Molecular potential variational method

Following Fey nman s original work, several authors pmsued extensions of the effective potential idea to construct variational approximations for the quantum partition function (see, e g., Refs. 7,8). The importance of the path centroid variable in quantum activated rate processes was also explored and revealed, which gave rise to path integral quantum transition state theory and even more general approaches. The Centroid Molecular Dynamics (CMD) method for quantum dynamics simulation was also formulated. In the CMD method, the position centroid evolves classically on the efiective centroid potential. Various analysis and numerical tests for realistic systems have shown that CMD captures the main quantum effects for several processes in condensed matter such as transport phenomena. 

The generalization of the pseudopotential method to molecules was done by Boni-facic and Huzinaga[3] and by Goddard, Melius and Kahn[4] some ten years after Phillips and Kleinman s original proposal. In the molecular pseudopotential or Effective Core Potential (ECP) method all core-valence interactions are approximated with l dependent projection operators, and a totally symmetric screening type potential. The new operators, which are parametrized such that the ECP operator should reproduce atomic all electron results, are added to the Hamiltonian and the one electron ECP equations axe obtained variationally in the same way as the usual Hartree Fock equations. Since the total energy is calculated with respect to this approximative Hamiltonian the separability problem becomes obsolete. 

The asymptotic behavior of the exchange-correlation potential far from the molecule has been identified as the key factor determining the accuracy of the ionization potentials of anions and electron affinities of neutral molecules.5 Recently, Wu et al.91 proposed a variational method, which enforces the correct long-range behavior of vxc. Indeed, a noticeable improvement compared to the Kohn-Sham results derived using conventional approximations (LDA-, GGA-, and hybrid functionals) was reported for atoms (H, He, Li, Be, B, C, N, O, and F) and diatomics (BeH, CH, NH, OH, CN, BO, NO, OO, FO, and FF). The still significant discrepancies between the experimental and calculated ionization potentials (or electron affinities) were attributed to errors of the exchange-correlation potential in the molecular interior. 

A related approach is due to Snijders, Baerends and Ros [71], who also use the discrete variational method for determining the wave-functions. However the Coulomb potential is handled more exactly by fitting the molecular charge... 

VAMP can be used with Tsar to provide quantum mechanically calculated descriptors for QSAR. Apart from molecular properties such as dipole, quadrupole, and octupole moments, ionization potential, electron affinity, polarizability (calculated as a default in VAMP by a variational method), etc., atomic properties such as Coulson-, Mulliken-, or MEP-derived charges, chemical shifts and atomic dipoles and quadrupoles, VAMP can also calculate surface electrostatic descriptors introduced by Politzer, and is useful for QSARs and QSPRs involving intermolecular interactions. Many of these descriptors can be exported directly into Tsar for analysis by classical regression techniques or artificial neural nets. ... 

The variational methods of the configuration interaction (Cl) type and the perturbative-type methods relying on the exponential coupled-cluster (CC) Ansatz are the most often used approaches in ab initio computations of highly accurate molecular properties, in particular of the potential energy surfaces (PESs) or curves (PECs) for the purposes of molecular dynamics [for recent reviews, see Refs. (1-4)]. In this latter case it is essential that the entire surface — or its various one- or multi-dimensional cuts — is available for a wide enough range of molecular geometries. 

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