In the field of hybrid quantum/classical (QC) methods, we are developing a hierarchy of charge-transfer models that stems from the exact quantum valence bond (VB) theory and leads to the classical, charge-equilibration (“QEq”) model. This set of methods will play a key role in the simulations of large systems (e.g. to describe the classical region of a large molecule interacting with a central quantum part, and to describe classical solvent molecules surrounding a quantum solute). Our theory allows for the first time a correct classical treatment of bond forming/breaking and dissociation processes within a classical region, and will be instrumental in the description of charge transfers across quantum/classical boundaries. These models imply a bond-related generalization of the concepts of electronegativity and hardness, suitable for reactive processes. Our present QC efforts are being concentrated on (1) the interfacing between different quantum theories and classical models, (2) the models relationship to statistical mechanics methods [maximum entropy valence bond (MEVB) theory], and (3) their dynamical formulation in the time-dependent variation principle (TDVP) framework.
In the field of quantum dynamics, we are further developing the electron nuclear dynamics (END) theory to study charge-transfer and reactive processes. This theory constitutes the first attempt to apply the concepts of quantum action and quantum Lagrangian within a chemical context. The END theory employs the time-dependent variational principle (TDVP) in order to obtain generalized phase-space dynamical equations, where coherent states play a unifying role. In its minimal realization, the END theory describes the electronic degrees of freedom by a single-determinantal wavefunction and the nuclear ones by frozen Gaussian wavepackets in the semiclassical limit. Without requiring predetermined potential energy surfaces, this theory has been successfully applied to the simulation of non-reactive, reactive and charge-transfer processes in scattering systems such as H+ + H2, H+ + CH4, and H+ + H2O, inter alia. Our present END efforts are being concentrated on (1) incorporating semiempirical methods for the electronic description, (2) developing time-dependent quantum/classical models, and (3) introducing solvent effects.
