A theory of molecules in molecules IV. Application to the Hydrogen Bonding Interaction in NH3 · H2O

The theory of molecules in molecules introduced in previous articles is applied to study the hydrogen bonding interaction between an ammonia molecule as proton acceptor and a water molecule as proton donor. The localized orbitals which are assumed to be least affected by the formation of the hydrogen bond are transferred unaltered from calculations on the fragments NH₃ and H₂O, the remaining orbitals are recalculated. A projection operator is used to obtain orthogonality to the transferred orbitals. Additional approximations have been introduced in order to be able to save computational time. These approximations can be justified and are seen to lead to binding energies and bond lengths which are in satisfactory agreement with the SCF values. The point charge approximation for the calculation of the interaction energy between the two sets of transferred localized orbitals is, however, not applicable in this case. An energy analysis of the effect of the hydrogen bond on the localized orbitals of the two fragments is given.     

A theory of molecules in molecules

SCF wave functions have been calculated using a minimal atomic basis set of Gaussian lobe functions for the para-, meta-, and ortho-forms of the molecules C₆H₄XY, where X, Y can be either of CN, OH, or F. It is found that in all cases the total energies increase in the sequence meta-, para-, ortho-compound. For the molecules containing the CN group the energy differences are extremely small (0.1–1 kcal/mole) for the other molecules they are one to two orders of magnitude larger. The reliability of these results is discussed. The theory of molecules in molecules is applied to these cases. The wave function of C₆H₄XY is constructed from the fragments C₆H₅X and HY by transferring some of the localized orbitals of the wave functions of the fragments and recalculating the orbitals in the region of interaction. For the molecules containing the CN group the energy differences are too small so that they are not correctly reproduced except by the most exact calculations, which involve no approximations other than the transfer of localized orbitals. For the other molecules satisfactory results are obtained.     

Valence-bond studies of AH2 molecules

Minimal Slater basis set calculations are reported for H₂S. The calculations used both natural and hybrid atomic orbitals. The calculations were performed at H-S-H bond angles of 90 °, 92.2 ° and 95 °. The results are compared with similar calculations on H₂O and with calculations using the molecular orbital approximation. The only definite trend found in going from H₂O to H₂S is that the importance of the SH⁺H^– structure decreases. Changes in the relative importance of covalent and ionic structures depend upon which measure of importance is used. Calculations using a set of orthogonal hybrid orbitals again find the hybrid orbitals exhibiting non-perfect following behaviour with the hybrids remaining at about the equilibrium bond angle. Localized molecular orbitals were found to move in the opposite direction to the change in the H-S-H bond angle.     

Natural spin orbital analysis of diatomic molecular wave functions in terms of generalized diatomic orbitals

Starting from the demi-H ₂ ⁺ -model for Rydberg states, ab initio calculations of the energy and the wave function for some excited states of H₂ have been carried out with the help of diatomic orbitals. The potential curves and wave functions for the following states: 2¹ _g< ^/+ , 3¹ _g< ^/+ , 1³ _g< ^/+ , 2³ _g< ^/+ , 1¹ _u< ^/+ , 2¹ _u< ^/+ , 1³ _u< ^/+ , 2³ _u< ^/+ , 3³ _u< ^/+ , 1¹ _g , 1³ _g , 1¹ _u , and 1³ _u , have been calculated by a complete CI (configuration interaction) calculation in the sense that all configurations of the state symmetry have been used which can be formed from a given basis set. From the wave functions thus obtained the natural spin orbitals are calculated subsequently to the variational calculations. The dependence of the occupation numbers of the natural spin orbitals on internuclear distance is interpreted according to the model and is used for the explanation of the special features like double minima and maxima which occur in the potential curves of H₂. For the curves of the occupation numbers a non-crossing rule in analogy to that for potential curves is valid. The potential curves for the states 1³ _g and 1³ _u have been improved by the use of linear combinations of diatomic orbitals with different nuclear charges, which allow a flexible transition to linear combinations of atomic orbitals.Dedicated to Professor Iwan N. Stranski on the occasion of his 80th birthday.     

Direct computation of second-order SCF properties of large molecules on workstation computers with an application to large carbon clusters

Summary The ab initio SCF computation of second-order properties of large molecules (with 50 atoms or more) on workstation computers is demonstrated for static dipole polarizabilities and nuclear magneting shieldings. The magnetic shieldings are calculated on the basis of gauge including atomic orbitals (GIAO). Algorithmic advances (semi-direct algorithms with efficient integral pre-screening, and use of a quadratically convergent functional for the polarizabilities) are presented together with an illustrative application to the fullerenes C₆₀ and C₇₀.     

Non-empirical LCAO-MO-SCF calculations of the electronic structure of SiF2

Non-empirical LCAO-MO-SCF calculations on SiF₂ using two Gaussian basis sets are reported. The larger basis set gives a calculated geometry in good agreement with experiment. The effect on the energy and population analysis of optimization of the Si 3d exponent was investigated. 3d orbitals are found to be much less important in the bonding than in the isoelectronic molecule SO₂.     

Application of the virial theorem to the study of molecular electronic wave functions

With aid of the virial theorem formulated for the energy differences of two electronic states some theorems on the wave functions of diatomic molecules have been proven. It is shown how proper Rydberg states can be distinguished from other electronic states with a diffuse outer orbital by virtue of the virial theorem and that a singlet-triplet pair of excited states cannot have the same equilibrium geometry and identical orbitals simultaneously. Furthermore if the two states have the same dissociation limit a theorem on the differences of the kinetic and the potential energy can be derived which allows an understanding of the shape of the electronic wave functions. As an application the wave functions and the ordering of the lowest states of H ₂ ⁺ and H₂ have been discussed.This work is part of the project Nr. SR 2.159.74 of the Schweizerischer Nationalfonds.     

Intensity distribution in the vibronic side bands of the Γ7(2 T 2g ) → Γ8(4 A 2g ) origin of ReX 6 2- doped K2PtCl6-type crystals

Intensities of vibronic transitions are calculated using an electronic vibrational coupling scheme of symmetrized and localized interactions. The model consists of an active central ion subject to a valence force field originating from nearest-neighbor displacements. The intensities of vibronic fundamentals are obtained from a generalized Lorentzian line shape function which is applied to the ₇(² T _2g ) ₈(⁴ A _2g ) transition of ReCl ₆ ^2- and ReBr ₆ ^2- in various cubic host crystals A₂MX₆ (A = Rb, Cs; M = Te, Sn, Pb; X = Cl, Br). Relative intensities of the odd vibronic side bands are calculated without knowing actual values for ligand field and spin-orbit coupling parameters, and considering only octahedral vibrational frequencies. The sidebands acquire intensity by a coupling which is cubic in the electron coordinates and linear in the nuclear normal coordinates. With some necessary approximations the present model is able to reproduce the experimental intensity distribution satisfactorily.Dedicated to Professor Dr. H. Hartmann on the occasion of his 65th birthday     

The electronic structure of molecules by a many-body approach

The vertical valence ionization potentials of cyclopropane, ethylene oxide and ethylene imine are calculated by a many-body Green's function method. For C₃H₆ the ordering of the ionization potentials is 2e(), 1e(), 2a₁(), 1a₂(), 1e(). The assignment of the 2a₁ and the 1a₂ ionization potentials which has been controversial is thus clarified. The ordering is in agreement with the result obtained via Koopmans' theorem. For ethylene oxide and ethylene imine Koopmans' theorem fails in predicting the correct order of ionic states. For C₂H₄O the ordering of the ionization potentials is 2b ₁(), 4a ₁, 1a ₂(), 2b ₂,3a ₁, 1b ₁(), 1b ₂, 2a ₁ and for C₂H₅N 6a, 5a, 3a, 2a, 4a, 3a, 1a, 2a. The agreement of the computed ionization potentials with the experimental values is very satisfactory.     

S 2p photoabsorption of the SF5CF3 molecule: Experiment,theory and comparison with SF6

The S 2p core excitation spectrum of the SF₅CF₃ molecule has been measured in the total ion yield mode. It resembles a lot the analogous spectrum of SF₆, also recorded in this study, displaying intense transitions to the empty molecular orbitals both below and above the S 2p ionization potential (IP) and weak transitions to the Rydberg orbitals. The S 2p photoabsorption spectra of SF₆ and SF₅CF₃ have been calculated using time-dependent density functional theory, whereby the spin–orbit coupling was included for the transitions below the S 2p IP. The agreement between experiment and theory is good for both molecules, which allows us to assign the main S 2p absorption features in SF₅CF₃.     

Ab-initio molecular dynamics simulation of monolayer C60 thin film on silicon (100) surface

Two dimensional band structure is calculated for a triangular lattice of C₆₀ molecules by using a mixed-basis approach in which wave functions are expanded with not only plane waves but also 1s and 2p atomic orbitals of carbon atoms. The present analysis modeling a charge transfer from Si dimers of the Si (100) surface suggests the existence of a small Fermi-surface. The resulting partial charge distribution is consistent with the recent STM observation of specific stripes, the direction of which is parallel to that of the topmost double bond of C₆₀, regardless of the intermolecular interaction. It is concluded that the orientation of C₆₀ on the Si surface is mainly determined by the direction of dimer arrays and not by the interaction between C₆₀ molecules.ACKNOWLEDGEMENT The authors are very grateful to the Institute for Supercomputing Research of RECRUIT Co. for the use of the NEC SX-2 supercomputer. Authors also thank IBM Japan and Japan IMSL Inc. for supporting them a good computer environment.     

Comparative theoretical study of the dissociation process of the isoelectronic molecules BH3CO,CH2CO,HNCO, CO2 and BH3N2, CH2N2, HN3, N2O

Anab initio study of the electronic structure of several 22-electrons molecules is presented. The equilibrium geometries of their ground state are calculated at the SCF level using the 6–31G basis set and are found to be in good agreement with the experimental geometries. The dissociation process of these molecules leading to the isoelectronic products CO or N₂ on the one hand and BH₃, CH₂, NH and O on the other hand is studied. The least-energy dissociation paths of the ground states determined at the SCF level are compared on the basis of electron density interactions. The dissociation energies corresponding to the two lowest dissociation channels are calculated. In these calculations, the correlation energy is taken into account using a non-variational method developed previously. The calculated values of dissociation energies are in good agreement with the existing experimental values. The results permit to predict values for HNCO, BH₃CO and CH₂N₂ and to confirm the instability of BH₃N₂.Aspirant du Fonds National Belge de la Recherche Scientifique.     

Theoretical studies of atmospheric molecules: SCF and correlated energy levels for the NO2, NO 2 + and NO 2 − systems

SCF and MC-SCF/CI calculations were carried out on the low-lying electronic states of NO₂, NO ₂ ⁺ and NO ₂ ^– , using a double-zeta quality basis set of contracted Gaussian functions. The calculations were performed primarily at the equilibrium geometry (R _NO = 2.25 a_o, _ONO=134 °) of theX ² A ₁ state of NO₂. SCF calculations on NO ₂ ⁺ in a linear conformation were also performed. Results are presented and compared with experiment and other calculations.Research supported in part by Air Force Delivery Orders F33615-72-M-5015 and MIPR889474-00117 and Air Force Office of Scientific Research and in part by the United States Energy Research and Development Administration.     

The physical nature of the lone pair

Despite the large number of experimental and theoretical studies on the size, shape, and orientation of lone pairs and their resulting stereochemical character, lone pairs still remain poorly defined in terms of quantitative observable properties of a molecule. Using the conformation of saturated molecules and barriers to internal rotation, experimental chemists have arrived at conflicting sizes and orientations for lone pairs. Most theoretical attempts to define lone pair properties have centered on such non-observables as localized molecular orbitals or have been based on studies on isolated molecules.The use of observable properties to construct a consistent set of physical models to analyze the physical nature of lone pairs is discussed. Much as one probes an electric field with a test charge, probes such as H⁺, H^–, He and H could be used to probe regions of molecules such as NH₃ and H₂O where lone pairs are often postulated to exist.Ab initio quantum mechanical studies can be analyzed using electron density (and resulting changes during interaction), total pair density of electrons, the electrostatic potential about the molecule and bond energy analysis to study lone pair properties. A simple study of NH₃ using an H⁺ probe is presented to clarify the approach.     

Bonding criteria for diatomic molecular orbitals and inter-relations among them

Bonding criteria for molecular orbitals in diatomic molecules are discussed. An orbital force criterion is shown to have several conceptual and practical advantages, providing a basis for the investigation of inter-relations among many of the commonly employed criteria.It is found that interconsistency among those criteria is guaranteed, within the framework of Koopmans' Theorem, if the orbital energies are monotonic in the range (R _e, ).The application of the orbital force criterion to the second row homonuclear diatomics exhibits reasonable chemical trends concerning the valence-shell orbitals, as well as indications of a slightly antibonding nature of the inner orbitals.Based on a section of a thesis to be submitted by Y.T. to the Senate of the Technion-Israel Institute of Technology, in partial fulfilment of the requirements for the D.Sc. degree     

Calculation of harmonic force constants,vibrational frequencies and integrated intensities of some organic molecules using the MINDO—Forces method

The harmonic force constants, vibrational frequencies and integrated intensity ratios of CH₂, H₂O, CH₂O, C₂H₂, CO₂, HCN, CH₃, CH₄, and C₂H₄ have been calculated using the MINDO—FORCES program and the Pulay method for the calculation of the molecular force constants. The results obtained are in general quite satisfactory when compared with available literature values. The results are, however, not as satisfactory in case of molecules containing heteroatoms, due to the neglect of some dipolar repulsion integrals for the heteroatoms by the MINDO/3 method. Calculated integrated intensities for CH₃ and C₂H₄ agree well with experimental results. The calculated integrated intensities for other molecules are obtained for the first time and no comparison with published data is therefore possible.Part of the M.Sc. Thesis of K. H. A. 1978.     

Electronic structure and one-electron properties of the MoO2Cl2 molecule. Electronic spectra of the MoO2Cl2, MoO2Br2 and WO2Br2 molecules

The SCF-X -SW method in an overlapping atomic spheres approximation has been used to calculate the electronic structure, ionization potentials, energies and oscillator strengths of the allowed optical transitions and also some of the one-electron properties of the MoO₂Cl₂ molecule. The electronic absorption spectra of vapours over molybdenum and tungsten dioxodibromides have been measured. Interpretation of the experimental electronic absorption spectra of the MoO₂Cl₂, MoO₂Br₂ and WO₂Br₂ molecules is discussed.     

Structure and electronic structure of [(CF3)2PN]2NVCl2, a molecule involving a planar six-membered ring (N3P2V)

Summary The SCF method is applied to determine the (gas phase) structure of [(CF₃)₂PN]₂NVCl₂, which agrees with the solid-state X-ray structure within typical errors of 2 pm and 2° in bond distances and angles. The electronic structure of atoms forming the ring is best described in terms of divalent N^– and tetravlent P⁺ with appreciable declocalization of nitrogen lone pairs into low-lying empty orbitals of neighbouring atoms P and V. No evidence for aromaticity of the ring system is found.     

Die Berechnung von Einelektronen-Integralen in der SCF-Xα-SW-Methode: I. Die Normierung

A normalization of the wave functions by means of the theoretical exact Multiple-Scattering-(MS)-formalism is discussed within the framework of the SCF-X-SW-method. For the atomic and extramolecular regions the integrals of normalization can be easily determined and the results can be described by the corresponding electronic charges. The calculation of the integral of the interatomic region is problematic. The needful volume integration is only necessary to theGreen's functions of the wave functions and can be solved by means of the residual theory. The further analytical calculation of the surface integrals leads to a complicated formalism which can be numerically evaluated.