Quantum Mechanics Molecular Mechanics

An effective Hamiltonian and time-independent perturbation theory

by Carlos E. Solivérez

Using a formalism set up by Bloch an effective Hamiltonian is introduced which, when expanded in powers of a... more Using a formalism set up by Bloch an effective Hamiltonian is introduced which, when expanded in powers of a perturbation V, generalizes the Rayleigh-Schrödinger perturbation theory. This effective Hamiltonian provides a simple way of handling degeneracies and the orthonormalization of the perturbed wavefunctions. As an illustration the spin Hamiltonian introduced by Pryce in paramagnetic resonance is derived up to third order terms, and the electron-lattice interaction is discussed showing that the © follows from first-order terms in the case of non-degenerate electronic ground state.

Combining quantum wavepacket ab initio molecular dynamics with QM/MM and QM/QM techniques: Implementation blending ONIOM and empirical valence bond …

by Isaiah Sumner

General Theory of Effective Hamiltonians

by Carlos E. Solivérez

Numerical Feynman integrals with physically inspired interpolation: Faster convergence and significant reduction of computational cost

by Nike Dattani

2012 - Published in AIP Advances

Vibration characteristics of bi-layer graphene sheets

by Rajib Chowdhury

Thin Solid Films, 519[18] (2011), pp. 6026–6032.

Bilayer graphene sheets (BLGSs) are currently receiving increasing attention. In this paper, the vibration... more Bilayer graphene sheets (BLGSs) are currently receiving increasing attention. In this paper, the vibration characteristics of BLGSs are investigated using analytical and atomistic finite element approaches. Various possible scenarios, namely different geometrical configuration (armchair and zigzag), boundary conditions, and aspect ratio are considered in the present study. The dynamic characteristics of BLGS studied have shown dependence on aspect ratio and the boundary conditions. The unique vibrational properties and large stiffness of BLGS identified in the present work make them suitable candidates for manufacturing nanosensors; electromechanical resonators also will aid the nanomaterials research community to design nanodevices.