Minimal electron nuclear dynamics

Thus, both the electronic structure of the reacting system and the nuclear dynamics are treated quantum mechanically. The crystal structure 2C12 with the inhibitor spermine was used to construct the Michaelis complex (MC) model through a combined minimization and molecular dynamics simulation technique. As it turns out, the computational MC structure was in excellent accord with a parallel study of the D402N-nitroethane X-ray structure. ... 

In this minimal END approximation, the electronic basis functions are centered on the average nuclear positions, which are dynamical variables. In the limit of classical nuclei, these are conventional basis functions used in moleculai electronic structure theoiy, and they follow the dynamically changing nuclear positions. As can be seen from the equations of motion discussed above the evolution of the nuclear positions and momenta is governed by Newton-like equations with Hellman-Feynman forces, while the electronic dynamical variables are complex molecular orbital coefficients that follow equations that look like those of the time-dependent Hartree-Fock (TDHF) approximation [24]. The coupling terms in the dynamical metric are the well-known nonadiabatic terms due to the fact that the basis moves with the dynamically changing nuclear positions. 

The scheme we employ uses a Cartesian laboratory system of coordinates which avoids the spurious small kinetic and Coriolis energy terms that arise when center of mass coordinates are used. However, the overall translational and rotational degrees of freedom are still present. The unconstrained coupled dynamics of all participating electrons and atomic nuclei is considered explicitly. The particles move under the influence of the instantaneous forces derived from the Coulombic potentials of the system Hamiltonian and the time-dependent system wave function. The time-dependent variational principle is used to derive the dynamical equations for a given form of time-dependent system wave function. The choice of wave function ansatz and of sets of atomic basis functions are the limiting approximations of the method. Wave function parameters, such as molecular orbital coefficients, z,(f), average nuclear positions and momenta, and Pfe(0, etc., carry the time dependence and serve as the dynamical variables of the method. Therefore, the parameterization of the system wave function is important, and we have found that wave functions expressed as generalized coherent states are particularly useful. A minimal implementation of the method [16,17] employs a wave function of the form ... 

Various choices of families of approximate state vectors are characterized by sets of time-dependent parameters, which serve as dynamical variables as the system of electrons and atomic nuclei evolves in time. Such parameters are, for example, molecular orbital coefficients, the coefficients of the various configurations in a multi-configurational electronic state vector, average nuclear positions and momenta, etc. Minimal END is characterized by the state vector... 

The CPMD approach exploits in another way the separation of fast electronic and slow nuclear motions, as compared to BOMD. The KS orbitals are imbued with a fictitious time dependence, that is, y/i t)—> y/i t,t), and a dynamics for the orbitals is introduced that propagates an initially fully minimized set of orbitals to subsequent minima corresponding to each new nuclear configuration. This task is accomplished by designing the orbital dynamics in such a way that the orbitals are maintained at a fictitious temperature that is much smaller than the real nuclear temperature T but are still allowed to relax qitiddy in response to the nuclear motion. 

---