Self-consistent Molecular Orbital Method Research Articles

Recent progress in approximate self-consistent-field theory

Progress in the development of self-consistent molecular-orbital methods for all valence electrons using zero differential overlap approximations is reviewed. Calculations of equilibrium bond lengths, bond angles, bending force constants, electric dipole moments and electron-nuclear hyperfine interactions are shown to be in moderately good agreement with experiment for a wide range of molecules and free radicals.

STM images of molecules on a metallic surface: a fast calculation based on a self-consistent semiempirical molecular orbital method

We developed a new computational tool for analyzing observations obtained by a scanning tunneling microscope (STM). Our methods are based on self-consistent semiempirical molecular orbital method, which requires fewer computational resources than ab initio calculations, while maintaining an acceptable accuracy for comparison with submolecular-scale measurements. We calculated STM images for a bare graphite surface and naphthalene-l,4,5,8-tetracarboxylic dianhydride (NTCDA) molecules adsorbed on a graphite surface. Both of them concur with previously reported measurements. Regarding the graphite surface, dependence of bias voltage is reproduced. For NTCDA, we found that the brightness and shape of the calculated image depend on molecular orientation against the surface. That fact is consistent with experimental observations and structural models that have been described by other authors.

Adsorption of oxygen on Si(100) steps: a study at semiempirical level

In this study oxygen adsorption on steps of the Si(100) surface is investigated with quantum mechanical detail. A cluster model represents the step structure and the oxygen impurity is deposited in this cluster above the dimer rows. A map of the total energy sensed by the adsorbate is constructed by displacing the oxygen atom on the terraces and down the step and allowing the system to relax to the total-energy-optimized configuration by a steepest-descent method. A self-consistent semiempirical molecular orbital method is applied to the evaluation of the total energy. Though the adsorption geometries are reminiscent of the ones observed for the flat surface, the effects of the step geometry are noticeable. They influence both the preferred adsorption sites and the properties of the electronic configuration of the adsorbed system.

Effect of oxygen on the optical properties of small silicon pyramidal clusters

Optical absorption and light emission of oxygen-incorporated small silicon $({\mathrm{Si}}_{30}{\mathrm{H}}_{40}{\mathrm{O}}_{i})$ pyramidal clusters as a function of oxygen content were theoretically studied using the self-consistent semiempirical molecular orbital method (modified neglect of diatomic overlap---parametric method 3). In the absolute majority of the cluster configurations with low oxygen content $(i<4)$ the excitations have a strong localized character and result in a significant shift from its equilibrium ground state position of one of the silicon atoms inside the cluster volume. The optical transition energies in those cases range from 2.05 to 2.35 eV. The typical Stokes shift for these structures is of the order of 100 meV. However, for some particular cluster configurations the excitations are localized at silicon sites directly adjacent to embedded oxygen atoms and this results in a considerable reduction of the emission energy down to approximately 1.40--1.60 eV and in an increase of the Stokes shift values to 600--800 meV. The same behavior was traced out for the case where the presence of a silanone $(\mathrm{Si}=\mathrm{O})$ bond at the surface of the ${\mathrm{Si}}_{30}{\mathrm{H}}_{38}\mathrm{O}$ cluster is considered. For intermediate and high oxygen content $(i>4)$ structures, a wide spread of the optical transition energies ranging from 1.60 to 3.00 eV is observed, due to the competition between two opposite tendencies. According to the first one, connected with the increasing of the quantum confinement effects due to oxidation, the optical transition energies tend to increase, whereas the enhanced possibility of involvement of oxygen or oxygen-adjacent silicon atoms in the process tends to decrease the energy transitions.

Optical spectra of high-symmetry isomers 60(CH3-r 6-H)n at n=3, 6

Earlier, we found the energies of formation and the electron band structures of the fullerene molecule C60 and its methylated and hydrogenated chemical derivatives with saturated r6 bonds of the type C60(CH3-r6-H)n with n from 1 to 6. Based on the self-consistent molecular-orbital method, we found the energies of singlet and triplet excitations for each molecule by the ΔSCF technique. We compared the electron structure of the fullerene molecule with experimental data and other theoretical calculations and showed that the semiempirical quantum-chemical technique used in our work satisfactorily explains the experimental photoluminescence spectra of fullerene-containing star-shaped polystyrenes. Partial or complete removal of the dipole inhibition for the transitions in isomers that are formed upon chemical saturation of double bonds makes it possible to follow changes in the electron structure of the pπ shell of the fullerene molecule by spectroscopic techniques. Specific optical spectra of the first excited singlet states (spectra of absorption, luminescence, and excitation of luminescence) as well as phosphorescence of the first spin-triplet state are described.

Oxygen effect on optical properties of nanosize silicon clusters

Optical absorption and light emission of oxygen-incorporated small silicon $({\mathrm{Si}}_{14}{\mathrm{H}}_{24})$ clusters as a function of oxygen content were theoretically studied using a self-consistent semiempirical molecular orbital method (modified neglect of diatomic overlap--parametric method 3). Two different models of oxygen incorporation were considered. Changes in the appropriate energies were traced when oxygen atoms were introduced either to the cluster surface (OH-group passivation) or inside the cluster. An increase of the number of oxygen atoms both at the surface and inside the cluster results in the decrease of the absorption energy with respect to the values typical for the cluster passivated only by hydrogen, while the emission energy appears to be influenced mainly by the incorporated oxygen content. There is a Stokes shift reaching the significant value of about 0.7 eV. It reduces with the increase of the oxygen content down to a value of 0.2 eV in the case of OH-group-terminated clusters, while it is almost constant for the oxygen-incorporated ones.

Electronic Properties of Nanosize Silicon–Oxygen Clusters

Optical absorption and light emission of oxygen incorporated small silicon (Si14H24) clusters as a function of oxygen content were theoretically simulated by using a self-consistent semiempirical molecular orbital method (MNDO-PM3). Two different models of oxygen incorporation were considered. Changes in the appropriate energies were traced when oxygen atoms were introduced either to the cluster surface (OH-group passivation) or inside the cluster. An increase of the number of oxygen atoms both at the surface and inside the cluster results in a decrease of the absorption energy with respect to the values typical for the cluster passivated only by hydrogen, while the emission energy appears to be influenced mainly by the incorporated oxygen content. There is a Stokes shift reaching the significant value of about 0.7 eV. It reduces with the increase of the oxygen content down to a value of 0.2 eV in the case of OH-group terminated clusters while it is almost constant for the oxygen incorporated ones.

Electronic Properties of Nanosize Silicon–Oxygen Clusters

Optical absorption and light emission of oxygen incorporated small silicon (Si14H24) clusters as a function of oxygen content were theoretically simulated by using a self-consistent semiempirical molecular orbital method (MNDO-PM3). Two different models of oxygen incorporation were considered. Changes in the appropriate energies were traced when oxygen atoms were introduced either to the cluster surface (OH-group passivation) or inside the cluster. An increase of the number of oxygen atoms both at the surface and inside the cluster results in a decrease of the absorption energy with respect to the values typical for the cluster passivated only by hydrogen, while the emission energy appears to be influenced mainly by the incorporated oxygen content. There is a Stokes shift reaching the significant value of about 0.7 eV. It reduces with the increase of the oxygen content down to a value of 0.2 eV in the case of OH-group terminated clusters while it is almost constant for the oxygen incorporated ones.

Characteristics of potassium diffusion and adsorption on perfect and stepped GaAs(110) surfaces

The authors have used a self-consistent semi-empirical molecular orbital method to investigate whether the adsorption properties of K atoms and formation of the K adsorbate chains or clusters in the low-coverage regime can be influenced by the nature of the semiconductor surface: perfect or stepped. In the process, they are able to determine the microscopic structures of monatomic and diatomic K molecules on perfect and stepped GaAs(110) surfaces. The results for K adsorption on the perfect GaAs(110) surface are consistent with recent scanning tunnelling microscopy (STM) observations for Na on GaAs(110), with the stable site for K being the bridge site encompassing one Ga and two As surface atoms. The equilibrium geometry for diatomic K has the second K atom occupying the next-nearest-neighbour bridge site, strongly supporting the information of an open linear structure parallel to the surface atomic zigzag chains. The calculated K-K distance in this equilibrium configuration is 8.02 AA, similar to the Na-Na distance (8 AA) from the STM experiment. The results for the stepped GaAs(110) surface suggest that a step is unlikely to assist clustering of K atoms, but, the formation of the linear adsorbate chain appears rather to be influenced by the orientation of the steps. However, the K adsorbates are bound more strongly at the steps than at the bridge sites on the perfect surface.

Nonlocal-density-functional bond-energy calculations of cage-shaped carbon fullerenes: C32 and C60.

The bond energies of ${\mathrm{C}}_{32}$ and ${\mathrm{C}}_{60}$ fullerenes have been calculated by a self-consistent molecular-orbital method based on nonlocal-density-functional theory with the generalized gradient approximation (GGA). These results were compared with those obtained with use of the local-density approximation (LDA). The bond energies calculated with the GGA (${\mathrm{C}}_{60}$, 7.24 eV/atom; ${\mathrm{C}}_{32}$, 6.88 eV/atom) were about 1.3 eV/atom (15%) smaller than those calculated with the LDA, and the GGA result for ${\mathrm{C}}_{60}$ was found to be in good agreement with the evaluated value from the experimental formation energy. The differences in bond lengths, force constants, and orbital energies for the same molecular structure ---except for the core orbitals---between the LDA and GGA were small, compared with the difference in bond energies.

The migration of self-interstitials in germanium

Molecular clusters of varying sizes from 65 to 82 atoms were used in the self-consistent semi-empirical molecular orbital method to calculate the total energies for the different interstitial configurations at different charge states of Ge. Relaxations were made for each calculation so that the most stable configurations were obtained. We found that the possible diffusion path for the positively charged interstitial is THT with a barrier height of 2 eV. The preferred diffusion path for neutral and negatively charged states is XTX with barrier heights varying from 0.58 to 1.45 eV. The Bourgoin-Corbett mechanism is found to be possible for p-type Ge.

The periodic MINDO molecular orbital method as a surface analytical technique

In previous work we have shown that the periodic LUC-MINDO molecular orbital method with optimized parameters is able to yield a good description of the bulk electronic and elastic properties of the homopolar covalent solids, diamond and silicon. In this paper we consider the extension of this semi-empirical technique to the study of semiconductor surfaces. This surfacemodified, self-consistent molecular orbital method is shown to be a rapidly convergent, computationally viable surface analytical technique which is capable of treating thick slabs and far more complex systems than the corresponding first-principles techniques. When applied to the Si(100)-2 × 1 surface it is shown to correctly predict both the reconstruction (dimerization) of the surface, and the fact that the surface electronic structure is semiconducting. The paper concludes with a brief outline of some proposed applications for this promising technique.

Bipolaron Formation in B12 and (B11C)+ Icosahedra

ABSTRACTBoron carbides, B1-xCx with 0.085 ≤ × ≤ 0.200, generally contain both B12 and B11C icosahedra. However, the electronic transport with 0.1 ≤ × ≤ 0.2 is believed to occur by means of bipolaron hopping between only B11 C icosahedra [i]. We have calculated the changes in energy, atomic positlions and charge distribution when a pair of electrons is added to the isoelectronic icosahedral clusters B12 and (B11C)+. We simulate an icosahedron in a neutral lattice by bonding the icosahedral atoms to hydrogenic atoms which we constrain to be neutral. The computations are performed with a self-consistent molecular-orbital method, PRDDO.We find a total energy reduction of -3.7 eV for two electrons added to a B12 icosahedron. Of this, -2.7 eV arises from the electrons filling the icosahedron's bonding orbitals. The remaining -1.0 eV comes from the contraction of the icosahedron's radius by -0.09 Å. For two electrons added to a (B11C)+ icosahedron we find a total energy reduction of -18.2 eV. Of this, -16.5 eV arises from filling the icosahedron's bonding orbitals. The remainder arises frop a -0.09 Å contraction of the icosahedron's radius. Thus, we find (B11C) icosahedra to be strongly energetically favored over B12 icosahedra as bipolaron sites.The positive charge associated with a (B11C)+ icosahedron is distributed over the eleven boron atoms. Concomitantly, we find the added two electrons of the bipolaron to be distributed over all twelve sites of the B11C icosahedron. We find the energy difference between an electron pair added to B12 and (B11C)+ icosahedra to arise principally from the increased Coulomic attraction provided by the extra positive charge of the (B11C) icosahedron.

Modelling of metal clusters as fragments of crystalline solids

The structural and electronic properties of pure and hydrogenated Li metal have been calculated by modelling the crystalline solid in terms of small clusters of constituent atoms. Using the self-consistent molecular orbital method in the Hartree-Fock approximation, the authors have investigated the minimum number of atoms necessary to distinguish among various crystalline phases. They find that with as few as three atoms in the molecular cluster, the BCC phase can be shown to be the most stable structure. They have calculated the dependence of the optimised lattice parameter as a function of cluster size for both FCC and BCC phases of Li. While the calculated lattice constants converge to the bulk value with only about 20 atoms in the cluster, the binding energy per atom shows no sign of saturation. Thus how well the properties of molecular clusters represent bulk characteristics depends on the properties being investigated. This aspect is further illustrated by calculating the equilibrium site of hydrogen in Li. It is shown that for small clusters consisting of less than 20 atoms, the preferential site of hydrogen depends not only on the cluster size, but also on the way the cluster is constructed. The distortion of the nearest neighbour atoms around the hydrogen atom is studied by minimising the total energy with respect to the nearest-neighbour Li-hydrogen distance. Contrary to the conventional wisdom, they find that the metal atoms surrounding hydrogen are not always displaced outward. For example, the Li atoms around an octahedral hydrogen atom relax outward, while those around a tetrahedral hydrogen atom relax inward. In both cases, the equilibrium distance between hydrogen and nearest Li atom is 3.48 au. This is comparable with the corresponding distance of 3.6 au in stoichiometric lithium hydride. They have also calculated the charge transfer between Li and hydrogen atoms and the population of various orbital states for all the Li atoms. The results are used to analyse the screening of impurities in the metallic environment and to shed light on Mossbauer isomer shifts in metal-hydrogen systems.

Self-consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets

Standard sets of supplementary diffuse s and p functions, multiple polarization functions (double and triple sets of d functions), and higher angular momentum polarization functions (f functions) are defined for use with the 6-31G and 6-311G basis sets. Preliminary applications of the modified basis sets to the calculation of the bond energy and hydrogenation energy of N2 illustrate that these functions can be very important in the accurate computation of reaction energies.

Self-consistent molecular orbital methods. XXIII. A polarization-type basis set for second-row elements

The 6-31G* and 6-31G** basis sets previously introduced for first-row atoms have been extended through the second-row of the periodic table. Equilibrium geometries for one-heavy-atom hydrides calculated for the two-basis sets and using Hartree–Fock wave functions are in good agreement both with each other and with the experimental data. HF/6-31G* structures, obtained for two-heavy-atom hydrides and for a variety of hypervalent second-row molecules, are also in excellent accord with experimental equilibrium geometries. No large deviations between calculated and experimental single bond lengths have been noted, in contrast to previous work on analogous first-row compounds, where limiting Hartree–Fock distances were in error by up to a tenth of an angstrom. Equilibrium geometries calculated at the HF/6-31G level are consistently in better agreement with the experimental data than are those previously obtained using the simple split-valance 3-21G basis set for both normal- and hypervalent compounds. Normal-mode vibrational frequencies derived from 6-31G* level calculations are consistently larger than the corresponding experimental values, typically by 10%–15%; they are of much more uniform quality than those obtained from the 3-21G basis set. Hydrogenation energies calculated for normal- and hypervalent compounds are in moderate accord with experimental data, although in some instances large errors appear. Calculated energies relating to the stabilities of single and multiple bonds are in much better accord with the experimental energy differences.

Self-consistent molecular orbital methods. 24. Supplemented small split-valence basis sets for second-row elements

The recently introduced 3-21G split-valence basis sets for second-row elements have been supplemented with functionsof d-type symmetry. The resulting basis sets, termed 3-21G(*), are for use in conjuction with unsupplemented 3-21G representationsfor first-row elements. Equilibrium structures calculated by using 3-21G(*) are generally in good accord with available experimentaldata and are markedly improved over the corresponding 3-2 1 G level geometries, especially for hypervalent compounds andfor molecules incorporating bonds between two second-row elements. 3-21G(*) level normal-mode vibration frequencies,hydrogenation energies, and electric dipole moments are also generally but not always in better agreement with their respectiveexperimental quantities than are those obtained by using the unsupplemented 3-21G basis set. Overall, the 3-21G(*) basisset yields molecular properties that are uniformly close to those obtained with the much larger 6-31G* representation. The3-21G(*) basis set is still relatively compact and as such is generally applicable to molecules of moderate size.

ChemInform Abstract: SELF‐CONSISTENT MOLECULAR‐ORBITAL METHODS. 22. SMALL SPLIT‐VALENCE BASIS SETS S FOR SECOND‐ROW ELEMENTS

Chemischer InformationsdienstVolume 13, Issue 34 Physical Inorganic Chemistry ChemInform Abstract: SELF-CONSISTENT MOLECULAR-ORBITAL METHODS. 22. SMALL SPLIT-VALENCE BASIS SETS S FOR SECOND-ROW ELEMENTS M. S. GORDON, M. S. GORDONSearch for more papers by this authorJ. S. BINKLEY, J. S. BINKLEYSearch for more papers by this authorJ. A. POPLE, J. A. POPLESearch for more papers by this authorW. J. PIETRO, W. J. PIETROSearch for more papers by this authorW. J. HEHRE, W. J. HEHRESearch for more papers by this author M. S. GORDON, M. S. GORDONSearch for more papers by this authorJ. S. BINKLEY, J. S. BINKLEYSearch for more papers by this authorJ. A. POPLE, J. A. POPLESearch for more papers by this authorW. J. PIETRO, W. J. PIETROSearch for more papers by this authorW. J. HEHRE, W. J. HEHRESearch for more papers by this author First published: August 24, 1982 https://doi.org/10.1002/chin.198234002AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume13, Issue34August 24, 1982 RelatedInformation

Self-consistent molecular-orbital methods. 22. Small split-valence basis sets for second-row elements

Self-consistent molecular-orbital methods. 22. Small split-valence basis sets for second-row elements

Semiempirical studies of inner-core energy levels: IX. Esca shifts of silicon atoms in various chemical environments by the scc-mo method

The semiempirical self-consistent charge molecular orbital (SCC-MO) method has been applied to a number of representative molecules involving Si atoms in various chemical environments. The calculated point charges were correlated with Si(2 p) inner-core energy level shifts by using ground state potential, relaxation potential and transition potential models (GPM, RPM and TPM). The results are in good agreement with experimental data. Various contributions to the relaxation energy are briefly discussed.