Ab initio crystal orbital method

For the analysis of the spectra of trans-(CH)x, valence-force-field calculations have been performed, the force constant being empirically fitted so as to reproduce the observed vibrational frequencies (Inagaki et al., 1975 Schiigerl and Kuzmany, 1981). The energy gradient scheme based on the ab initio crystal orbital method has also been attempted for the study of the vibrational structure of trans- and c -(CH)x (Teramae et al., 1984). The calculated result of the vibrational frequencies has been found to depend upon the quality of the basis set. It has been demonstrated that, e.g., for the 4-31G basis, a uniform scaling of the force constants, multiplying by 0.8, is required to adjust the vibrational frequencies of the trans-(CH), (Table III). 

Kertesz, M., J.Koller and A.Azman. On the Electronic Structure of Polydiacetylenes as Studied by the Ab Initio Crystal Orbital Method, Chem.Phys. 27 (1978)... 

Trans to Gauche, Helical angle dependence of the band structures of parent polysilanes was calculated by the ab initio crystal orbital method . When the screw axis is taken to be coincident with the Cartesian z axis, the pxi and pyJ basis functimis belonging to the j i cell from the reference cell can be obtained by the relationships of the Cartesian Px-) and pyj orbitals... 

This chapter presents some examples of the application of the ab initio crystal-orbital method described in Chapter 1. Though these applications range from the field of plastics (polyethylene and its fluoro derivatives) through highly conducting polymers [polyacetylenes and polydiacetylenes, (SN) c, TCNQ and TTF stacks] to biopolymers (homopolynucleotides and homopolypeptides), they are only illustrative. No attempt has been made to review the numerous other applications performed by the Namur group and by other researchers, as this would increase unduly the size of this book. 

The ab initio crystal orbital method 2-4 is by now an established tool for the evaluation of ground state properties of polymers. 

The investigation of the response of macromolecules to external mechanical forces or to electromagnetic fields may basically contribute to our understanding of the structural and functional properties of these systems. The starting point of all studies of this kind is the proper description of the equilibrium (ground) state of the molecule without external fields. In our a priori calculations, the ground state energy is obtained in two steps as a zeroth order approximation the Hartree-Fock (HF) contribution is calculated by the ab initio crystal orbital method (1,2) and electronic correlation effects are included by perturbation theory afterwards. 

The availability of detailed information about the electronic states of PDAs makes them ideal systems to test molecular quantum mechanical theories. The earliest calculation for a model PDA chain with simple sidegroups gave rather poor values for the band-gap, see (7). In most of these calculations Coulomb correlations were neglected so that only band structures were deduced. Further work along these lines has included the use of an ab initio crystal orbital method [105), studies of the ground state geometries [106), a priori Hartree Fock crystal orbital calculations (107) and a non-empirical effective Hamiltonian technique [108). These show... 

These slight differences are mainly due to the smearing of electron density caused by thermal vibration of the Co atom in crystals. Johansen has also calculated the theoretical deformation density of Co0610 by the ab initio molecular orbital method (39), on the assumption of a regular octahedral geometry with high-spin state (t2g )Heg)2. The as-phericity of 3d electron density is similar to that observed for [Co(N02)6]3. ... 

In a-cyanoacetohydrazide, where there is both strong inter- and intramolecular hydrogen bonding and large dipole interactions, the conformer observed in the crystal is the eighth highest in calculated energy, with a difference of 37 kJ mol-1 over the minimum calculated by ab-initio molecular orbital methods [267]. 

For hydrogen bonds weaker than OH 0=C or NH 0=C, theory predicts smaller differences in the X-H bond lengths and negligible changes in the nonhydrogen bonds. TWo models have been studied theoretically with the ab-initio molecular orbital method at the HF/3-21G level of approximation. These are formaldehyde oxime cyclic dimer versus the monomer [378] and formaldehyde hydrazone cyclic dimer versus the monomer [379]. Except for the O-H and N-H bonds, these differences are too small to be detected by single crystal X-ray or neutron diffraction methods, as shown in Fig. 5.2. 

Richard Fenske arrived as Assistant Professor at the University of Wisconsin in 1961 after having completed his PhD, with Donald Martin at Iowa State University on applying crystal-field theory to square-planar platinum complexes [19]. Fenske was interested in developing a method more closely tied to the ab initio molecular orbital method described so beautifully by Roothaan [20]. Building on some previous suggestions [21], he and his first students, especially Ken Caulton and Doug Radtke, developed an approximate self-consistent field method that had no empirical or adjustable parameters. With some later refinements by this author, the method became widely known as the Fenske-Hall method [22], and in this form it is still being used today [23]. 

Deformation density maps have been used to examine the effects of hydrogen bonding on the electron distribution in molecules. In this method, the deformation density (or electrostatic potential) measured experimentally for the hydrogen-bonded molecule in the crystal is compared with that calculated theoretically for the isolated molecule. Since both the experiment and theory are concerned with small differences between large quantities, very high precision is necessary in both. In the case of the experiment, this requires very accurate diffraction intensity measurements at low temperature with good thermal motion corrections. In the case of theory, it requires a high level of ab-initio molecular orbital approximation, as discussed in Chapter 4. 

The electronic structures of poiy(fluoroacetylene) and poly(difluoroacetylene) have been investigated previously using the ab initio Hartree-Fock crystal orbital method with a minimum basis set (42). Only the cis and trans isomers with assumed, planar geometries were studied. The trans isomer was calculated to be more stable in both cases, and the trans compounds were predicted to be better intrinsic semiconductors and more conductive upon reductive doping than trans polyacetylene. However, our results show that head-to-tail poly(fluoroacetylene) prefers the cis structure and that the trans structure for poly(difluoroacetylene) will not be stable. Thus the conclusions reached previously need to be re-evaluated based on our new structural information. Furthermore, as noted above, addition of electrons to these polymers may lead to structural deformations that could significantly change the conductive nature of the materials. 

The self-consistent-field (SCF) ab initio Hartree-Fock crystal orbital method is applied with success to polysulfur nitride (SN)X, chains using non-local exchange and evaluating all integrals over atomic orbitals within 5 atomic neighbours accurately. 

Relativistic and electron correlation effects play an important role in the electronic structure of molecules containing heavy elements (main group elements, transition metals, lanthanide and actinide complexes). It is therefore mandatory to account for them in quantum mechanical methods used in theoretical chemistry, when investigating for instance the properties of heavy atoms and molecules in their excited electronic states. In this chapter we introduce the present state-of-the-art ab initio spin-orbit configuration interaction methods for relativistic electronic structure calculations. These include the various types of relativistic effective core potentials in the scalar relativistic approximation, and several methods to treat electron correlation effects and spin-orbit coupling. We discuss a selection of recent applications on the spectroscopy of gas-phase molecules and on embedded molecules in a crystal enviromnent to outline the degree of maturity of quantum chemistry methods. This also illustrates the necessity for a strong interplay between theory and experiment. 

A variety of methods can now be used to probe intermolecular interactions. The structural information on intermolecular interactions obtained from X-ray and neutron diffraction studies can be compared with gas-phase experimental data from pure rotational or rotation-vibrational spectra [1] and the energies obtained from ab initio molecular orbital calculations. It is found that each of these methods generally gives essentially the same result. While most X-ray diffraction studies are on crystals of small molecules, comparisons with the lower-resolution results of protein crystallographic studies give information on interactions in an environment that consists of about 50 % water by volume [8]. 

These results were in agreement with a previous calculation done using an ab initio Hartree-Fock crystal orbital method with a 7s/3p minimal basis set with the zW-trans geometry taken from the Extended Huckel calculation [12]. This method allowed complete... 

Owing to the central role of DNA in biochemistry and biophysics, the computation of the electronic structure of periodic polymers constructed from nucleotide bases, base pairs, and nucleotides by applying the ab initio Hartree-Fock crystal-orbital method has attracted much... 

It can be seen from Table 2.6 that the physically most important valence and conduction bands in the later ab initio calculations are much broader (0.435-0.789 and 0.245-0.820 eV, respectively) than those obtained by application of different semiempirical crystal-orbital methods. With the simple PPP-CO approximation, the corresponding values for the highest filled bands are 0.218-0.299 eV and those for the conduction band are about 0.109 eV. Energy-band-structure calculations for the base stacks taking into account the effect of the other valence electrons with the aid of the CNDO/2 CO method give again broader bands (valence bandwidths of 0.136-0.490 eV and conduction band-widths of 0.109-0.245 eV), while the MINDO/2 CO results indicate somewhat less-broad bands (valence bandwidths of 0.027-0.299 eV and conduction bandwidths of 0.027-0.163 eV). For futher details on the semiempirical crystal-orbital calculations see also Chapter 3. 

The preceding methods were applied to a number of periodic polymers with a small unit cell. Many of these calculations used different all-valence electron semiempirical crystal-orbital methods (CNDO/2, — INDO, — MINDO, and MNDO CO methods). At this point we shall discuss only some of the not very numerous ab initio vibrational calculations and also an MNDO CO work on fra/is-polyacetylene (PA), because in this investigation disorder in PA due to soliton and polaron formation was also taken into account. ... 

ABSTRACT, - After a short review of the ab initio SCF LCAO crystal orbital method the negative factor technique for the determination of the density of states in a disordered chain is presented. After this the problem of electron correlation in polymers is discussed and the generation of correlated (quasiparticle) valence and conduction bands is reviewed. 

The PIXEL code and documentation (OPiX package) can be downloaded at the author s site http //users.unimi.it/gavezzot. Computing times on an ordinary PC are of the order of a few seconds for a molecular dimer, to a few minutes for a complete crystal structure. PIXEL has been repeatedly shown to give results of accuracy comparable to ab initio MO methods [51]. For an example. Fig. 5 [52] shows a comparison between MP2, PIXEL, uncorrected and corrected periodic-orbital... 

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