There are several ways to compute the geometric phase in molecules within the Born–Oppenheimer framework. One way is through the "non-adiabatic coupling M × × M matrix" defined by τ τ i j μ μ = ⟨ ⟨ ψ ψ i | ∂ ∂ μ μ ψ ψ j ⟩ ⟩ , where ψ ψ i is the adiabatic electronic wave function, depending on the nuclear parameters R μ μ . The nonadiabatic coupling can be used to define a loop integral, analogous to a Wilson loop (1974) in field theory, developed independently for molecular framework by M. Baer (1975, 1980, 2000). Given a closed loop Γ Γ , parameterized by R μ μ ( t ) , where t ∈ ∈ [ 0 , 1 ] is a parameter, and R μ μ ( t + 1 ) = R μ μ ( t ) . The D -matrix is given by D [ Γ Γ ] = P ^ ^ e ∮ ∮ Γ Γ τ τ μ μ d R μ μ (here P ^ ^ is a path-ordering symbol). It can be shown that once M is large enough (i.e. a sufficient number of electronic states is considered), this matrix is diagonal, with the diagonal elements equal to e i β β j , where β β j are the geometric phases associated with the loop for the j -th adiabatic electronic state.