlist and rust among the lice and itch of a camp for $4 a month were certainly not worth their countries crying about, unquote. So you can imagine people reacting that way to US casualties in current culture. But in the 19th century, there was much disdain for the permanent federal troops in this way. Now, they did not feel that way among militia troops, the state troops, the local troops of which many Americans were members, they had quite a different view. The part-time soldier was viewed as something far more respectable and glorious and hardworking because of course he was a farmer most of the time and then in his spare time would go train and volunteer service to his community. And the idea of the standing army thus persisted well into the 19th century. And so there were a lot of policies designed to encourage and protect local militias in this way. And we can look and see how some of these really took form. And let's look at some of the details here that I think we can, let's see. I want to provide you with some of these pictures of what these local militias looked like. All right, here we go, here's some good details. By the end of the 18th century, we begin to see more and more semi-private militias. These were alongside the common militia, that is what in many cases were conscripts at the state level, which were far more used in the very early 19th century and the late 18th century where there was forced military service in many states. A common belief among Americans is that there wasn't a draft until the Civil War, but that's not true. There was draft for state troops at the local level going back even to the revolution. But that actually died out at least in the Midwest and North by the mid 19th century. They still had conscripted troops in the South because they had forced people to do slave patrols. But in the North they didn't care about that. And they basically got rid of the common militia that had conscription. And it just became that the militia became dominated by the semi-private groups that were generally chartered at the state and local level. And they were often called the uniform militia because they had to buy their own uniforms, often very extravagant, beautiful uniforms in many cases. They were independent of a centralized state militia system even in many cases, just simply had some letter of approval from the state legislature for what they can do. They elected their own officers, were self-funded and trained on their own schedules. Although they were ostensibly commanded by the state governors, this system of functionally private militias became an established part of daily life for many Americans. These were local volunteer militias with names like the Richardson Light Guard, the Detroit Light Guard, or the Asmonian Guard. They were essentially private clubs composed of gun owners who were expected to assist in keeping law and order within the cities and towns of the United States. Separate from the so-called common militias, which, as we've stated, were more official and often had a conscription element. By the Jacksonian period, however, these volunteer militias were really the dominant group and they saw a remarkable growth in the mid-19th century. The number of volunteer units had been expanding since the American Revolution, but after the war of 1812, it exploded. 300 sprang up in California alone between 1849 and 1846. These groups were, in the words of Marcus Cunliffe, volunteer companies existing independently of the statewide system of militia and they held themselves aloof from the common mass. They provided their own uniforms. And so you could see that in many cases, they would simply write a letter off to the state government, hey, we got a bunch of guys here, we wanna form a local militia and someone would write back from the state, it says, sound good, but you're on your own, you gotta fund yourself, but we'll add you to the list of people that the governor will call upon in case of need. And since, of course, it wasn't funded by the states, then it was basically a large, local, independent operation. But you can look at the way some of these units came about and the way they were funded, if we look at, say, the Richardson Light Guard, which comes from South Reading, Massachusetts, in response to a perceived shortage of militia men in the years following the Mexican War, at the time, all that was necessary for the militia to be regarded as legally sanctioned was the group to petition the governor. And the dues could be expensive, however, so they would go to fundraisers and they would offer honorary to funders and they would offer honorary memberships in these militias in exchange for money. And what happened with the Richardson Light Guard is the largest donor in that case was a man named Richardson, after whom the militia ended up being named. So funding from prominent community members also added legitimacy to the group and ensured it would continue to be regarded as a community sanctioned group of armed men. They were enmeshed very much in the community. The modern idea of militias as came about in the 90s in the last 20 years is that you have these malcontents who are off meeting in the forest somewhere and they're all plotting some kind of revolution and maybe they're white supremacists or something. These militia groups were like the mayor and state legislators and your local business leaders and your local rich guys who are funding the group. By the way, I don't necessarily think that image of the modern militia is correct, but that is a dominant feeling about how they should be described and certainly how they're described by left-wing scholars on the topic. But you can't get much more establishment than these militias in the 19th century in terms of funding, in terms of who's in them, in terms of the approval they get from the state and local government. But they have no tie whatsoever to the federal government. They don't get funding, they don't take any sort of oath to the federal government and it's just simply not a significant issue for them. And so a lot of these groups, they become really institutions for integrating people into just United States society overall. And even in this period, they were taking on, as well, arms became more affordable to middle-class America. They became more common and just kind of more middle-class and feel less associated with the upper classes because that's who could afford guns in the early years. But by the 18 and 40s and 50s, regular people could go out and buy some pretty decent guns. They're forming their own groups and they're giving themselves names like softball teams. So some of these militias, they call themselves the Invincibles, the Avengers, the Snake Hunters. They have names like this. And a lot of them were made up of a lot of immigrants. This is a point that Cunliffe makes, is because of their local nature, many militias reflected local character as well. And access was hardly limited to national ethnic majorities. By the 1850s, immigrants had come to dominate many volunteer militias with Irish, Scottish and German militias becoming especially common. The Scottish militia men wore kilts as part of their parade uniforms. The Italians created a Guardia Nazionale Italiana. Robert Ernst notes that the significance of the immigrant military companies is evident in the fact that in 1853, more than 4,000 of the 6,000 uniform militia in New York City were a foreign birth. It would be interesting to see if a bunch of Venezuelans got together and formed up a militia today in New York City, how that would be received. But of course, in this setting, setting up a militia integrates you into essentially the ruling class. It creates a way of social advancement. It creates a way of regularizing yourself, of announcing that we're middle class and we're part of this society and we're part of its legal system, essentially. Normal militia groups limited to Christians. Jack D. Foner recounts in the American Jewish Archives Journal. Jews in New York City formed military companies of their own. Troupe K, Empire Hussars was composed entirely of Jews as was the Young Men's Lafayette Association. The third unit, the Asmonian Guard, consisted of both Jewish and Christian employees of the Asmonian, one of the earliest Anglo-Jewish weekly newspapers. Our employees commented the newspaper have been seized with this military mania as they have enrolled themselves into an independent core, unquote. And to this day, there are some surviving aspects of these groups. As part of this, a lot of local military schools and institutions cropped up where you could send the youth that would become integrated into the idea of the local militia, local military, and a lot of even the existing military schools today, that was their original, their origins was in preparing for a local militia and military-type service. And that's where we get the marching bands from, right? I mean, on college campuses, they have these military-esque uniforms, right? Now, all of these militia groups, they had their own marching bands, their own musical detachments. They were always doing local parades and events and firemen had their own militia groups, the police had their own militia groups. And it was just this whole milieu of all of these groups that were there and were very much at the forefront of really today, what you would look at, like the Knights of Columbus and the Elks Club and the Rotary Club and all that sort of stuff. They all had the military branch of the Rotary Club was the thing and the military branch of the Optimus Club, right? This was basically how it was structured. And so if you're like one of these extreme decentralized types and you're like, yes, we want there to be a very robust military culture out of reach of the central federal military, this sounds like a really great situation because you can imagine then, like how much power monopoly does the federal government have where cities are filled with these independent militia groups that answer only to the city or to the state. It did not survive really much beyond the American Civil War. So it's heyday was in the mid 19th century and survived a bit into the late 19th century. But the fact of the Civil War brought about a standardization in military use and military strength that relied much, much more than on federally controlled troops. They had, of course, experimented then with a federal conscription act at this point. They had called forth all of the state militia groups that had then been federalized and gotten used to being under the command of federal soldiers. And then you had all of these veterans, huge numbers of veterans after the war who began to associate themselves with military service in service of the federal government. So this really changed the tenor, the military tenor of the country in terms of what is the military, who serves in it, what's the, this whole idea where they had all this contempt for federal soldiers that largely died out because of the prestige of veterans after the American Civil War. And so that then led into what we now find is recognizable and what we're told is actually the militia system in the United States. And this was, this can be traced really to a specific piece of legislation, 1902, called the DIC Act or the Militia Act of 1982. This brought this final realization of having this professional trained state militia system that was essentially under the federal control and could be easily called forth by the feds and turned into a federal group. So ostensibly it looked like a state militia, but it wasn't because it was increasingly under the command of federal troops. It was funded by the federal government. And yes, after 1903 the National Guard still had a high degree of allegiance to the state, but the National Defense Act of 1916 allowed the National Guard to be deployed outside their own states. So it was chipping away this old idea from Kentucky and Connecticut where, okay, these troops are here to defend our state. Nope, no longer, after 1916 we can move National Guard around anywhere we want. And then after 1933 new amendments to the National Defense Act were passed which made members of the National Guard units members of both their state's National Guard and the federal military. So they started taking oaths to both their state and to the federal military and were considered employees essentially or troops of both. And so by 1970 this was pretty much all gone. Now if you're old enough to remember the Vietnam War you'll remember that in many cases men avoided service in Vietnam by joining their National Guards. And this was a common use tactic by some of the guys who were fast thinking because you had to get in early in the conflict in order to do this. But if you saw the war coming you could then enlist in your state's National Guard put in your time in the National Guard and then once you were released from the National Guard it was considered you had done your military service and you couldn't be drafted at that point. You'd already done your bit. And so this was a common tactic in California I know some people who did that. I know people who joined the Texas National Guard to avoid being shipped off to Vietnam because at the time it was still written into the law that state National Guards could not be stationed overseas and also that the governors would maintain a veto on the use of these troops anyway. And so that continued for a period and that wasn't changed until after the war. And so in the 70s and 80s then you saw a continued movement toward bringing them under federal control. And the final nail in the coffin then was what I call in here the governors revolt of 1986. So Vietnam War is over. There was still a perceived veto that state governments had over the deployment of state troops, the state National Guard troops. But in the heat of the Cold War military conservative Cold Warrior types specifically a guy named Sonny Montgomery from Mississippi decided he didn't like this idea that state governors were stepping in to avoid and stepping in to prevent the president from sending troops to Central America. This was a very heated topic at the time where they were sending American National Guard troops to Central America to train troops there, many of which were troops of these despotic regimes in Central America at the time. So a lot of left-wing governors they didn't want their troops being shipped off to Central America to do this. And so this Cold Warrior guy, Montgomery's like well we can't let that happen. Wherever the president says troops should go they should go. So they passed new legislation in 1986 finally eliminating the last vestiges of state veto on the use of National Guard troops. And that then that was that. And that's how you have today this situation where you probably maybe know some people who've been in a National Guard unit and then they're just minding their own business working at their regular job they're in the National Guard. Next thing they know they get a call that they're being deployed to Afghanistan or they've got a training stint coming up in Indonesia. Well that would have been unimaginable of course in the 19th century that you could send National Guard troops to a foreign country and especially with a war not being declared and the idea that they could be called up and sent to anywhere at any time. So this was totally contrary to the idea of the Second Amendment totally contrary to the idea of state controlled militias and military power and that the idea that they could counterbalance federal power that was just clearly all gone. And today we see that in the fact that essentially the National Guard is just the army reserves. It's a reserve force that gets called up and sent to wherever the president wants to have a war. And there is no counterbalancing anymore. There's no real issue here where the state National Guard could offer any sort of resistance against federalization of those troops and the use of those troops in a federal effort. They're funded by the federal government. They're in the chain of command of the federal government and unless the law significantly changed that's going to remain the situation. Now historically in 1986, the governors tried to go against that and start announcing that, okay, well now you've made it law that you can use these troops whenever you want but we're not gonna let you, we're gonna somehow stand up for ourselves and we're gonna resist even if it's just quasi legal. Well, the Defense Department immediately responds and even though they were unwilling to push the issue of you have to do what you say, what they did was they said, if you refuse to use the National Guard in the way we say you must, we're refusing, we're withdrawing all federal military funding from your state. So of course the federal government, they put lots of money into army bases into army equipment, they pay army salaries in these states and any time a state since the 80s has attempted to resist the deployment of state troops for federal purposes, the Pentagon sends in generals and threatens local politicians and says we will inflict as much pain as possible on you for attempting to control your use of state troops and you see this today and the same reaction in legislation that's now used in a variety of state legislatures. It's come up several years now, the last five years or so, where various states they have what's called Defend the Guard legislation and this is an attempt to assert some state control back over the guard. Normally the way the bill is written is that you cannot deploy any of our state troops unless Congress has actually declared war on the relevant country in question. So the only way you would then be able to deploy US troops to Indonesia, to Afghanistan would be for Congress to formally declare war on those countries, which Congress never does anymore. So this was an attempt then to really rein in federal power over state troops. It hasn't passed in any legislature, largely for the reasons that attempts to control the guard failed in the 80s is that Pentagon comes in and they start saying, think of all the jobs you'll lose, think of all the money we'll withdraw from your state and we'll make sure that you don't get reelected. We'll point out all the money you've cost your state through your attempt to veto federal power on us. And so that's where we are now and so you'll still hear people claim, oh, well, the militia system exists. It's the National Guard system, which it's not at all. The National Guard system is nothing even remotely has no resemblance to what was imagined when they talk about militias in the Second Amendment and this idea that militias are necessary to the preservation of a free state. When they're talking about that, they're talking about a decentralized military force controlled only by the state and locals and outside the reach of the federal government. And that was their idea, that was their plan, that was the way it was supposed to work and that's the fundamental idea behind the Second Amendment was that it was about decentralizing the coercive power of the state, but that has failed. And so now you do have these state militias but they don't function as intended at all. So in order to recapture the essence of what the Second Amendment was supposed to be, you would have to return to something like you saw in the 19th century with the state and local chartered groups that are not funded by the feds and truly independent in terms of who they answer to. And so it would be nice to see some progress in that direction, but I'm not hopeful at the moment I don't see any real concerted efforts to accomplish that right now. So that's all I have to say about this topic. I just find that people generally don't know where the National Guard comes from or really what is the philosophy underlying the Second Amendment as regards that militia clause there. Why is that there? Hopefully this has given you some information that clears up some misconceptions on that. So thank you very much. I don't know if you have any questions. So obviously I'm pro-Second Amendment. I believe it's there for the common defense, no restrictions on any type of firearm. However, my issue with the argument for the Second Amendment is obviously I can say yes, we should be able to own anything from pistols to machine guns to tanks. However, even when I've heard the argument for this, I have a hard time rationalizing where does it stop? Because eventually the argument goes all the way up to atomic weapons. So what is the counter argument to saying people should not own atomic weapons while staying consistent with the argument for the Second Amendment? So in terms of the Second Amendment as positive law, how is it imagined to function as law? The Second Amendment was written to limit the federal government only on this. So their answer then, the people who wrote the amendment would have said, this is just here to prevent the federal government from regulating any of those arms. So imagine an 18th century where atomic weapons exist, where in a alternate universe. And so someone saying, well, what about the Second Amendment? Why doesn't it limit atomic weapons? Their answer would have been, that's for the state governments to debate and limit. Our job is just to ensure that this amendment doesn't in any way interfere with the state's ability to raise militias and to arm their citizens in a way that will defend those states against federal dominance. And so they're imagined, and not just in guns, but the way they imagined the constitution at the time is that the heavy lifting on all of this stuff would be done by state constitutions and state bills of rights. And so they would have said, oh, you wanna know what needs to be limited in terms of from knives to atomic weapons, what is legal in this sense? They would say, go to the state constitutions and fight it out there. And so if we are talking about the Second Amendment, that's the easy out, which is that, okay, this is just here to keep the federal government off the backs of the state governments. Now that doesn't save us the question of, okay, well, what is legal at the state constitutional level? What should the state's limit there? There's no clear line there. You will talk to diehard anarcho-capitalist type libertarians who have some fairly sophisticated arguments about how in a totally private society, where, for example, most people rely on, say, insurance or covenant communities to protect their rights, that those covenant communities would not permit their residents to have nuclear arms because of the potential for destroying the entire community. Right, so in a totally private system where there was no state power, where all government and coercive power was by contractual agreement, theoretically, that it would be something akin to, okay, in order to live in this location, you can only arm yourself with these sorts of weapons. And we won't allow you to have nuclear weapons because of the potential for disaster and that sort of thing. So you could potentially have a totally private society that would still limit those weapons for the same reason that you would have local governments want to limit atomic weapons as well. So it would seem that if you wanted to apply some kind of objective measure to it, it would have to just be, I think, proportional to the potential for unintentional or massive harm, just based on mistakes, based on just one single person being able to act alone and inflict massive damage. And that's probably what the debate would mostly be over. But of course, when we're talking about the Second Amendment, we don't have to worry about any of that because that wasn't its intention was to limit that. We'll let the state governments do that. I know that in places like Switzerland where every citizen is armed and has a gun, they have the lowest crime rate. So wouldn't it benefit America to maybe do the same because it would be less likely for someone to go out there and commit a crime if they know that their neighbor is going to be able to defend themselves against that? Well, part of the reason that, well, there's a couple of things going on in Switzerland. I don't know that I would attribute their low crime rate to the high gun ownership rate just because all the surrounding countries have very low crime rates as well and they have much less gun ownership. So the correlation isn't totally clear there. Obviously, I favor the fondness for private weapons ownership in Switzerland. I think that's good. They have a whole culture around that like shooting is the national pastime. However, a big reason for widespread gun ownership in Switzerland is because everybody serves in the militia. So all of the people who have legal access to the full blown machine guns and such, these are people who have performed their military service through their local militia or through the Swiss army. And so we would be, imagine a similar situation here, right? Where, and we talked about this at dinner a little bit. Imagine if the US National Guard function in a way that the Swiss National Guard works, right? All of these people are required to do a year of service. I'm opposed to the draft, by the way, but if you're gonna do it, the Swiss way is a less objectionable way to do it. You're expected to, unless you wanna pay an extra tax, you have to give your year of military service. Well, of course, those Swiss troops are not deployed to Asia. They're not deployed to Afghanistan. They're in Switzerland learning how to defend Switzerland. And so all of these people, they go through this and they're part of this group socially. And of course, service in the Swiss military brings with it certain social benefits and such. And all those people have real military training and they know how to use these machine guns that they've got. And in fact, up until the 1960s, the right to vote in Switzerland was connected to your military service, which was then, of course, connected to your ownership of arms. And there was very much a established connection between all of this, that citizenship and military service and voting was all kind of in this bundle. So you can imagine if the United States did something similar to that, where the National Guard did not send its troops to the other side of the planet, where if you signed up for the Oklahoma National Guard, you knew that all of your service was gonna take place in Oklahoma, in lieu of invasion from a foreign force.  You could see how that would have a very important social function, it would build social cohesion. It would also ensure that people who have guns know how to use them safely and properly and would just have a variety of benefits. But, and you would also probably get much more enrollment, right? People would probably much more readily enlist in that if I know I'm not gonna be sent off to Iraq. But I know that I might be sent down the road to do some training with my neighbors and to defend my home state in the process. You could see how that would be much more appealing to a much larger number of Americans. And I get to shoot guns and stuff and like bomb things and watch things blow up. Lots of young men like this sort of thing, right? And many people do join the National Military because they like that. They like the bombs and the explosions and the guns and all that stuff. But they end up signing up for the National Military and the next thing they know, they're shipped off to some country where they don't even know why they're there. And so you could see how this would be a very different sort of dynamic if the state militia functioned in a different way. But as we have it, it doesn't work that way at all. I wish it was more like the Swiss system. Unfortunately it is not. I do think the fact that there's all the Swiss gun ownership is for the best, but I don't think that's the reason for the low crime just because that's the European experience in general. But yeah, yay Switzerland. I mean, I think they do a lot of things right and that's probably good. So personally, I can perhaps get along with decentralization of the militia or the military onto a certain level. I see me personally, the issue that I see once we get to such a local level can be exemplified by this example, which I'm glad you actually brought up the Mormons in Utah and that example there. However, I would like to kind of go back still with the Mormons, but to Missouri in the executive order that was proposed at the time that would basically call for the elimination and extermination of the Mormons while they were in Missouri. So my concern is when we start going to such a localized level, especially given our polarized time today, if we are trying to propose legislation to change the way we do things to a more localized level, that there will be a conflict of ideologies that could perhaps say, you have to say, let's take the Lions Club and you have some other club who disagree with each other on some ideological belief system in some state, could we perhaps see that without a per se the state or a some higher intervention of whatever may be, even if you per se God or whoever it is, some higher intervention that comes into say to bring some sort of peace deal so we don't have such conflict of interest and conflict of ideologies like we did in the Missouri example I provided with the Mormons who were all coming in and saw Zion being in Missouri and the local people there, local malicious, malicious appointed by the state as well, all getting involved to exterminate a different religious belief system. Well, you see that in use of non-malicious too, right? You don't need a militia for the state government to employ its course of power against certain groups. We could point to, for example, the use of the Texas Rangers against Mexican Americans during the Mexican Revolution. There was a lot of lynching going on at the hands of the Texas Rangers in 1916 because of a perceived race war that Mexican revolutionaries were supposedly starting. And you had, interestingly in that case, you had the Mexican Americans fleeing the state troops and trying to get into Fort Bliss in El Paso to escape the state, the state government hoping that the federal government, which is more indifferent to them, might protect them that way. And so yes, what you do want is a level of decentralization where you can escape. And that was, I think, their main concern was that we need some sort of, rather than a large unified federal force from which there is no escape and which faces no serious opposition from within the borders of the United States, we need something here that would provide some sort of pushback and help them provide an alternative force that people could retreat to and find some shelter in. And sometimes that has worked in favor of like, in the case of 1916 where they escaped, well, we're essentially state troops hoping to find some shelter with the federal troops. But the larger concern was that the federal government so much larger and so much wealth, so much better funded was that there was no escape unless there was a countervailing force at the state and local level. And I mean, you're just, a conflict is to be assumed in cases like that. What you're trying to do is localize the conflict as much as possible and try and provide opportunities for people to at least move out of harm's way. So you could at least leave the state of Missouri and find some safety that way. And I mean, that's what the Mormon's got real good at, right? It was moving around to escape whatever, Illinois, Missouri, whatever the local officials were trying to do there. That's why they went out to the middle of nowhere in Utah where they still couldn't escape. But then they send the federal troops. So that proved, right? They thought they were escaping the Missouri troops and then low and behold, they send the federal troops out all the way to Utah. At least you knew Missouri wasn't gonna send Missouri troops to Utah. So you could at least be, you could at least escape that group. So the idea that they had, that these liberals had in the 18th century was that you're never gonna be able to fully escape conflict. There's always going to be elites that are fighting against other elites and attempting to exert power in ways among themselves and against people that they can get away with oppressing. What they were trying to do was set up some sort of obstacle that would prevent these elites from fully exercising their full power. And so that's the vision here. But it's hard to imagine a case where you can truly nip in the bud any sorts of conflict that might arise. And that's just, just anytime you have political power at stake, right?  And the liberal view is that if at least it is localized and you have many choices where you can move across borders to get to a different legal regime, that's preferable to just having a unitary government. But it doesn't work perfectly by any means. That's for sure. And that's recognized. So almost a year ago today, the House and Maine advanced legislation that would ban paramilitary training in the state and then it would have to pass the Senate. If it does pass, that would make it the 27th state to ban this type of training, which is kind of concerning because that encompasses over half the states in the United States that currently ban this type of paramilitary training. You kind of touched on the reasons why the 19th century model was just fell out of popularity from historical phenomena such as like the Civil War and depends on federal funding. But now we also kind of this obstacle of there's actually legislation that bans this type of training. Keeping this in mind, I mean, we have these popularity principles but also now this legislation poses significant obstacles. Do you think that a path back to the principles of the 19th century militia exists today? Well, it would certainly require change in ideology, right? People have come so far away from that level of civic engagement to that relationship with firearms. Remember people just grew up around firearms all the time. Nine year old boys are running. There's a great book called The Virgin Vote referring to your virgin vote in those days was your first vote that you cast at age 21. This is a history book by a guy named John Grinspan and the books about youth culture in the 19th century in this period that we're talking about. And he was talking about what it meant to be a young person growing up in that time period. And just your average middle class person just went around shooting things like small animals all the time. There was a familiarity with it and it wasn't viewed in the way that it's viewed now. You would have to recapture something like the Swiss idea of shooting as a national pastime, I think to get people to be less afraid of the idea. And then on an institutional level, you could probably then, if you could convince state governments to be more proactive in terms of funding and chartering their own real state militia groups that this has our approval and you're gonna get proper training and you're gonna be supervised so that you know that the people who come out of these state militias that of true state militias, not the National Guard, you come out of them and you have some level of training and you've undergone the background checks and you've been integrated into the community and you're considered a safe person like you're supposed to believe about police officers today. That if you could imbue these institutions with some sort of state imprimatur of sorts that I think then you could start to reclaim that idea but there's of course no interest at the state level for creating those sorts of institutions or that sort of institutional approval. A state could do that. I don't see any reason why not. They would have to cough up some funding to make that possible, which most of them don't wanna do. Some of the larger states do have state defense forces that aren't the National Guard and are professional military detachments that answer just to the state government. Florida has one, California has one. But they don't do a whole lot of training. They're mostly aging military people who already got their training and that and they're not heavily funded. But it's legal, the states could do it but they're going in the opposite direction because they're banning any sort of locally funded military. I don't hold out much hope for something like the Asmonean Guard or the Snake Hunters or the Invincibles coming about anytime soon where it's just a local group. But if the state came out and said, okay, this group is fine, I could see people getting behind a military auxiliary of the fire department. I mean, firemen, they're revered basically in this country still. You might be able to convince people that that was okay. Look at these fine upstanding firemen. They sacrifice themselves for our community and also they're a ready-made militia group to come to spring to the public defense. Maybe that would be a good starting place. But I have yet to see any state legislation that's trending in that direction. But I think it would be good if it did.


Over the last few classes we have written a lot of mathematical expression, done some algebra, done some calculus and we have not done most of it. Most of it I have said that it can be done this problem in this book, that problem in that book you can do it yourself, to tedious and we have not done it. We have not done it for a reason. If you try to do it then it is impossible to stick to the limits of NPTEL and also it will be very boring to go through all that mathematics and then we lose the site of chemistry. As I said many times what we really need to understand is the philosophy and the logic that goes into this. Mathematical detail and we do not really need so much. We do but we do not have to work out everything at least for now. But today it is more or less a storytelling session. Well the story also involves a lot of mathematical expressions but we will just do some very very simple algebra by and large I will just tell you what happens when something is done. And to start with I show you a picture of an elephant and you might be wondering what is going on here. Do we have an elephant in the room? No actually look at this picture carefully. It is really a plot is not it? x axis is something independent variable y axis is a function of x and to know more about the functional form you can visit this website. But the point that we wanted to stress here is that by using proper combination of mathematical functions one can actually generate whatever shape one wants. What you need is sufficient number of terms. This if you go into this website you will see this is the picture of an elephant generated using a single parameter. What that is? What is the detail that we will not get into? I was actually looking for this picture of an elephant that is drawn using 30 exponential functions I did not find it on the net I found this. And the reason why we show this is that this is the way we are headed now. Until now we have been talking about exact solutions, approximate solutions, worrying about analytical form and trying to make sense of it out of it. Slowly we are entering a regime where we cannot do that any longer. It will all boil down to drawing the shape we require like an elephant using a suitable combination of functions. And while doing that the saving grace of course is variation theorem or upper limit theorem which tells you that you can never get an energy that is less than the actual energy. So, let us see how far we can get today. Last day we had talked about the perturbation theoretical treatment of atoms. Today we will talk about variational methods and we will need maybe one or two more lectures before we can complete our discussion of atoms. So, to recapitulate we now are sufficiently familiar with the Hamiltonian of many electron atoms. We know that it is a sum of n number of one electron Hamiltonians and there are these Nc2 combination of electron-electron repulsions. These you cannot ignore you have to account for them somehow and the way we are accounting for this so far is considering something called your shielding constant and considering that this the effective nuclear charge is what an electron sees and effective nuclear charge is the actual nuclear charge minus the repulsion that an electron experiences from the other electrons. And doing that what we have done is we have modified the wave function instead of z will write z effective and then we showed you some result remember this value minus 78.99 this is the energy of your helium atom. So, we are trying to get close to this 78.99 electron volt that is where we want to get in this simple shielding constant kind of calculation we are showing you minus 77.68 electron volt and today finally we will see how we can get to the shielding constant using variational method. And also this is something that we will not use today but in the next class we are going to get back to this later determinant determinant way of representing wave functions after today's lecture. And one thing that we talked about yesterday is that from now on to just make things a little simpler we are going to use atomic units where mass is the mass of an electron unit of mass is mass of an electron unit of charge is charge of an electron unit of angular momentum is our good old h cross unit of permittivity is 4 pi epsilon 0 electric potential has unit as potential of an electron in the first pore orbit and I have not corrected this m to n yet where it is of copy paste and Bohr magneton is the unit of magnetic moment energy unit is Hartree remember and one Hartree again I am stressing this because it is very easy to lose sight of this one Hartree is actually 27.21 electron volt substantial in atomic scales. So when you use all this Hamiltonian for helium atom that we have written earlier was down to something simpler in atomic units but while doing this please do not forget that this m h cross square 4 pi epsilon 0 they are all there if you want it in if you want to write it in the expanded form you should not forget which goes where of course when we calculate energy then we do not have to worry because we have this conversion 27.21 electron volt is equal to one Hartree all right and with that background I have kept this same as what we have written earlier from next slide onwards you will see that we have written it in atomic units. So we discuss a perturbation theoretical treatment for ground state of helium atom where the sum of the one electron Hamiltonians is taken as unperturbed Hamiltonian and the term involving electron-electron repulsion is taken as the first order correction to Hamiltonian the uncorrected wave function or 0th order wave function is taken as the product of the 2 1 s orbitals it about helium so 2 1 s orbitals so again we are working within the ambit of orbital approximation and then we said that first of all e 0th is z square by 2 minus z square by 2 that is equal to minus z square in Hartree and we said that we just go through this problem 6 of chapter 8 of McQuarrie's book on quantum chemistry you will get to learn that the first order correction to energy is 5 8th of z in Hartree so energy in Hartree is minus 2.75 which translates to minus 74.83 electron volt remember what was the value experimentally minus 78.99 is it not 78.99 So that is where it is we are not really we are not really there yet and then we said that this is only first order correction you can work on second order correction higher order correction and 13th order correction more or less gets close to the value today now we are going to talk about variational method for treating this many electron atom problem we are going to talk about helium atom and we are going to arrive at what we had talked about earlier this effective nuclear charge here I have written the Hamiltonian in atomic units half del 1 square minus half del 2 square minus z by R 1 minus z by R 2 plus z by R 1 2 of course half del 1 square minus z by R 1 that is the Hamiltonian for electron number 1 half del 2 square minus z by R 2 is the Hamiltonian for electron number 2 and the z by R 1 2 is the term for which we have to do so much of discussion the electron electron repulsion term okay what is the trial wave function we start with the same trial wave function okay but of course we will play around with it as you will see same trial wave function we take 2 1s orbitals I hope you remember that 1s orbital is of this form root over z cube by by pi multiplied by e to the power minus z rj okay this is the 1s orbital written in terms of the jth electron if you do not remember the coefficient it is okay but one thing you should know is that this 1s orbital is essentially an exponential decay in r alright this is my trial wave function I start from there okay trial wave function again is the same wave function that we had in our orbital approximation 1 electron hydrogenic wave function orbital next thing to do in variation method as we know is to find out this functional epsilon of pi which is the similar expression as energy just instead of the exact wave function psi we are using the trial wave function phi so we will work with this functional epsilon of pi integral of phi star h hat phi over all function space in this case over all values of rj and phi star is equal to phi in this case we are talking about 1s orbital now what is the variational parameter what we will do is well even before that now when we talked about time dependent perturbation theory we had referred to problem 6 now we refer to problem 7 of the same chapter if you go through this if you work it out you will get this expression for epsilon of phi z square minus 27 z by 8 right so then looking at this expression and also looking at the expression of psi if you think what is the handle that we have what is the parameter that we can play around it what can be our variational parameter can we play around with rj makes no sense right rj in any case and we have to formulate the problem that way so the only thing that is left really is z okay nuclear charge and it makes sense to use z as the variational parameter because as we have discussed qualitatively already that this nuclear charge is not really the charge that is failed by an electron and electron feels an effective nuclear charge which is nuclear charge minus some shielding constant sigma and essentially we are trying to find out sigma so one way of finding out sigma is to keep changing the value of z vary the value of z and see for which value of z we get a minimum in the value of the functional epsilon we will call it E min as usual and that is going to set an upper limit to the energy of the system right so z will be the variational parameter also wherever we get the energy minimum that is going to be the effective nuclear charge so I am not really calculating sigma I am calculating effective nuclear charge and I will I can find sigma by subtracting the effective nuclear charge from the actual whole nuclear charge that is there in case of helium it is 2 we are talking about helium do not forget okay so z is my variational parameter this is the expression for the functional so what is the next thing to do I want to find the minimum of the epsilon of the functional epsilon so I have to take the first derivative with respect to z equate to 0 what is the first derivative 2z minus 27 by 8 right first derivative of epsilon with respect to z is 2z minus 27 by 8 very easy and that is going to be equal to 0 for us to get the minimum value of the functional epsilon okay as we have said that would be the upper limit of the energy calculated for the system and as we have also said correspondingly the z value for which the minimum is obtained that is going to be z effective okay so it is well formulated very easy algebra it is all done what is the value of z here this z is z effective as we said we will write z effective 2z minus 27 by 8 equal to 0 so a class 5 class 6 student can work out that z effective in this case is 27.16 what is 27.16 it is 1.6875 I hope I have got the division right please work it out yourself in case it is wrong I do not think it is wrong it is fine so the point is it is less than 2 what is the actual nuclear charge it is 2 what we see is we have calculated a value of z effective which is less than the actual nuclear charge and from here we can calculate the value of sigma shielding constant to be 2 minus 1.6875 that will come to how much 0.3125 isn't it yeah 3125 0.3125 that is the value of sigma that we get from this very simple variational treatment of the helium atom ground state problem okay so we know how to find the energy minimum which is the upper limit of energy actually do not get confused because I am saying energy minimum and upper limit energy minimum means minimum of epsilon the functional epsilon that sets the upper limit of the energy calculated by this method okay remember upper limit theorem so we have not only been able to find the energy that we are looking for we have also been able to determine the effective nuclear charge and that is great okay now what will we do to find the value of this epsilon we take this effective nuclear charge and plug it in there not to find the value of epsilon sorry to find the value of imine right so we know z effective we plug the value of z effective in the expression for epsilon to find imine let us do that imine turns out to be 1.6875 square minus 27 by 8 1.6875 75 that turns out to be minus 2.8477 which translates as 77.49 electron volt okay so we are getting close but perhaps not close enough that is the problem close but not that close also so to understand the problem let us have a look and let us compare with what we get the minus 2.8477 this value is perhaps wrong but anyway first order perturbation theory gives me a value of minus 2.75 second order perturbation theory gives me a value of minus 2.91 13th order perturbation theory no it is okay gives me a value of minus 2.90372433 and so on and so forth so this is where we should get and so what we see is by the simple variation method that we have used here we are doing better than first order perturbation theory but not as good as second order perturbation theory and definitely not good as good as 13th order perturbation theory so this is definitely not the end of the road this is definitely not the end of the story and also to make a point that whatever we have discussed first order or variation method they are not all that great that comes out nicely if you look at another molecular property and that is ionization energy okay we all know what ionization energy is in gas phase the energy difference between the ion helium plus and the uncharged atom helium that is ionization energy okay so now what we will do is we will work out ionization energy that is calculated using variation method as well as first order perturbation theory now energy of helium plus is very easy to calculate as helium plus means it is a one electron system right one electron system will have an energy of minus z square by 2 where z is equal to 2 okay there is no question of effective nuclear charge anymore there is no question of shielding there is only one electron so it feels the entire nuclear charge that is there okay so 2 square by 2 minus 2 square by 2 that gives you minus 2 atomic unit so energy of helium plus is minus 2 atomic unit ionization energy then would be minus 2 minus minus 2.8477 in case of your variation method 2.75 in case of perturbation theory and these are the values that you get and you appreciate the picture properly when we take it to electron volt remember electron volt is a larger number is not it one atomic unit is 27.2 electron volt so if I translate that we see it better that is all you might not think that 0.84 0.75 in our minds we think that okay it is little less than 1 what is the difference of course if I told you 7500 and 8477 you would have seen the difference but let us see the difference in electron volt multiply by this 2 27.2 the numbers you get are 20.4 for first order perturbation theory and 23.1 for variation method so you see a significant difference is there between the two calculations and then when you look at the experimental value 0.904 this is the correct value then you get an ionization energy of 24.6 so 20.4 electron volt is definitely very very far away from 24.6 electron volt ionization energy is 23.1 close enough well definitely better than 20.4 but see the difference between 23.1 and 24.6 the number calculated from variation method and the number obtained experimentally is 1.5 electron volt 1.5 electron volt is not a small number in this context because typically this 1.5 electron volt would be of the order of the bond strength strength of a chemical bond would be about 1.5 electron volt or little more little less so since you are talking about atomic and molecular systems this difference is not really small this is sufficiently large so we have miles to go before we sleep we need to do better than this simple variation method that we have adopted. And to just convey how long it has taken to do better we will show you some timelines shortly. So now what we do is we start thinking of more general trial wave functions remember our previous discussion of variation method we had said that you can actually use any function to construct the wave function that is there remember the elephant that I showed in the opening slide okay to get the elephant I can use whatever function whatever polynomial whatever exponential I want as long as it finally gives me the shape of the elephant. So there is no need for us to stick to hydrogen atom wave function okay so we introduce the first wave function which is sort of a deviation from hydrogen atom wave function okay sort of but not a very far deviation when you do any theory you do not do something in white today and tomorrow you do something in black that it can take you very very far away from reality. So we always take baby steps and the baby step we are talking about is that of Slater orbital let us have a look at this form of Slater orbital here we are writing S for Slater S it is characterized by NLM three quantum numbers very much like your hydrogen atom wave functions orbitals atomical orbitals and it is a function of r theta phi if you work in spherical polar coordinates the expression for Slater orbital is the normalization constant which is a function of N and L multiplied by r to the power n minus 1 very similar to what we had for atomic orbitals hydrogen atom wave functions one electron wave functions multiplied by well I will read the last factor first multiplied by y l m of theta and phi this is familiar to us the angular part of the wave function form might be different that we will see and the second factor is e to the power minus zeta r what would that function have been in case of atomic orbital it would have been e to the power minus z r is not it so z is your nuclear charge right atomic number so instead of z we are using a variational parameter zeta okay it replaces z in the expression for an for a hydrogen atom wave function and again to think of it we have already done this what did we do in our previous treatment of variation method for helium atom we use z as a variational parameter didn't we so essentially we use z as zeta we just didn't call it zeta we still called it z here Slater called it zeta that is one but is that all as we saw just by using this z or zeta as variational parameter we do not get very close to the real real value we do not get very close to the reality so what Slater did was that he introduced one more variational parameter he used n as variational parameter as well now this might sound counterintuitive we know what n is for hydrogen atom n is the principal quantum number it has to be 1 2 3 4 so on and so forth how can I use it as a variational parameter and get something like 0.9 0.8 1.2 what sense does it make well the sense it makes is this we are not dealing with one electron systems any longer we are trying to stick to one electron wave functions as long as we can because they are familiar to us we know how to handle them and also many electron wave function is sort of a it builds upon one electron wave functions right you can think that you start with one electron wave function then add some complication you get many electron wave function many electron atom starting from one electron atom but it is not completely uncorrelated is it right there has to be some kind of a correlation there has to be some kind of a gradual evolution from a one electron system to a many electron system so we want to go gradually as well right the problem is we cannot write the exact form so the right thing to have do have done perhaps is to have added a term we do not know which term to add so what we are doing is we are essentially scaling the wave function by a variational parameter we are multiplying by a factor to arrive at a wave function that gives us the correct energy right now we only bother about energy okay we do not worry about how exactly we get the wave function it is a and ends justify the means sort of approach you if you want to call it that right and again we have said this earlier I will just remind you again it is sort of using sort of like using the activity coefficient right and pretending as if not all of the concentration of a reactor of a molecule is available for doing reactions whereas the reality is that all of the concentration is available it is just that they run slower okay it is similar kind of a scaling problem so nothing very new this has been used for a long long time okay so since we cannot work with one parameter we are trying to compensate by playing around with another okay that is why so do not we do not feel it is a sacrilege that we are going to get non integral values of n and the problem is I think I wanted to show you a value of n that we get after optimization but I have forgotten to write it well I remember I will show it the next day otherwise just read McQuarrie's book please it is given there when you get n something like 0.995 for helium okay so using this and this is where you get n equal to 0.995 so you use a product of slater orbitals instead of wave functions and you vary n as well as xi zeta sorry when you do that you get energy of minus 2.8617 atomic unit ionization energy of 23.4 electron volt which is a little amount of improvement from 21.23.1 electron volt or something that we got earlier okay so this is sort of a limit which is called Hartree-Fock limit and for the first time in this course we take the name of Hartree and Fock and in the next one or two modules we are actually going to discuss in as much detail as we can the Hartree-Fock approach to this multi electron problem many electron problem okay for now let us just say that this is the Hartree-Fock limit that one can reach using this kind of an approach okay and again what kind of a problem is it? It is a minimization or an optimization problem I have two parameters zeta is one n is the other I need to minimize z sorry minimize energy with respect to zeta as well as n okay so you know how to do it take derivative in this case partial derivative equate to 0 in many cases it will not be able we will not be able to do it like that we have to do it numerically as we have briefly mentioned earlier perhaps we will come back to it in more detail when we discuss Hartree-Fock in the next modules all right. So this is what is called Slater orbital and using it you can get a little bit of improvement but not really what you want so you want to try out other forms of orbitals and now that we have opened the flood gate we have said that we do not have to stick to hydrogen atom wave functions then there is actually no need to even retain the form here the rough framework of hydrogen atom wave function is retained with the introduction of the variational parameter. So in the subsequent kinds of orbitals and we will discuss maybe a couple of more in the next class but today let me show you at least one more Hylerus for example use this kind of a wave function is a function of r1, r2 and r12 the inter nuclear separation and the functional form that he used was product of two exponential functions one in r1, one in r2 multiplied by 1 plus a function g a polynomial g in terms of these three independent variables g is a polynomial now see you can play around with the number of terms in polynomial each term will be associated with the coefficient each coefficient will be a variational parameter and of course you can play around with z and arrive at what effective nuclear charge you get the only issue with that is that some of this correction for effective nuclear charge might go in the coefficients of g. So it becomes a numerical problem and you need computation you need to do you need good computers to handle systems like this because you try to do it by hand you will grow very old before you can solve even the helium problem. So as you see as computational power grew from 1929 to 1957 to 1959 this was a timeline I was talking about earlier Hylerus used 10 terms he could use only 10 I do not know what kind of computer Hylerus had if at all perhaps he did everything by hand he got an energy of minus 2.90363 and ionization energy of 0.904 which is a remarkable improvement over what we had earlier remember then Ginoshita in 1957 published this result with 39 parameters and you get minus 2.93 7 225 for energy atomic units ionization energy remains 0.904 Pecker is used 1078 parameters that means 1078 terms and published this result in 1959 you see at this huge increase in number of terms and the improvement is there right minus 2.903 I think I missed a 0 here I am sorry about that it is not minus 2.9372525 it is minus 2.9037225 so you get something like this. So what we see is that you keep on increasing the number of terms at one point of time it is going to saturate it is not going to get any better it will get as good as it gets and you cannot it makes no sense to increase the number of terms beyond that I mean you can no harm done because upper limit theorem tells us that in any case you will stop at the actual value of energy right you will stop a little more than that you will never go beyond so the chance of overshooting is not there but if you increase the number of terms the question is how good a computer you have what is your computational power so that is always the tradeoff more number of terms gets us closer to the realistic value but it becomes computationally more expensive okay if you have better computers be my guest use as many terms as you want does not matter okay so with that I do not know why I have animated this with that the field is set for us to now try to see how we can draw this elephant well elephant is allegorical of course how we can generate whatever wave function we need using the Hartree-Fock method and since we are running out of time I will not elaborate now next day we will also learn that Hartree-Fock method uses something called a self consistent field model very exciting challenging and opens up the field for addressing more complicated problems like molecules at later time that is what we are going to discuss in the next couple of classes


Moldovan president, Russia wants to remake the Soviet Union. Moldovan president Maya Sandu believes that if Russia had successfully taken over Ukraine, it would have continued its expansion by bringing its troops to Moldova. Sandu said this in an interview with the Financial Times. I don't believe the Russians would have stopped at the border. We are only safe today thanks to Ukraine, the president of Moldova emphasized. According to Sandu, Russia's aggression against Ukraine is an attempt to remake the Soviet Union. We bring back the old days and we don't want this. Moldova has been part of the buffer zone for 30 years and for us this meant poverty, corruption, bad governance, emigration. We want to be part of the democratic world, she said.