Perturbative calculation

Dalgarno A and Lewis J T 1956 The representation of long-range forces by series expansions. II. The complete perturbation calculation of long-range forces Proc. Phys. Soc. A 69 59... 

Wesolowski T A and Warshel A 1994 Ab initio free energy perturbation calculations of solvation free energy using the frozen density functional approach J. Phys. Chem. 98 5183... 

Mark, A.E. Free energy perturbation calculations. Encyclopaedia of Computational Chemistry, Wiley, New York, (1998) (in press). 

HyperChein perforins ab initio. SCK calculations generally. It also can calculate the coi relation energy (to he added to the total -SCK energy) hy a post Hartree-Fock procedure call. M P2 that does a Moller-Plesset secon d-order perturbation calculation. I he Ml 2 procedure is on ly available for sin gle poin t calculation s an d on ly produces a single tiuin ber, th e Ml 2 correlation energy, to be added to the total SCF en ergy at th at sin gle poin t con figuration of th e ti iiclei. 

Pearlman D A and P A Kollman 1989. A New Method for Carrying Out Free-Energy Perturbation Calculations - Dynamically Modified Wmdows. Journal Of Chemical Physics 90 2460-2470. 

FIGURE 3.2. A free-energy perturbation calculation of the free energy associated with an adiabatic charging of an Na+ ion in water (Ref. 10). The parameter A transforms the solute from it uncharged (A = 0) to its charged form (A = 1). 

It will be seen that the second-order treatment leads to results which deviate more from the correct values than do those given by the first-order treatment alone. This is due in part to the fact that the second-order energy was derived without considerar-tion of the resonance phenomenon, and is probably in error for that reason. The third-order energy is also no doubt appreciable. It can be concluded from table 3 that the first-order perturbation calculation in problems of this type will usually lead to rather good results, and that in general the second-order term need not be evaluated. 

According to Bartell (1961a), the relative motion of the interacting non-bonded atoms is described by means of a harmonic oscillator when the two atoms are bonded to the same atom, and by means of two superimposed harmonic oscillators when the atoms are linked to each other via more than one intervening atom. It is the second case which is of interest in connection with the biphenyl inversion transition state. The non-bonded interaction will of course introduce anharmonicity, but since a first-order perturbation calculation of the energy only implies an... 

To conclude, we think that valuable information can ce obtained from such relaxation experiments. They could provide a direct, kinetic proof of the conjecture that the Berry mechanism is the most probable one, as is indicated by some recent experimental and theoretical work. The applicability of this model is however restricted to situations where the energy of the molecule does not depend on the distribution of the ligands on the skeleton and where, as a consequence, there is one rate constant for each process. If this is not true, the present description could be the first-order approximation of a perturbation calculation. Such a work will be undertaken soon. 

An area of development is the inclusion of code necessary for free energy perturbation calculations for internal, van der Waals and electrostatic energy terms ( ). Another area of development is the option to use lookup tables for both nonbond energies and for constraint energy terms such as a solvent boundary energy term (16). Other features and options are routinely added as needed to aid in the execution of current projects underway within the NIH. 

The MCSCF and the subsequent perturbation calculations were done using a 6-31+G basis set expanded by a set of spd Rydberg functions. Exponents of this additional gaussians were 0.032 and 0.028 for the s and p shells for the oxygen atom, and 0.023 and 0.021 for the carbon atom. For the d functions, a common value of 0.015 was chosen for both heavy atoms. 

The variational calculations were performed using the Alchemy II package [67] while the further perturbation calculations used a code derived from the original CIPSI module. Proper interfaces between the two programs were developed. 

By including the effect of the rotation (at a given T temperature, for the level v = 0) in a perturbation calculation, we have obtained (5) ... 

Ishikawa, Y. and Koc, K. (1997) Relativistic many-body perturbation calculations for open-shell systems. Physical Review A, 56, 1295-1304. 

However, in the first excited state the degree of degeneracy is equal to four. Hence, the first-order perturbation calculation requires the application of Eq. (62). The wavefunctions for the first excited state can be written in the form... 

Wesolowski, T. A. and A. Warshel. 1994. Ab initio Free Energy Perturbation Calculations of Solvation Free Energy Using Frozen Density Functional Approach. J. Phys. Chem. 98, 5183. 

Pearlman, D. A. Kollman, P. A., The overlooked bond-stretching contribution in free energy perturbation calculations, J. Chem. Phys. 1991, 94, 4532-4545... 

Chipot, C. Millot, C. Maigret, B. Kollman, P. A., Molecular dynamics free energy perturbation calculations. Influence of nonbonded parameters on the free energy of hydration of charged and neutral species, J. Phys. Chem. 1994, 98,11362-11372... 

Lu, N. Kofke, D. A. Woolf, T. B., Improving the efficiency and reliability of free energy perturbation calculations using overlap sampling methods, J. Comput. Chem. 2003, 25, 28-39... 

Wood, R. H. Muhlbauer, W. C. F. Thompson, P. T., Systematic errors in free energy perturbation calculations due to a finite sample of configuration space. Sample-size hysteresis, J. Phys. Chem. 1991, 95, 6670-6675... 

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