Beyond Molecular Electronic Calculations

Ultimately the computational chemist wants to make the model theories as realistic as possible, and the next step in the computation of NLO properties is not just to obtain more accurate and more efficient methods for the elec- 

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A very important difference between H2 and molecular orbital calculations is electron correlation. Election correlation is the term used to describe interactions between elections in the same molecule. In the hydrogen molecule ion, there is only one election, so there can be no election correlation. The designators given to the calculations in Table 10-1 indicate first an electron correlation method and second a basis set, for example, MP2/6-31 G(d,p) designates a Moeller-Plesset electron coiTclation extension beyond the Hartiee-Fock limit canied out with a 6-31G(d,p) basis set. 

At this stage we are at the very beginning of development, implementation, and application of methods for quantum-mechanical calculations of molecular systems without assuming the Born-Oppenheimer approximation. So far we have done several calculations of ground and excited states of small diatomic molecules, extending them beyond two-electron systems and some preliminary calculations on triatomic systems. In the non-BO works, we have used three different correlated Gaussian basis sets. The simplest one without r,y premultipliers (4)j = exp[—r (A t (8> Is) "]) was used in atomic calculations the basis with premultipliers in the form of powers of rj exp[—r (Aj (8> /sjr])... 

The theoretical results described here give only a zeroth-order description of the electronic structures of iron bearing clay minerals. These results correlate well, however, with the experimentally determined optical spectra and photochemical reactivities of these minerals. Still, we would like to go beyond the simple approach presented here and perform molecular orbital calculations (using the Xo-Scattered wave or Discrete Variational method) which address the electronic structures of much larger clusters. Clusters which accomodate several unit cells of the crystal would be of great interest since the results would be a very close approximation to the full band structure of the crystal. The results of such calculations may allow us to address several major problems ... 

Many-body perturbation theory in its lowest order form, which is often designated MP2, continues to be the most widely used of the ab initio approaches to the molecular electronic structure problem which go beyond an independent particle model and take account of the effects of electron correlation. The main focus of the present review has been on some of the emerging fields in which MP2 calculations are being carried out. Obviously, within the limited space available it has not possible to cover all of the fields of application. Some selectivity has been necessary, but the choices made do provide a snapshot of the range of contemporary applications of chemical modelling using many-body perturbation theory. 

Twenty years ago Car and Parrinello introduced an efficient method to perform Molecular Dynamics simulation for classical nuclei with forces computed on the fly by a Density Functional Theory (DFT) based electronic calculation [1], Because the method allowed study of the statistical mechanics of classical nuclei with many-body electronic interactions, it opened the way for the use of simulation methods for realistic systems with an accuracy well beyond the limits of available effective force fields. In the last twenty years, the number of applications of the Car-Parrinello ab-initio molecular d3mam-ics has ranged from simple covalent bonded solids, to high pressure physics, material science and biological systems. There have also been extensions of the original algorithm to simulate systems at constant temperature and constant pressure [2], finite temperature effects for the electrons [3], and quantum nuclei [4]. 

The assumption implicit throughout this book is that the parameters used to fit or represent molecular transition frequencies and intensities contain insights into molecular structure. These insights can be more useful than the multi-digit fit parameters themselves, especially when simplifying assumptions axe made and tested. Comparisons of observable or effective parameters to those obtained from an exact calculation (true parameters) or a simplified electronic structure model (one-electron orbital parameters) are seldom trivial or unique. The purpose of this book is to help experimentalists and theorists to go beyond molecular fit parameters to terms in the exact microscopic Hamiltonian on the one hand and to approximate electronic structure models on the other. Physical insight, not tables of spectral data and molecular constants, is the ultimate purpose of fundamental experimental and theoretical research. 

This method, known as Configuration Interaction (Cl) or superposition of configurations is a widely-used model for the calculation of molecular electronic structures beyond the Hartree-Fock model. We shall look at this model in Chapter 20. 

Melius, C. F. and Goddard, W. A. Ill, Ab initio effective potentials for use in molecular quantum mechanics, Phys. Rev. AlO 1528 (1974) Kahn, L. R., Baybutt, P., and Truhlar, D. G., Ab initio effective core potentials Reduction of all-electron molecular structure calculations to calculations involving only valence electrons, J. Chem. Phys. 65 3826 (1976). For calculations involving atoms beyond the second long row of the periodic table, it is common to exclude inner-shell electrons from the calculation and to introduce an effective one-electron potential (a pseudo-potential) which accounts for these electrons. These two papers describe an ab initio procedure for deriving such a pseudo-potential. 

The calculated lowest unoccupied molecular orbital (LUMO) for BF3 is shown by solid red and blue lobes. Most of the volume represented by the LUMO corresponds to the empty p orbital in the sp -hybridized state of BF3 (located perpendicular to the plane of the atoms). This orbital is where electron density fills (bonding occurs) when BF3 is attacked by NH3. The van der Waals surface electron density of BF3 is indicated by the mesh. As the structure shows, the LUMO extends beyond the electron density surface, and hence it is easily accessible for reaction. 

One would prefer to be able to calculate aU of them by molecular dynamics simulations, exclusively. This is unfortunately not possible at present. In fact, some indices p, v of Eq. (6) refer to electronically excited molecules, which decay through population relaxation on the pico- and nanosecond time scales. The other indices p, v denote molecules that remain in their electronic ground state, and hydrodynamic time scales beyond microseconds intervene. The presence of these long times precludes the exclusive use of molecular dynamics, and a recourse to hydrodynamics of continuous media is inevitable. This concession has a high price. Macroscopic hydrodynamics assume a local thermodynamic equilibrium, which does not exist at times prior to 100 ps. These times are thus excluded from these studies. 

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