Molecular orbitals first principles calculations

The ultimate goal of quantum mechanical calculations as applied in molecular modeling is the a priori compulation of properties of molecules with the highest possible accuracy (rivaling experiment), hut utilizing the fewest approximations in the description of the wave-function. Al> initio. or from first principles, calculations represent the current state of the an ill this domain. Ah i/tirio calculations utilize experimental data on atomic systems to facilitate the adjustment of parameters such as the exponents ol the Gaussian functions used to describe orbitals within the formalism. 

We evaluated adsorbed SO3 configuration on Pt (111) surface by using the first-principles calculations with a slab model in a periodic boundary condition. On the basis of the result of the calculations with a slab model, we evaluated the electronic states of SO3 in detail using the relativistic DV-Xa molecular orbital method. 

The electronic state calculation by discrete variational (DV) Xa molecular orbital method is introduced to demonstrate the usefulness for theoretical analysis of electron and x-ray spectroscopies, as well as electron energy loss spectroscopy. For the evaluation of peak energy. Slater s transition state calculation is very efficient to include the orbital relaxation effect. The effects of spin polarization and of relativity are argued and are shown to be important in some cases. For the estimation of peak intensity, the first-principles calculation of dipole transition probability can easily be performed by the use of DV numerical integration scheme, to provide very good correspondence with experiment. The total density of states (DOS) or partial DOS is also useful for a rough estimation of the peak intensity. In addition, it is necessary lo use the realistic model cluster for the quantitative analysis. The... 

Although the ligand field theory is based on the several critical approximations, a first-principles calculation based on the ligand field theory can also provide a useful information when the results are compared to those of the DV-ME calculations. For example, a comparison between the calculations based on the LFT using the pme atomic orbitals (AOs) and the DV-ME calculations using the molecular orbitals (MOs) provide a clear separation of the effect of covalency. Therefore, in the present work, we also carried out the calculation of the multiplet structure of ruby based on the LFT. In this approach, the parameters representing the electron-electron repulsion are calculated using the pure 3d atomic orbitals of the... 

The first-principles calculations for theoretical XANES spectra consist of three procedures, that is obtaining the self-consistent charge density, the discretized continua and the X-ray absorption spectra. The self-consistent charge densities for the chemical species were calculated with software called SCAT which implemented the DV-Xa molecular orbital method (15). For calculations of the continua and X-ray absorption spectra, the method was extended within the framework of square-integrable (L ) discretized wavefunction method (9-11). 

The steps involved are, first, calculation of the one-electron molecular orbital energies for the field of the nuclei and (T—bond electrons. Usually much more detailed account is taken of molecular geometry than is done in the simple MO theory. The repulsions between the electrons in the same and different molecular orbitals are then calculated for particular electronic configurations (such as the lowest state). The usual MO coefficients are used to determine the fraction of the time a given electron spends in a particular orbital. The exclusion principle is employed to reject all terms that amount to having two electrons with the same spin in a given atomic orbital. 

Initially, the PL mechanism is mainly studied by the molecular orbit theory, and this theory only treats some high-symmetry crystal. For intrinsic PL materials, first-principles calculations are used extensively to discuss the PL origin. From the calculation result, the fundamental crystal information and electronic properties can be obtained. The electronic-transition modes and their allowed or forbidden transition nature can be revealed. Thus, the theoretical results can predict the excitation and emission band positions approximately, which helps to perform the band assignment in the experimental spectra. After knowing the luminescent mechanism, we can modify the luminescence intensify and shift peak position as well as broaden the emission ranges by utilizing various experimental strategies. 

Semiempirical molecular quantum-mechanical methods use a simpler Hamiltonian than the correct molecular Hamiltonian and use parameters whose values are adjusted to fit experimental data or the results of ab initio calculations. An example is the Hiickel MO treatment of conjugated hydrocarbons (Section 17.2), which uses a one-electron Hamiltonian and takes the bond integrals as adjustable parameters rather than quantities to be calculated theoretically. In contrast, an ab initio (or first principles) calculation uses the correct Hamiltonian and does not nse experimental data other than the values of the fundamental physical constants. A Hartree-Fock SCF calculation seeks the antisynunetrized product d> of one-electron functions that minimizes / dr, where H is the true Hamiltonian and is thns an ab initio calcnlation. (Ab initio is Latin for from the beginning and indicates a calculation based on fundamental principles.) The term ab initio should not be interpreted to mean 100% correct. An ab initio SCF MO calculation uses the approximation of taking as an antisynunetrized product of one-electron spin-orbitals and uses a finite (and hence incomplete) basis set. 

The fourth aspect of molecular structure, after connectivity, symmetry and geometry, is electron density. This is at the heart of the concept of chemical bonding, and is important in the interpretation of data from both experiments and quantum mechanical calculations. On the one hand, high-resolution X-ray diffraction of well diffracting crystals can provide us with three-dimensional electron density maps (Section 10.9), and on the other ab initio molecular orbital theory and density functional theory allow us to simulate them directly using first-principles calculations (Section 3.6). Either way, we get information with a real physical meaning. 

For large systems the parametrisation method has to be efficient and provide fast convergence. The reference values can be obtained either by higher level first principles - calculations or, preferably, from the experimental measurements of certain properties. Useful reference quantities are energy differences among frontier molecular orbital levels, the electric dipole moment, the symmetry and eharge distribution of specifie orbitals, fragment populations, etc. For instanee, the cost (or penalty) function can be defined as... 

HyperChem currently supports one first-principle method ab initio theory), one independent-electron method (extended Hiickel theory), and eight semi-empirical SCFmethods (CNDO, INDO, MINDO/3, MNDO, AMI, PM3, ZINDO/1, and ZINDO/S). This section gives sufficient details on each method to serve as an introduction to approximate molecular orbital calculations. For further details, the original papers on each method should be consulted, as well as other research literature. References appear in the following sections. 

We shall illustrate these rules first with H2 and then with other diatomic molecules. The same principles apply to polyatomic molecules, but their molecular orbitals are more complicated and their energies are harder to predict. Mathematical software for calculating the molecular orbitals and their energies is now widely available, and we shall show some of the results that it provides. 

The recent interest in the exploration of electrocatalytic phenomena from first principles can be traced to the early cluster calculations of Anderson [1990] and Anderson and Debnath [1983]. These studies considered the interaction of adsorbates with model metal clusters and related the potential to the electronegativity determined as the average of the ionization potential and electron affinity—quantities that are easily obtained from molecular orbital calculations. In some iterations of this model, changes in reaction chemistry induced by the electrochemical environment... 

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