Molecular system total energy

The most important equation, derived in this work, is the extended Born-Handy formula, valid in the adiabatic limit as well as in the case of break down of the B-0 approximation. Since due to the many-body formulation the extended Born-Handy formula can be expressed in the CPHF compatible form, the extended CPHF equations, describing the non-adiabatic systems, will immediately follow from the presented theory. We shall call them COM CPHF equations. Whereas in the adiabatic limit the extended Bom-Handy formula represents only small corrections to the system total energy, in non-adiabatic systems it plays three important roles (1) removes the electron degeneracies, (2) is responsible for the symmetry breaking, and (3) forms the molecular and crystalline stmcture. 

A quantum mechanical treatment of molecular systems usually starts with the Bom-Oppenlieimer approximation, i.e., the separation of the electronic and nuclear degrees of freedom. This is a very good approximation for well separated electronic states. The expectation value of the total energy in this case is a fiinction of the nuclear coordinates and the parameters in the electronic wavefunction, e.g., orbital coefficients. The wavefiinction parameters are most often detennined by tire variation theorem the electronic energy is made stationary (in the most important ground-state case it is minimized) with respect to them. The... 

The following sections give an overview of the functional form of the PFF and a short explanation of the various contributions to the total force field energy of a molecule or molecular system. 

A typical molecular dynamics simulation comprises an equflibration and a production phase. The former is necessary, as the name imphes, to ensure that the system is in equilibrium before data acquisition starts. It is useful to check the time evolution of several simulation parameters such as temperature (which is directly connected to the kinetic energy), potential energy, total energy, density (when periodic boundary conditions with constant pressure are apphed), and their root-mean-square deviations. Having these and other variables constant at the end of the equilibration phase is the prerequisite for the statistically meaningful sampling of data in the following production phase. 

Th c in pin, th e Ham ilton ian describes th e particles of the system the output, H, is the total energy of the system and the wave function, 4, con stitn tes all we can know ami learn about the particn lar molecular system represented by... 

Ihe one-electron orbitals are commonly called basis functions and often correspond to he atomic orbitals. We will label the basis functions with the Greek letters n, v, A and a. n the case of Equation (2.144) there are K basis functions and we should therefore xpect to derive a total of K molecular orbitals (although not all of these will necessarily 3e occupied by electrons). The smallest number of basis functions for a molecular system vill be that which can just accommodate all the electrons in the molecule. More sophisti- ated calculations use more basis functions than a minimal set. At the Hartree-Fock limit he energy of the system can be reduced no further by the addition of any more basis unctions however, it may be possible to lower the energy below the Hartree-Fock limit ay using a functional form of the wavefunction that is more extensive than the single Slater determinant. 

Molecular dynamics calculations use equations 25-27. HyperChem integrates equations 26 and 27 to describe the motions of atoms. In the absence of temperature regulation, there are no external sources or depositories of energy. That is, no other energy terms exist in the Hamiltonian, and the total energy of the system is constant. 

The total energy in an Molecular Orbital calculation is the net result of electronic kinetic energies and the interactions between all electrons and atomic cores in the system. This is the potential energy for nuclear motion in the Born-Oppenheimer approximation (see page 32). 

For a quantum mechanical calculation, the single point calculation leads to a wave function for the molecular system and considerably more information than just the energy and gradient are available. In principle, any expectation value might be computed. You can get plots of the individual orbitals, the total (or spin) electron density and the electrostatic field around the molecule. You can see the orbital energies in the status line when you plot an orbital. Finally, the log file contains additional information including the dipole moment of the molecule. The level of detail may be controlled by the PrintLevel entry in the chem.ini file. 

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