Conformational analysis of dimethylphosphate with quantum-mechanical and classical methods

In order to shed light on the conformational behavior of polynucleotide chains, and in particular to clarify the origins of the barriers to internal rotation in the phosphodiester linkage, we computed, with a quantum-mechanical ab initio procedure, the energies associated to 86 combinations of the two torsion angles in the dimethylphosphate anion (CH₃O)₂PO₂ ^–, and then we sought for an analytical expression apt to reproduce these energies with the highest possible accuracy. An excellent agreement (standard deviation of the fitted energies from the ab initio energies 0.28 kcal/mole) with the quantum-mechanical calculations was reached with a potential consisting of four terms: 1) a 6–12 Lennard-Jones contribution, in which different parameters are used to describe the interactions of methyls with the ester oxygens and with the anionic oxygens; 2) a contribution with twofold periodicity, accounting for the anomeric effects connected to the interactions between the lone pair electrons and the polar bonds of phosphorus with the anionic oxygens; 3) a contribution with threefold periodicity, representing the usual bond-staggering term; and 4) a Coulombic contribution, arising from electrostatic interactions between partially charged atoms.     

Charging effects in a CdSe nanotetrapod

The charging effects in a CdSe nanotetrapod have been theoretically investigated by using an atomistic pseudopotential method. We showed that the simple quasiparticle equation based on classical electrostatic consideration can be derived from the many-body GW equation under proper approximations. We found that the surface polarization potential can significantly change the electron wave functions, and there is an incomplete cancellation for this potential between the single particle energies and the electron-hole Coulomb interaction. Thus, it is necessary to include this potential in the calculation for complex unconvex systems. We also calculated the electron addition energies for a tetrapod. Unlike a simple spherical quantum dot, in which the addition energies are almost a constant, there is a large variation in the calculated addition energies for different numbers of electrons in a tetrapod.     

Elastic scattering of low and intermediate-energy electrons by Kr and Xe atoms

The many-body correlation forces, which act between the impinging electron and the bound electrons of the two heaviest rare gas atoms, are treated here using a newly developed correlation-polarisation potential that originates from the calculation of correlation energies in electronic bound-states of atoms and molecules. The new formulation of such forces, already tested by us for the lighter atomic targets, is particularly effective for the present systems and can be implemented very easily even for heavy atomic targets. The calculations reported in this paper show clearly that very good accord is obtained with more sophisticated theoretical treatments and with several experimental data on integral cross sections, momentum transfer cross sections and angular distributions.Von Humboldt — Prize Awardee 1992     

Solvatons. II. Aqueous dissociation of hydrides in the MINDOS approximation

A simple electrostatic model of solvation is presented which allows the interaction with solvent to be included systematically within semiempirical SCF calculations. Solvent effects are incorporated into the Hamiltonian for a solute molecule through a series of imaginary particles, solvatons, which represent the oriented solvent distribution around the solute.The proposed model is based on an algorithm for approximating the enthalpy of solvation of each atomic center from its charge in the molecular system and the experimental hydration enthalpies of its various ions. The calculated atomic solvation energy of one center is then modified to include the interaction with other charged atomic centers in the molecule. The method, developed here for the MINDO/3 approximation, has been applied to the calculation of the aqueous dissociation of a series of hydrides. In general, it leads to fairly accurate solvation enthalpies andpK _a values when applied to systems with fixed molecular geometries. A general discussion of the problems associated with the development of a solvation model within a semiempirical framework is also presented.     

Application of potential constants: Charge transfer and electric dipole moment change in the formation of heteronuclear diatomic molecules—IV

The harmonic and anharmonic potential (force) constants of heteronuclear diatomic molecules, which are usually available from normal coordinate analyses, are applied to problems of determining the number of electrons transferred (charge transfer) and electric dipole moment functions of such molecules. The approach developed here is mainly based on Slater's orbital expansion method, that is, in a non-spin-polarized calculation atomic energies in a molecule are expanded with respect to the occupation number of electrons of atomic orbitals. To confirm the accuracy and the reliability of the approach, we have calculated the number of electrons transferred and electric dipole moments for alkali halides and other heteronuclear diatomic molecules. Specially, detailed analyses of electric dipole moment functions have been carried out on hydrogen fluoride (HF) and hydrogen oxide (OH) for which reliable experimental dipole moment functions are presently known over a wide range of internuclear distances. It is concluded from these analyses that the present approach is simple and useful in evaluating the charge transfer and the dipole moment change in the formation of heteronuclear diatomic molecules.     

Theoretical study of the potential energy curves of the series of diatomic radicals MeIIX. I. Method and its application to BeF radical

A method for calculating potential energy curves of some low lying states of the diatomic radicals Me_IIX (Me_II = second group metal, X = halogen) is outlined. Because of the electronic structure of these compounds, applications to electronic transition lasers can be made. The first calculation regards the most simple example of this series, i.e. the BeF radical. The division of the procedure into separated steps allows a sure control of the quality of the results.     

Ab initio crystal orbital studies on linear chains of H atoms

Anab initio crystal orbital method is used to calculate the energies of an infinite chain of H atoms and of linear arrangements of H₂ molecules with different interatomic distances. The H₂ arrangements are not stable in respect to isolated molecules. The cohesive energy of an optimized arrangement of H atoms chain is 0.0354 a.u.     

Quantum calculation of the intrinsic torsional barrier of C-C and C-O bonds

PCILO and ab initio calculations have been performed to investigate the energies associated to rotation about the central bond in n-butane and methyl ethyl ether. Quantum mechanical energies have been fit to a classical intramolecular force field, containing torsional and nonbonded (Lennard-Jones 6–12 plus Coulomb) contributions, with a standard deviation comprised between 0.03 and 0.09 kcal mol^–1. Two conditions have proved indispensable to reach such level of accuracy: (a) the use of a torsional potential with threefold periodicity, which corrects for the part of the rotation barrier not covered by van der Waals repulsions and may be interpreted as bond-bond repulsion; (b) the introduction in the force field for ethers of terms accounting for orbital interaction effects of different nature than the normal molecular mechanics nonbonded interactions; these terms are represented either by low order rotational potential functions or preferably by interactions of atoms simulating lone-pair orbitals and bonded to oxygen in such a way as to render it sp ³-hybridized. According to ab initio, the height of the threefold torsional potential about C-C and C-O bonds is comparable and is of the order of 3 kcal mol^–1. According to PCILO, it is larger for C-C (ca. 1.5 kcal mol^–1) than for C-O (ca. 0.5 kcal mol^–1).     

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.     

Localized impurity states in the Hartree-Fock,LCAO approximation. I.

One-electron energies and wave functions for deep trap impurity electrons in a crystal are calculated by the Hartree-Fock, single determinant method. The interactions arising from a many-electron single determinant crystal wave function, with automatic inclusion of exchange effects, are those which determine the one-electron functions and energies. The crystal plus impurity system has no translational symmetry and hence the Bloch theorem is not applicable for the solution of the essentially infinite Hartree-Fock eigenvalue matrix. Thus we develop a technique in which the Hamiltonian and overlap matrices are written in terms of bordered matrices, with the interaction of the impurity functions with the rest of the crystal environment contained in the bordering rows and columns. The resulting secular equation explicitly includes the effects of orthogonalization of the entire basis set, including the impurity functions. This technique could be used in an iterative calculation of the electronic structure of a small number of electrons, assuming that the rest of the electrons in the environment are fixed according to an initial estimate.     

Correlation energies in the spin-density functional formalism

It has been shown recently that dynamical correlation effects can be adequately described by using an electron-gas expression for correlation between electrons of different spins. In this paper the method is applied to the calculation of excitation energies for the first- and second-row atoms and to the determination of ground-state properties for small polyatomic molecules, such as CH₂, CH₄, CH ₄ ⁺ , CH ₅ ⁺ . Additionally, deficiencies of the method for cases with few electrons and strongly varying electron density are investigated and an empirical correction to the electron-gas approximation is proposed. This correction is based on atomic data and gives an overall improvement for test molecules with two to four electrons.     

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.     

Theoretical studies on the imine germylenoid HNGeNaF and its insertion reaction with R-H (R = F, OH, NH2, CH3)

The geometries and isomerization of the imine germylenoid HNGeNaF as well as its insertion reactions with R-H (R = F, OH, NH₂, CH₃) have been systematically investigated at the B3LYP/6-311+G^∗ level of theory. The potential barriers of the four insertion reactions are 117.2, 172.6, 219.7, and 322.3 kJ/mol, respectively. Here, all the mechanisms of the four reactions are identical to each other, i.e., an intermediate has been formed first during the insertion reaction. Then, the intermediate could dissociate into the substituted germylene (HNGeHR) and NaF with a barrier corresponding to their respective dissociation energies. Correspondingly, the reaction energies for the four reactions are 185.0, 208.1, 224.4, and 266.9 kJ/mol, respectively, which are linearly correlated with the calculated barrier heights. Compared with the insertion reaction of HNGe: and R-H, the introduction of NaF makes the insertion reaction occur easily though it is more difficult to proceed than that of insertion reaction between H₂GeNaF and R-H. Furthermore, the effects of halogen (F, Cl, Br) substitution and inorganic salts employed on the reaction activity have also been discussed. As a result, the relative reactivity among the four insertion reactions should be as follows: H-F > H-OH > H-NH₂ > H-CH₃.     

Real space Hartree-Fock configuration interaction method for complex lateral quantum dot molecules

We present unrestricted Hartree-Fock method coupled with configuration interaction (CI) method (URHF-CI) suitable for the calculation of ground and excited states of large number of electrons localized by complex gate potentials in quasi-two-dimensional quantum dot molecules. The method employs real space finite difference method, incorporating strong magnetic field, for calculating single particle states. The Hartree-Fock method is employed for the calculation of direct and exchange interaction contributions to the ground state energy. The effects of correlations are included in energies and directly in the many-particle wave functions via CI method using a limited set of excitations above the Fermi level. The URHF-CI method and its performance are illustrated on the example of ten electrons confined in a two-dimensional quantum dot molecule.     

A theoretical investigation of electronic reorganizations accompanying core and valence ionization in simple hydrogen bonded systems

Non-empirical LCAO MO SCF calculations have been carried out on the ground state and core ionized states of some hydrogen bonded dimers, and in the particular case of H₂O the trimer has also been investigated. Comparison of absolute and relative binding energies and relaxation energies with respect to the corresponding monomers reveals that substantial changes occur in going to the associated species. The relaxation energies for a given core hole are shown to increase on going from monomer to dimer indicating that intermolecular contributions to relaxation energies are of the same sign irrespective of the sign for the shift in core binding energy. Creation of a core hole in the dimer species is shown to give rise to substantial changes in hydrogen bond energies compared with the neutral species. In the particular case of valence holes dominantly of 2s and 2p character it is shown that trends in shifts and relaxation energies parallel those for the core hole states.     

Bond functions,covalent potential curves,and the basis set superposition error

In the current practice of quantum chemistry, it is not clear whether corrections for basis set superposition errors should be applied to the calculation of potential energy curves, in order to improve agreement with experimental data. To examine this question, spectroscopic parameters derived from theoretical potential curves are reported for the homonuclear diatomics C₂, N₂, O₂, and F₂, using a configuration interaction method. Three different basis sets were used, including double zeta plus polarization, triple zeta plus double polarization, and double zeta polarization augmented by bond functions. The bond function basis sets, which were optimized in the preceding paper to obtain accurate dissociation energies, also gave the most accurate parameters. The potential curves were then corrected for basis set superposition error using the counterpoise correction, and the spectroscopic parameters were computed again. The BSSE-corrected curves showed worse agreement with experiment for all properties than the original (uncorrected) curves. The reasons for this finding are discussed. In addition to the numerical results, some problems in the application of the BSSE correction to basis sets containing bond functions are shown. In particular, there is an overcounting of the lowering due to the bond functions, regardless of which type of correction is applied. Also, genuine BSSE affects cannot be separated from energy-lowering effects due to basis set incompleteness, and we postulate that it is the latter which is strongly dominant in the calculation of covalent potential curves. Based on these arguments, two conclusions follow: (1) application of BSSE corrections to potential curves should not be routinely applied in situations where the bonding is strong, and (2) appropriate use of bond functions can lead to systematic improvement in the quality of potential curves.     

Application of intermolecular SCF-perturbation theory to the regioselectivity in the Diels-Alder reaction

Intermolecular perturbation theory in the density matrix formalism is applied to investigate the directional behaviour of an electron-donating (-CH₃) or an electron-accepting (-CN) group in 1- or 2-substituted butadienes in the Diels-Alder reaction with acrylonitrile. The calculated CNDO/2 perturbation energies are analysed in three different ways by considering: a) the different perturbation energies, b) the diatomic parts of the interaction energy and c) the HOMO-LUMO contribution to the second-order energy. The regioselectivity is due to a subtle balance of charge-transfer interactions and steric effects of the substituents on the diene and the dienophile. The changes of intra- and intermolecular diatomic energy contributions are correlated with the process of bond formation and bond weakening. The intermolecular perturbation energies are dominated by pairwise interactions between the terminal C-atoms and by the secondary Woodward-Hoffmann interaction. These three localized interactions determine the endo addition and reflect the orienting power of the substituents.     

Ionization potential of clusters in liquids

Time-resolved observations of the fast electron transfer from an electron donor to metal ions adsorbed on metal clusters in solution have shown that a critical size of the cluster is required to make it capable of accepting electrons. The threshold is attributed to a size dependent redox potential of the cluster, increasing with the nuclearity (in contrast with the ionization potential in the gas phase which decreases when n increases): it corresponds to the nuclearity for which the cluster redox potential becomes more positive than the potential of the electron donor acting as a monitor.New data of redox potentials (or IP) of Ag_n clusters (hydroquinone as monitor) and Cu_n cluster (sulfonatopropylviologen anion as monitor) are derived. The influence of n and of the solvation or the ligand is discussed.