Functional variation Gaussian basis functions

The picture here is of uncoupled Gaussian functions roaming over the PES, driven by classical mechanics. The coefficients then add the quantum mechanics, building up the nuclear wavepacket from the Gaussian basis set. This makes the treatment of non-adiabatic effects simple, as the coefficients are driven by the Hamiltonian matrices, and these elements couple basis functions on different surfaces, allowing hansfer of population between the states. As a variational principle was used to derive these equations, the coefficients describe the time dependence of the wavepacket as accurately as possible using the given... 

Variational one-center restoration. In the variational technique of one-center restoration (VOCR) [79, 80], the proper behavior of the four-component molecular spinors in the core regions of heavy atoms can be restored as an expansion in spherical harmonics inside the sphere with a restoration radius, Rvoa, that should not be smaller than the matching radius, Rc, used at the RECP generation. The outer parts of spinors are treated as frozen after the RECP calculation of a considered molecule. This method enables one to combine the advantages of two well-developed approaches, molecular RECP calculation in a gaussian basis set and atomic-type one-center calculation in numerical basis functions, in the most optimal way. This technique is considered theoretically in [80] and some results concerning the efficiency of the one-center reexpansion of orbitals on another atom can be found in [75]. 

An interesting approach for comparison with XPS experiments is a generalization of the Floating Spherical Gaussian Orbital (FSGO) technique. In this method, each electron pair is represented by a single Gaussian basis function whose exponent and position are obtained by a variational procedure or by reference... 

Kinghom, D.B. and Adamowicz, L. 1997. Electron Affinity of Hydrogen, Deuterium, and Tritium A Nonadiabatic Variational Calculation Using Explicitly Correlated Gaussian Basis Functions. Journal of Chemical Physics 106 4589-4595. 

The electron-nucleus (e-n) correlation function does not describe electron correlation per se because it is redundant with the orbital expansion of the antisymmetric function. If the correlation function expansion is truncated at Fi and the antisymmetric wave function is optimized with respect to all possible variations of the orbitals, then Fi would be zero everywhere. There remain two strong reasons for including Fi in the correlation function expansion. First, the molecular orbitals are typically expanded in Gaussian basis sets that do not satisly the e-n cusp conditions. The e-n correlation function can satisly the cusp conditions, but F/ influences the electron density in regions beyond the immediate vicinity of the nucleus, so simple methods for determining Fi solely from the cusp conditions may have a detrimental effect on the overall wave function. Careful optimization of a flexible form of is required if the e-n cusp is to be satisfied by the one-body correlation function [115]. 

Mendive-Tapia D, Lasome B, Worth GA, Robb MA, Bearpark Ml (2012) Towards converging non-adiabatic direct dynamics calculations using frozen-width variational Gaussian product basis functions. J Chem Phys 137 22A548... 

Finally, some comments on two recent studies on methods for quantum dynamics simulations. In the first study, by Mendive-Tapia et al., the convergence of non-adiabatic direct dynamics in conjunction with frozen-width variational Gaussian product basis functions is evaluated. The simulation of non-adiabatic dynamics can be subdivided into two groups semi-classical methods (like the trajectory surface hopping approach) and wavepacket methods (for example, the... 

Two variations of the new VVIO functional were established [78], and a new, simpler " and the corresponding analytic gradients were derived. A self-consistent version with Gaussian basis sets was implemented in Q-CHEM. For r y - 0 the correlation kernel of VVIO approaches a constant, thereby satisfying the known constraint [41]. Parameters in VVIO were fixed to reproduce the compilation of dispersion coefficients from [76] and S22 benchmark energies for the combination ... 

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