When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. Levine, Benjamin G., E-mail: demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.ĭOE Office of Scientific and Technical Information (OSTI.GOV) Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties.
We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections
This feature permits pocket-calculator evaluation of the corrections within thermochemical accuracy (10(-1) mhartree or kcal/mol).
#Poly bridge 2 diagonal elevator series
An almost constant contribution per electron is identified, which converges with system size for specific series of organic molecules. Recent post-Hartree-Fock calculations of the diagonal-Born-Oppenheimer correction empirically show that it behaves quite similar to atomic nuclear mass corrections. Semiempirical evaluation of post-Hartree-Fock diagonal-Born-Oppenheimer corrections for organic molecules. The connection to adiabatic-to-diabatic transformations in non-adiabatic dynamics is explored and complications arising from biorthogonal nature of CC theory are identified. One of this agrees with the formula used in the current literature. On this basis, different computational schemes for evaluating DBOC using approximate CC wave-functions are derived. This is shown to lead to a biorthogonal version of SOS formula with similar properties. A biorthogonal formulation suitable for DBOC computations using standard unnormalised coupled-cluster (CC) wave-functions is presented. A sum-over-states (SOS) formula for DBOC which explicitly exhibits this invariance is derived. By viewing this freedom as a kind of gauge-freedom, it is shown that DBOC and the resulting associated mass-dependent adiabatic PES are gauge-invariant quantities. We examine how geometry-dependent normalisation freedom of electronic wave-functions affects extraction of a meaningful diagonal Born-Oppenheimer correction (DBOC) to the ground-state Born-Oppenheimer potential energy surface (PES). Diagonal Born-Oppenheimer correction for coupled-cluster wave-functions
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