Energy computation

Frenkel D 1986 Free-energy computation and first-order phase transitions Moiecuiar Dynamics Simuiation of Statisticai Mechanicai Systems ed G Ciccotti and W G Hoover (Amsterdam North-Holland) pp 151-88... 

Prenkel, D. Pree energy computation and first order phase transitions. In Molecular Dynamic Simulation of Statistical Mechanical Systems, Enrico Fermi Summer School, Varenna 1985, G. Ciccotti and W. Hoover, eds. North Holland, Amsterdam (1986) 43-65. 

Th is last equation is the nuclear Schriidinger equation describing the motion of nuclei, Th e electron ic energy computed from solving the electronic Schrbdinger equation (3) on page 163 plus tfie nuclear-nuclear interactions y, (R,R) provide a potential for nuclear motion, a Potential Knergy Surface (PHS). 

The quaniity, (R). the sum of the electronic energy computed 111 a wave funciion calculation and the nuclear-nuclear coulomb interaciion .(R.R), constitutes a potential energy surface having 15X independent variables (the coordinates R j. The independent variables are the coordinates of the nuclei but having made the Born-Oppenheimer approximation, we can think of them as the coordinates of the atoms in a molecule. 

Recently, molecular dynamics and Monte Carlo calculations with quantum mechanical energy computation methods have begun to appear in the literature. These are probably some of the most computationally intensive simulations being done in the world at this time. 

The force fields available are MM2, MM3, AMBER, OPLSA, AMBER94, and MMFF. The asterisk ( ) indicates force fields that use a modification of the original description in the literature. There is support for user-defined metal atoms, but not many metals are predefined. MM2 has atom types for describing transition structures. The user can designate a substructure for energy computation. 

How is electronic potential energy computed Electrons, which are more than three orders of magnitude lighter than nuclei, are too small for classical mechanics calculations. Electronic energy must... 

Single point energy calculations can be performed at any level of theory and with small or large basis sets. The ones we ll do in this chapter will be at the Hartree-Fock level with medium-sized basis sets, but keep in mind that high accuracy energy computations are set up and interpreted in very much the same way. 

In a higher level energy calculation, values for the energy computed using the more accurate procedure appear shortly after the Hartree-Fock energy. Here is the output from a formaldehyde calculation done at the MP2 level (RMP2 replaces RHF in the route section ... 

In Table 1.1 a comparison is made of the differences in free energies for two different zeolites. Note the large repulsive energies computed for the intermediates and their sensitivity to zeolite structure. 

For large systems, the computation of the energy can require 98% or more of the total computational effort, and within the energy computation, the pair interaction energy (van der Waals and electrostatic terms) can represent more than 90% of the total effort. For this reason, the aspects of the program that deal with the generation of the nonbond list and the computation of the nonbond energy are of critical importance. 

The Gibbs free energy (computed in the harmonic approximation) were converted from the 1 atm standard state into the standard state of molar concentration (ideal mixture at 1 molL-1 and 1 atm). 

The activation free energies computed both in the gas phase and in aqueous solution (Table 2.6) suggest that the generation of an alkylating QM (QM-NI) becomes a much easier process, passing from the protonated quaternary ammonium salt NI to its zwitterionic form NI. ... 

The variational principle now states that the energy computed via equation (1-11) as the expectation value of the Hamilton operator H from any guessed xTtrial will be an upper bound to the true energy of the ground state, i. e.,... 

In Table 12-5 we compare the binding energies computed using several hybrid functionals and basis sets, attempting to approach the basis set limit for each functional in a systematic (but not necessarily cost effective) way. At first we note the reasonable performance of all functionals. The converged results, however, indicate a slight tendency to underestimate the experimental value by about 1-2 kcal/mol. This trend is slightly more emphasized for... 

Second, AEQM xgj ) is calculated as the difference between the QM subsystem energy computed form the ab initio calculation (Eqm(QM)), and the QM/MM electrostatic energy computed classically (Eeiectrostatics(QM/MM)) [13]. 

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