Showing papers in "Theoretical Chemistry Accounts in 1990"

Energy-adjustedab initio pseudopotentials for the second and third row transition elements

Abstract: Nonrelativistic and quasirelativisticab initio pseudopotentials substituting the M(Z−28)+-core orbitals of the second row transition elements and the M(Z−60)+-core orbitals of the third row transition elements, respectively, and optimized (8s7p6d)/[6s5p3d]-GTO valence basis sets for use in molecular calculations have been generated. Additionally, corresponding spin-orbit operators have also been derived. Atomic excitation and ionization energies from numerical HF as well as from SCF pseudopotential calculations using the derived basis sets differ in most cases by less than 0.1 eV from corresponding numerical all-electron results. Spin-orbit splittings for lowlying states are in reasonable agreement with corresponding all-electron Dirac-Fock (DF) results.

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

Abstract: Generally contracted basis sets for second row atoms have been constructed using the Atomic Natural Orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over several atomic states, positive and negative ions, and atoms in an external electric field. The contracted basis sets give virtually identical results as the corresponding uncontracted sets for the atomic properties, which they have been designed to reproduce. The design objective has been to describe the ionization potential, the electron affinity, and the polarizability as accurately as possible. The result is a set of well balanced basis sets for molecular calculations. The starting primitive sets are 17s12p5d4f for the second row atoms Na-Ar. Corresponding ANO basis sets for first row atoms have recently been published.

Coupled cluster approaches with an approximate account of triexcitations and the optimized inner projection technique. I: General orthogonally spin-adapted formalism

Abstract: A general orthogonally spin-adapted formalism for coupled cluster (CC) approaches, with an approximate account of triexcited configurations, and for optimized inner projection (OIP) technique is described. Modifying the linear part of the CC equations for pair clusters (CCD) we obtain the orthogonally spin-adapted, non-iterative version of the CCDT-1 method of Bartlett et al. [J. Chem. Phys. 80, 4371 (1984), 81, 5906 (1984), 82, 5761 (1985)]. Similar modification of an approximate coupled pair theory corrected for connected quadruply excited clusters (ACPQ) yields a new approach called ACPTQ. Both the CCDT-1 and ACPTQ methods can be formulated in terms of effective interaction matrix elements between the orthogonally spin-adapted biexcited singlet configurations. The same matrix elements also appear in the orthogonally spin-adapted form of the CCD + T(CCD) perturbative estimate of triply excited contributions due to Raghavachari [J. Chem. Phys. 82, 4607 (1985)] and Urban et al. [J. Chem. Phys. 83, 4041 (1985)], and in the OIP method when applied to the Pariser-Parr-Pople (PPP) model Hamiltonians. We use the diagrammatic approach based on the graphical methods of spin algebras to derive the explicit form of these interaction matrix elements. Finally, the relationship between different diagrammatic spin-adaptation procedures and their relative advantages are discussed in detail.

The calculation of the dipole moments of NiH, TiO, and FeO

Abstract: We explore several computational strategies for computing the dipole moment of theX2Δ state of NiH, theX3Δ state of TiO, and theX5Δ state of FeO. The averaged coupled-pair functional (ACPF) method gives consistently the best agreement with experiment, but can become intractable, as rather large zeroth-order reference spaces can be required. At the ACPF level, unlike the multireference configuration-interaction (MRCI) level, the dipole moments determined as an expectation value and by finite-field methods are similar, and are insensitive to natural orbital iteration. Our best theoretical results for NiH are in excellent agreement with experiment, whereas our best dipole moments for TiO and FeO are both about 10%–15% larger than the recently measured values.

Constant-isomer benzenoid series and their topological characteristics

Abstract: New constant-isomer series are presented. Two classes of constant-isomer series based on the topological correspondence of their member benzenoids are identified. The isomer numbers for the constant-isomer series alternate between singlet and doublet occurrence. Constant-isomer series with the same isomer number possess a pairwise one-to-one topological correspondence between their benzenoid membership. A correspondence also exists between threefold monoradical and diradical benzenoids belonging to these constant-isomer series. These topological relationships represent a new paradigm that we ascribe as an edge effect of our periodic table for benzenoids.

Generators of the character tables of generalized wreath product groups

Abstract: A method based on the cycle-type matrix algebra is devised to generate the character tables of generalized wreath products which are useful in describing the symmetry groups of non-rigid molecules, NMR groups, groups of non-rigid van der Waals complexes, the groups of space types in configuration interaction calculations, etc. This newly developed method is illustrated with examples.

Enhanced Li+ binding energies of some azines: a molecular orbital study

Abstract: Hartree-Fock calculations with the 6–31G* basis have been performed to investigate the structure and Li+ binding energies of the complexes between Li+ and pyridine, diazines, triazines and tetrazines. Structures have been fully optimized at the 3–21G level. As for azole-Li+ and methyldiazole-Li+ complexes, a topological analysis of the Laplacian of the electronic charge density reveals that the azine-Li+ is a typical closed-shell interaction and that the stabilization of the complex is mainly electrostatic. BSSE is quite significant, specially for Li+-bridging complexes. The correlation between calculated Li+ binding energies and proton affinities follows two different linear relationships, one for those cases where Li+ is singly coordinated and a different one for those cases in which an additional three-membered ring is formed. The enhanced stability of these particular conformations explains why while polyazines are less basic than pyridine when the reference acid is a proton; pyridazine and 1,2,4 triazine are more basic than pyridine when the reference acid is Li+. The effect on Li+ binding energies of systematic nitrogen substitution roughly follows an additive model.

Theoretical thermochemistry of some LiXH/sub n/ and BeXH/sub n / compounds

Abstract: In this theoretical work, we consider the geometrical, electronic and energetic properties of some lithium and beryllium derivatives. The standard heats of formation of these compounds have been calculated at the MP4=SDTQ/6-31+G(2df, p)//MP2=FULL/6-31G(d, p) level. The values obtained at this level of the theory are also compared with the heats of formation deduced from a composite procedure in which it is assumed that some corrections can be treated separately and combined in an additive manner. We find that the values determined with the complete 6-31+G(2df, p) basis set are the more accurate.

Direct evaluation of one-electron properties in coupled cluster methods

Abstract: An analysis of a method for approximate calculations of expectation values for one-electron operators from available coupled cluster amplitudes is presented and illustrated numerically for the polarizability of the Be atom. The one-particle density matrix resulting from the present approach is accurate through the fourth order in the electron correlation perturbation. It has been found that, in order to obtain quantitative agreement between the energy derivative results and the approximate expectation value formalism, the third orderT 1 T 2∣Ф(0)〉 wave function term must be included into the calculation of the one-particle density matrix. The present method is also considered as a promising tool for calculations of higher-order atomic and molecular properties from high level correlated wave functions.

Relativistic perturbation theory of chemical properties

Abstract: Double perturbation theory is developed for the case where relativity is one perturbation and the other perturbation describes a chemically interesting observable such as molecular structure, force constant or polarizability. Relativity is treated according to Rutkowski's nonsingular perturbation approach. Expressions for four-component and two-component wave-functions and for the Hartree-Fock approximation are given. The method is applied analytically to the relativistic corrections of the electric polarizability of the H atom, and algebraically to the potential curve of the H 2 + molecule. Second and third order double perturbation interchange relations are numerically verified. In the present formalism, terms up to third order are needed to qualitatively understand the relativistic corrections of chemical observables.

Gradient optimization of polarization exponents in ab initio MO calculations on H2SO→HSOH and CH3SH→CH2SH2

Abstract: Analytical gradients were used to optimize the polarization function exponents in the 6-31G(d) and 6-31G(d, p) basis sets for the reactants, transition structures and products in the reactions H2SO → HSOH and CH3SH → CH2SH2. The optimizedd exponents on the heavy atoms change by ±10% in the course of the reactions and depend on the bonding of the heavy atoms. Thep exponents on the hydrogens change by as much as a factor of 5 and depend on the element to which the hydrogen is bonded and its valency. The effect of exponent optimization on the relative energies is small (±3 kcal/mol). With the 6-31G(d, p) basis set, optimization of the polarization exponents can make some of the bonds significantly more polar, as judged by the Mulliken charges.

Configuration interaction calculations on the propane radical cation, C3H8+

Abstract: Proton isotropic hyperfine coupling constants have been calculated for three low-energy nuclear conformations on the ground state potential surface of the propane cation, using a multireference singles and doubles configuration interaction (MR-SDCI) wave function. The lowest point found on the potential surface hadC 2v symmetry and the electronic wave function at this point had2B2 symmetry. At this point, the largest isotropic coupling constant is calculated to be 88.6 G, which is in fair agreement with the experimental value of 98 G obtained in an SF6 matrix at 4 K. No support is found for a “long-bond” ground state of lower symmetry thanC 2v . AnotherC 2v minimum on the ground state potential energy surface was found at which the wave function had2 B 1 symmetry. At this point, two large coupling constants of 198 G and 35 G were calculated. AC 2v stationary point was also found on the ground state potential surface at which the wave function had2 A 1 symmetry. At this point, couplings of 86 G and 25 G were obtained. None of these agree closely with the other experimental result of couplings at both 100–110 G and 50–52.5 G which was obtained in freon matrices. It is suggested that the latter spectra might correspond to a dynamical average of two distorted2 A' states inC s symmetry.

Electron energy level crossings in the time-dependent Born-Oppenheimer approximation

Abstract: We summarize the results of a mathematical study of the time-dependent Born-Oppenheimer approximation near crossings of two non-degenerate electron energy surfaces. We illustrate our techniques by relatively simple examples that contain the essential ingredients of the general cases. We discuss all generic types of crossings of two non-degenerate electron energy surfaces.

Enumeration of non-rigid molecules by means of unit subduced cycle indices

Abstract: Unit subduced cycle indices (USCIs) are applied to the enumeration of isomers derived from a non-rigid parent molecule, the non-rigidity of which stems from bond-rotations. The parent is divided into a rigid skeleton ofG-symmetry and mobile moieties ofH-symmetries, where each mobile moiety is linked to a root that is a terminal vertex of the skeleton. In the first step, isomeric mobile moieties are enumerated with respect to theH-symmetry in terms of USCIs forH. Second, the mobile moieties counted are regarded as substituents on the vertices of the rigid skeleton. This formulation allows us to enumerate mobile isomers by means of USCIs for theG-symmetry.

Calculation of the maximum bond order

Abstract: Based on the maximum overlap method, an alternative scheme for the calculation of the maximum bond order defined by Jug is introduced to simplify the calculation procedure.

Application of coset representations to the construction of symmetry adapted functions

Abstract: A coset representation (G(/Gi)), which is defined algebraically by a coset decomposition of a finite groupG by its subgroupGi, is shown to be a method for the decomposition of a regular body into its point group orbits. This proof also shows that each member of theG(/Gi) orbit belongs to theGi site-symmetry. In addition, a general equation concerning the multiplicities of such coset representations is derived and shown to involve Brester's equations and thek-value equations of framework groups as special cases. The relationship of the coset representation and the site-symmetry affords a general procedure for obtaining symmetry adapted functions.

Comparison of potential energy maps and molecular shape invariance maps for two-dimensional conformational problems

Abstract: It is well known that many molecular properties are strongly dependent on internal nuclear arrangements. Two possible, independent approaches can be followed while studying changes in molecular characteristics as functions of the nuclear geometry. These are the analysis of potential energy surfaces and the analysis of molecular shape. In this work, we seek to establish relationships between potential energy maps and shape invariance region maps, where each point of these maps represents a nuclear configuration. The study is performed by analyzing the occurrence and lack of certain symmetries in both types of maps. As illustrative examples, we consider the three structural isomers of the dihydroxybenzene molecule. Potential energy is computed at the STO-3G ab initio level, while the shape is described by the shape group method as applied to fused-sphere van der Waals surfaces. It is shown that the symmetry of the shape invariance maps follows closely, but not exactly, the symmetry of potential energy surfaces. The molecular surface is thus “blind” to some small changes of the potential (a feature to be expected to hold also for molecular surfaces defined in terms of electronic charge density). Our findings suggest that a crude fused-sphere model may suffice to describe some of the structural changes in molecular surfaces, as well as their relationships to the electronic energy.

Computational analysis of some possible initial steps in the unimolecular thermal decompositions of 1,3-diazacyclobutane and its 1,3-dinitramine derivative

Abstract: We have investigated some possible initial steps in the unimolecular thermal decompositions of 1,3-diazacyclobutane and its 1,3-dinitramine derivative, the latter being selected as the simplest example of a symmetric cyclic nitramine. Vibrational analyses were used to identify normal modes that, in the extreme limits, would correspond to bond rupture and molecular decomposition. The energy requirements for ring fragmentation and N-N bond-breaking were computed at the MP4/6-31G level, using SCF 3-21G optimized structures. It was concluded that ring-fragmentation is a probable initiating step in the decomposition of the unsubstituted molecule, and that it is roughly competitive with N-N bond scission for the dinitramine. The nitronitrite rearrangement is predicted, on the basis of SCF calculations, to be less likely than either of the other two processes. It is proposed that N-N bond-breaking may be of primary importance for nitramine stability, but that energetic performance may be determined more by decomposition pathways having energy barriers.

Theoretical analysis of the internal rotation and determination of molecular structures of HSSH, HSSF and FSSF

Abstract: A detailed investigation of the internal rotation of hydrogen persulfide and fluoro-derivatives is presented. High quality potential functions containing only three and four parameters were determined through a very simple interpolation method. Reduced torsional potentials are defined and used to assess the quality of the interpolated functions. Equilibrium structures and barriers to internal rotation reported here are in close agreement with the available experimental data. High barrier heights and the comparative analysis of structural parameters of all three molecules indicate significant π bonding through the mechanism of hyperconjugation.

Bulk properties from finite-cluster calculations

Abstract: Geometries of linear hydrogen fluoride clusters with 1–10 unit cells are optimized at the HF/6-31G** level. MP2/6-31G** energies at the HF/6-31G** optimized geometries are calculated for clusters with 1–6 unit cells. Application of Pade approximants to the electronic properties of finite clusters results in the following estimated bulk properties: dipole moment per unit cell: 2.66±0.01 [D], bond lengths: 0.913±0.001/1.686±0.001 [A], stabilization energy per unit cell relative to the HF molecule: −7.44±0.01 [kcal/mol] (HF), −8.66±0.02 [kcal/mol] (MP2). The extrapolated atomic charges based on the generalized atomic polar tensors (GAPT) are 0.61±0.01 as compared to the value of 0.42 for the monomer.

On subspectral problem—benzenoid hydrocarbons with common eigenvalues ±1

Abstract: The method for the contraction and expansion of graphs is used to treat the subspectrality of benzenoid hydrocarbons in relation to eigenvalues ±1. Counts of benzenoid hydrocarbons together with degeneracies of eigenvalues have been carried out for all species having h ⩽ 7 hexagons. In addition, twelve homologous series are evaluated, and the closed results for the distribution of eigenvalues ± 1 and degeneracies in terms of the number of repeated units are tabulated. This method is universal and applicable to cases sharing other eigenvalues and to nonbenzenoid systems.

Phase-space dynamics and quantum mechanics

Abstract: In a recent paper Deal has postulated a new dynamical equation for quantum mechanical phase-space distribution functions. We analyze the new equation and show that it may be related to the traditional standard and antistandard phase-space representations of quantum mechanics. A brief review of these and other representations is also given.

Reaction graphs and a construction of reaction networks

Abstract: A general definition of reaction graphs is presented. For a pair of isomeric molecular graphs \(\mathbb{G}_1 \) and \(\mathbb{G}_2 \), related by a chemical transformation \(\mathbb{G}_1 {\text{ }} \Rightarrow {\text{ }}\mathbb{G}_2 \), the reaction graph \(\mathbb{G}_R^{{\text{(}}\omega {\text{)}}} \) is determined using a maximal common subgraph defined for vertex mapping \(\omega :V(\mathbb{G}_1 ) \to V(\mathbb{G}_2 )\). A binary operation ‘ ⊕ ’ defined for graphs constructed over the same vertex set enables us to decompose the reaction graph \(\mathbb{G}_R^{(\omega )} \) into the sum of prototype reaction graphs. A decomposition of an overall reaction graph can be advantageously used for the construction of a reaction network. An oriented path in this network beginning at \(\mathbb{G}_1 \) and ending at \(\mathbb{G}_2 \) corresponds to a breakdown of the transformation \(\mathbb{G}_1 {\text{ }} \Rightarrow {\text{ }}\mathbb{G}_2 \) into a sequence of intermediates.

MRINDO/S-CI calculation on the electronic spectra of higher azines

Abstract: MRINDO/S calculation completed by singly excited configuration interaction was performed on the higher aziness-triazine,s-tetrazine and pentazine. The results enable the main characteristics of the observed electronic spectra to be interpreted. The importance of outer (Rydberg) atomic orbitals is stressed and it is found that a few singlet-singlet transitions of the higher azines lead to an excited state with considerable Rydberg character.

Semiempirical study of electronic and bonding properties of iron silicide clusters

Abstract: Molecular orbital calculations of iron, silicon, and iron silicide clusters have been carried out using the UHF-MINDO/SR method. The nature of the bonding in these compounds has been investigated by analyzing the importance of bonding indexes and diatomic components of the total energy. It has been found that in iron silicide the strongest bond is formed between Fe-Si and that it arises mainly as the result ofsp-sp type orbital interactions. Althoughd orbitals show very little overlap withs-p orbitals, they do contribute significantly to bonding through electrostatic type diatomic interactions. By means of a detailed analysis ofsp, andd orbitals and total density of states (DOS) of Fe7Si7, Si7Fe7, Fe15, and Si17 clusters, the present calculations have permitted us to explain the origin of the iron silicide UPS experimental peaks.

Theoretical study of the6Σ+,6Π, and4Σ+ van der Waals states of NO

Abstract: Potential energy curves for the weakly bound6Σ+,6Π, and4Σ+ states of NO are presented at various levels of correlation treatment. The binding energies for the van der Waals minima vary from about 30 cm−1 for the6Σ+ state to about 20 cm−1 for the4Σ+ and6Π states. We investigate the importance of constraining the wave function to dissociate to a spherically symmetric O atom where the oxygen 2p orbitals are equivalent. For high levels of correlation treatment, we find that these restrictions have little effect on the potential, while greatly increasing the length of the CI expansion.

Dipole Cauchy moments of the atoms H through Ar

Abstract: Dipole Cauchy moments of the atoms through Ar are calculated using the hydrodynamic formulation of time-dependent Kohn-Sham theory. The exchange-correlation energy density functional is approximated by the gradient expansion for atoms. Using variational trial functions that contain both linear and nonlinear variational parameters, we are able to reproduce (to three or four significant figures) the static dipole polarizabilities obtained by explicitly solving the relevant differential equations. The resulting dipole Cauchy moments provide a convenient starting point for calculating other properties which result from the linear interaction of atoms with a time varying electric field.

A note on the electronic structure of O2

Abstract: The electronic spectrum of O2− is reinvestigated using CASSCF and CI methods In particular, a previously noted curious flattening of theA2Πu curve has been studied in detail The present analysis disagrees with the previous one where this flattening was found to be a result of an avoided curve crossing between a valence and a Rydberg state of O2− A simple procedure is suggested to determine whether a wavefunction is of real Rydberg character or if the bound character of the state is just an artefact of the calculation

Isomorphic electron orbitals for vibronic flexibility in a cyclopropenyl radical molecular device

Abstract: The vibronic character of this molecular device has been studied using isomorphic electron orbitals. The leading role of the softest vibrational mode for the electron transport process is stressed by the quantum mechanical treatment of the rearrangement operator. The theory was used to investigate the possible function of the soliton valve, which has been suggested as a switching tip. The electronic flexibility of the cyclopropenyl radical with respect to molecular vibrations, which is important for the function of the molecular device, is well characterized by the hardness and softness of the electron structure in terms of the orbital energy-occupation number correlation diagram.

The estimation of electron affinities fromab initio 1s orbital energies

Abstract: It has been found that the electron affinities of alkoxy-radicals can be estimated using a correlation with the 1s orbital energy of the oxygen on the associated alkoxy-anion, EA=−0.64503 * (1s orbital energy) −351.58. The method assumes that the species of interest accepts the electron into an orbital which is localized on the oxygen.