Calculation using molecular orbital

A configuration interaction calculation uses molecular orbitals that have been optimized typically with a Hartree-Fock (FIF) calculation. Generalized valence bond (GVB) and multi-configuration self-consistent field (MCSCF) calculations can also be used as a starting point for a configuration interaction calculation. 

Five molecular descriptors, A-E, have been calculated using molecular orbital computations for 32 PAHs, 10 of which are have carcinogenic activity (A) and 22 not (I), as given below, die two groups being indicated ... 

This is the basic equation used to derive normal coordinate analysis [110] as well as to define the vibrational quantities to be calculated using molecular orbital theory [79,94], The coefficients, g , are the forces acting on the nuclei, which are zero at equilibrium geometiy. This leaves the quadratic terms Vs the first term in the change of potential energy with instantaneous vibrational displacement. The quadratic terms Fy, are conveniently ordered as a matrix which is known as the force field or force matrix. These terms correspond to the derivatives of the potential energy V ... 

We note that much care has to be taken when Koopman s theorem is used to estimate the transfer integrals in asymmetric dimers, as has been extensively discussed elsewhere [58,59], In such instances, part of the electronic splitting can simply arise from the different local environments experienced by the two interacting molecules, which create an offset between their HOMO and LUMO levels prior to their interaction due to polarization and/or electrostatic effects. In order to evaluate the effective couplings, this offset can be accounted for by performing calculations using molecular orbitals localized on the individual units as basis set [59] or by applying an electric field to promote the resonance between the electronic levels, as done by Jortner and coworkers [56], This artifact can also be prevented when... 

This molecular-orbital model of metallic bonding (or band theory, as it is also called) is not so different in some respects from the electron-sea model. In both models Ihe electrons are free to move about in the solid. The molecular-orbital model is more quantitative than the simple electron-sea model, however, so many properties of metals can be accounted for by quantum mechanical calculations using molecular-orbital theory. 

The molar absorption (extinction) coefficient, Einstein coefficient and absorption cross-section are commonly used measures of transition probability. The first three are used for atomic and molecular species in the gas or solution phase, while the latter is commonly used in solid-state studies. These are absolute measures of absorption probability and are ultimately derived from the transition dipole moment, and are therefore all related. They can be measured experimentally firom the absorption spectrum and can, in some cases, be calculated using molecular orbital theory programs. (Note that generally MO calculations will give the oscillator strength for any forbidden transition as zero). 

Marathe, V.R., Trautwein, A. Calculation of charge density, electric field gradient and internal magnetic field at the nuclear site using molecular orbital cluster theory. In Thosar,... 

Group 2 complexes are formally electron deficient and conformationally floppy only small energies (often only 1-2 kcal mol-1) are required to alter their geometries by large amounts (e.g., bond angles by 20° or more). In such cases, the inclusion of electron-correlation effects becomes critical to an accurate description of the molecules structures. Both HF/MP2 and density functional theory (DFT) methods have been applied to organoalkaline earth compounds. DFT approaches, which implicitly incorporate electron correlation in a computationally efficient form, are generally the more widely used. Molecular orbital calculations that successfully reproduce bent... 

Similarly, the structure of 5-nitro-2,4-dihydro-377-l,2,4-triazol-3-one (NTO) 6 has been scrutinized using molecular orbital calculations using the 6-31+G and 6-311+G basis sets. These calculations examined the various tautomers of NTO and give an insight into the molecular mechanisms involved in its explosive decomposition <1996JA8048>. 

The general approach is illustrated in detail for the case of aqueous ferrous and ferric ions, and the calculated rate constant and activation parameters are found to be in good agreement with the available experimental data. The formalisms we have employed in studying such complicated condensed phase processes necessarily rely on numerous approximations. Furthermore, some empirical data have been used in characterizing the solvated ions. We emphasize, nevertheless, that (1) none of the parameters were obtained from kinetic data, and (2) this is, as far as we are aware, the first such theoretical determination to be based on fully Ab initio electronic matrix elements, obtained from large scale molecular orbital (MO) calculations. A molecular orbital study of the analogous hexaaquo chromium system has been carried out by Hush, but the calculations were of an approximate, semi-empirical nature, based in part on experi-... 

Equations (16) and (17) were then used to calculate the molecular orbital contributions to and - just as Oddershede and Sabin did in their more accurate calculations - a table for the velocity-dependence of core, bond, and lone-pair contributions to Se for protons was constructed [25,42], These results together with equation (10) lead to the calculation of the proton stopping cross section in compound materials with chemical binding effects incorporated. 

Ab initio calculations are based on first principles using molecular orbital (MO) calculations based on Gaussian functions. Combinations of Gaussian functions yield Slater-type orbitals (STOs), also called Slater determinants. STOs are mathematical functions closely related to exact solutions for the hydrogen atom. In their ultimate applications, ab initio methods would use Gaussian-type wave functions rather than STOs. The ab initio method assumes that from the point of view of the electrons the nuclei are stationary, whereas... 

A unified theoretical explanation using molecular orbital theory has been proposed. Grimme [65] investigated the PFR of phenyl acetate as well as the photo-Claisen rearrangement of allyl phenyl ether and the 3-cleavage of para-substituted phenoxyacetones. A unified description of the three reactions has been invoked according to MNDOC-CI and AMl/AMl-HE calculations. No matter what ex-... 

Maruthe,V.R. Trautwein, A. (1983) Calculation of charge density, electric field gradient and internal magnetic field using molecular orbital cluster theory. In Thosar, B.V. (ed.) Advances in Mossbauer spectroscopy. Elsevier, Amsterdam, 398-449 Matijevic, E. Cimas S. (1987) Formation of uniform colloidal iron(lll) oxides in ethylene... 

In molecular orbital calculations, the molecular orbitals are represented as a linear combination of atomic orbital functions (Xi). A variety of different mathematical functions may be used to represent these atomic orbital functions. If a very sophisticated mathematical function is used, then the resulting answer is higher in quality, providing very accurate energies and geometries for the drug molecule being studied however, such calculations may be extremely expensive in terms of computer time required. If a... 

Generally, the atomic, outer, and interatomic sphere radii are chosen so as to minimize the volume between the spheres. Other physical considerations, such as empirical atomic or ionic radii, can also influence the initial choice of sphere sizes. It has also been recently shown that overlapping spheres may be used since the various expansion theorems are still valid (192). This technique has been used to calculate the molecular orbitals of Zeise s salt and ferrocene discussed later in this review (191, 193). 

It is essential to have tools that allow studies of the electronic structure of adsorbates in a molecular orbital picture. In the following, we will demonstrate how we can use X-ray and electron spectroscopies together with Density Functional Theory (DFT) calculations to obtain an understanding of the local electronic structure and chemical bonding of adsorbates on metal surfaces. The goal is to use molecular orbital theory and relate the chemical bond formation to perturbations of the orbital structure of the free molecule. This chapter is complementary to Chapter 4, which... 

Unfortunately there seems to be no way at present absolutely to characterize the behavior of a plasticizer in terms of some fundamental property. The reason is that the behavior of the plasticizer is intimately tied up with the polymer to which it is added, and the polymer, in turn, depends greatly on its previous history. For example, one can prepare two samples of film from the same batch of polymer yet, by drawing one to a greater extent, it will increase in crystallinity owing to better orientation of the chains, and the effect of the plasticizer will, therefore, be quite different. Whereas one can use molecular orbital calculations to predict, for in-... 

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