Basis sets/functions computational quantum mechanics

Figure 21. The (So — S2) absorption spectrum of pyrazine for the reduced three-dimensional model using different spawning thresholds. Full line Exact quantum mechanical results. Dashed line Multiple spawning results for — 2.5, 5.0, 10, and 20. (All other computational details are as in Fig. 20.) As the spawning threshold is increased, the number of spawned basis functions decreases, the numerical effort decreases, and the accuracy of the result deteriorates (slowly). In this case, the final size of the basis set (at t — 0.5 ps) varies from 860 for 0 = 2.5 to 285 for 0 = 20.

Ab initio quantum mechanics is based on a rigorous treatment of the Schrodinger equation (or equivalent matrix methods)4-7 which is intellectually satisfying. While there are a number of approximations made, it relies on a set of equations and a few physical constants.8 The use of ab initio methods on large systems is limited if not impossible, even with the fastest computers available. Since the size of an ab initio calculation is defined by the number of basis functions in the system, ab initio calculations are extremely costly for anything past the second row in the periodic table, and for all systems with more than 20 or 30 total atoms. 

A review of the Journal of Physical Chemistry A, volume 110, issues 6 and 7, reveals that computational chemistry plays a major or supporting role in the majority of papers. Computational tools include use of large Gaussian basis sets and density functional theory, molecular mechanics, and molecular dynamics. There were quantum chemistry studies of complex reaction schemes to create detailed reaction potential energy surfaces/maps, molecular mechanics and molecular dynamics studies of larger chemical systems, and conformational analysis studies. Spectroscopic methods included photoelectron spectroscopy, microwave spectroscopy circular dichroism, IR, UV-vis, EPR, ENDOR, and ENDOR induced EPR. The kinetics papers focused on elucidation of complex mechanisms and potential energy reaction coordinate surfaces. 

When one refers to a quantum mechanical solvent model, the word model reverts to its usual sense in die context of QM methods it is the level of electronic structure theory used to describe die solvent. Thus, diere is no real distinction between the solvent and die solute in terms of computational technology - the wave function for the complete supersystem (or the DFT equivalent) is computed without resort to methodological approximations beyond those inherent to the level of electronic structure theory. To avoid problems with basis-set imbalances, one might expect calculations representing the solvent in a fully QM fashion to employ a common level of theory for all particles, but this does not have to be the case. 

The ab initio approach includes all a- and 71-electrons and seeks to use either analytical or numerical solutions to the integrals that occur in the quantum mechanical problem. This procedure was initially carried out within the framework of the one electron HF-SCF method using the basis sets described above. Subsequently it has been implemented using density functional theory (DFT). If the electron density in the ground state of the system is known, then in principle this knowledge can be used to determine the physical properties of the system. For instance, the locations of the nuclei are revealed by discontinuities in the electron density gradient, while the integral of the density is directly related to the number of electrons present. Ab initio methods are obviously computationally intensive. 

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