ALBERT

Notes: The Gaussian lobe representation of 2p and 3dxy functions of a one-electron atom has been reconsidered. Contrary to earlier results, it has been found that the minimum energy associated with the simplest case of these functions is reached when the expansion centers coincide with the nucleus. This also seems to be true for representations with larger expansion lengths. Under similar conditions, Whitten's octahedral representation of the 2p function gives a better energy value than Poshusta's tetrahedral one.

Notes: Ab initio calculations of various expectation energies have been made for the reactant and product species in six reactions that involve only small linear molecules. The reactions include fission by hydrogen, addition of hydrogen, exchange of triply bonded atoms, fluorination, and oxygen atom transfer. The change in total electronic energy is not invariably the result of changes in inner shell energy and outer shell σ- and π-electron energies simply augmenting each other, but in several cases there is a complex interplay of opposing effects. This approach gives a different insight into the energetic aspects of changes in bonding from that derived from the concept of shared electron pairs in σ and π bonds together with lone pairs in valence shells. Changes in π-electron energy are shown to be important in a reaction in which neither reactant nor product molecules contain π bonds in the usual chemical sense. While in a reaction in which there is a complete change in the nature of the triple bonds, and hence the π bonding, the change in π-electron energy makes a smaller contribution than either the change in inner shell or the outer shell σ-electron energies.

Notes: Pair correlation in the ground state of the Li isoelectronic sequence is studied through four approximate wave functions which incorporate inter- and intrashell pair correlation. Of these functions, two possess symmetry appropriate to a three-electron system, while two do not. The functions are not variational functions in the usual sense. They are instead fixed linear combinations of products of orbitals and pair functions for the appropriate states of two-electron atoms. They are considered here as zero-order approximations to the exact wave functions, and the corresponding zero-order Hamiltonians are obtained. The simplest of these functions is improved by the introduction of a screening parameter for the “outer” electron. This latter function is found to be a satisfactory compromise between accuracy and simplicity and is proposed for study via higher-order perturbation theory.

Notes: The second-order dispersion energy between interacting hydrogen pairs has been evaluated by the Borel-integral method. The results are in complete harmony with those obtained by the method of Padé approximants.

Notes: Two previous schemes for the calculation of dynamic multipole polarizabilities of atomic systems, namely, a hydrodynamic analogy to quantum mechanics and a perturbation expansion of the energy in multipoles, follow also from the conventional time-dependent perturbation scheme.

Notes: A generalization of optimized diatomics-in-molecules method that provides an accurate treatment of overlap integrals is presented. The possibilities of the method to reproduce potential surfaces of the 4B2, 2B2, and 2A1 states of the H3 molecule are investigated. It is shown that satisfactory results can be achieved only for a single state under consideration, but not for the three states simultaneously.

Notes: A temperature correction to the Thomas-Fermi (TF) model of a neutral compressed atom has been given by Marshak and Bethe. The aim of the present work is to point out that, by formulating a variational principle, one may obtain approximate analytical solutions of the temperature-perturbed TF equation. As a test of the proposed theory, the total energy of a Ne atom, confined to a spherical container, has been calculated as a function of the container radius at T = 0°K. Comparison of the data obtained with energy values calculated by Ludeña, using a self-consistent-field Hartree-Fock approach, shows reasonable agreement. It is, therefore, concluded that the variational approach suggested in this paper is a sound one.

Notes: The Van der Waals molecules Ar · HF, Ar · H2O, and Ar · HCl have been analyzed with potential surfaces obtained by SCF energies corrected for the basis set superposition error and by including dispersion forces. The computed properties for these Van der Waals molecules are in good agreement with recent experimental observations.

Notes: The Coulomb correlation hole distribution function has been computed with respect to various reference centers in the HCN molecule, using standard SCF+CI type wave functions. The extent to which statistical correlation between unlike-spin electrons is introduced into an SCF wave function through the inclusion of configuration interaction has been assessed by an examination of the range and depth of such holes, and compared with the behavior of analogous Fermi distribution functions. Our results show that the range of Fermi correlation is consistently longer than that of the corresponding Coulomb correlation.

Notes: Relationships are formulated to explain the variation in dihydrofolate reductase inhibitory potency for a series of 25 substituted quinazolines, with an antineoplastic potential. Highly significant correlations are obtained using CNDO/2-3R calculated indices and/or the empirically estimated molecular polarizability as independent variables. The MO calculated indices employed are the atomic polarizability, as defined herein, and bond energy. The molecular polarizability is represented by a simple sum of environment independent partial atomic polarizabilities. The partial polarizabilities, reported here for H, C, N, O, F, S, Cl, and Br, are obtained from a multiple regression forced through the origin.

Notes: Within the framework of the nonrelativistic Schrödinger equation, the Coulomb field case is used to assess the range of validity of the Thomas-Fermi statistical theory of atoms. In particular, attention is focused on (a) the x-ray scattering factor, which is the Fourier transform of the electron density; and (b) the momentum density. In each case the predictions of the statistical theory are compared with the exact results for the Coulomb potential. These can conveniently be calculated using earlier work of Fock. Some assessment is also made of the accuracy of the statistical approximation for the kinetic energy density; this is of interest in connection with the density functional approach. Finally, some brief comments are made on the relation between the self-consistent Thomas-Fermi method and the Hartree theory for atoms.

Notes: An ab initio Hartree-Fock-Slater procedure was applied to the calculation of the electronic structure of polysulfanes, H2Sn (n = 1-4) and the ions HSn- and Sn2-. Charge densities, overlap populations, and deprotonation energies are calculated; the latter appear well correlated with the first and second acidity constants.

Notes: A modification of the overlap approximation for triplet pair correlation energies is presented. The modification allows the use of either the canonical absolute overlap or the minimum absolute overlap. When applied to the b 3∑u+ state of H2, this approximation reproduces the observed correlation energy to within 0.0002 hartree (or ±3%) for all internuclear distances from 1.3 bohr to infinity.

Notes: A mathematical model to relate order and rotational motion in lipid hydrocarbon chains in biological membranes is proposed. Schrödinger equations with suitable potential functions for C—C rotations in lipid hydrocarbons chains have been solved to obtain wave functions characterizing these motions. For a free chain a threefold potential function has been assumed. The effect of collisions between neighboring chains in a membrane is considered by including another term (δ function) in the potential function.

Notes: The influence of side-chain disorder on the electronic structure of proteins has been investigated in the case of polypeptides containing two or three different amino acid residues. It has been found that due to the different potentials of different side-chain groups, the original valence and conduction bands of the homopolypeptides are split into narrow bands. The comparison of the densities of electronic states in simple homopolypeptides and in composite polymers shows that new forbidden regions in the energy spectrum of proteins may develop. The consequences of these effects for the semiconductive properties of proteins are discussed.

Notes: Monte Carlo simulation results are reported for clusters consisting of 250 water molecules surrounding serine, both in the neutral form and in two zwitterionic conformers (in order to gain some insight into conformational effects). Calculations were carried out at 300 K and using two-body potentials obtained by means of quantum-mechanical calculations. The spatial dependence of the average interaction energies was investigated. The solvation structure was investigated by means of radial distribution functions and probability density maps, which showed a few water molecules directly solvating the hydrophilic groups and, beyond them, a more or less rich and complex hydrogen-bonded network of solvent molecules.

Notes: In a previous paper, a scheme of integral approximation was proposed, in which a large number of two-electron integrals containing a certain kind of orbital pairs, i.e., weakly related pairs, can be neglected. A new criterion for partitioning orbital pairs into two groups, i.e., strongly and weakly related pairs, is introduced in order to allow for neglect of more integrals without sacrificing the accuracy of a computation. Test calculations on the BH3—C2H4 complex show that by the use of the new version, results of roughly the same accuracy as was obtained by the old version is obtained by retaining 80% of the integrals used in the old version. This kind of saving is more significant for larger molecules. For example, in a calculation on Cu-porphine with 203 CGTO'S, the revised version will require about 2.0 × 106 integrals, while the original version will require about 4.5 × 106. And these two approximate calculations are expected to give the results of roughly the same accuracy.

Notes: Cooperative phenomena may be involved in the biological effects of magnetic fields (H), since its effects on isolated atoms or ions, at room temperature, are very weak. It is suggested that interactions at the social level can considerably increase the efficiency of H in orienting the displacements of animals. This effect is discussed with a simple mathematical model inspired on superparamagnetism. In case of very weak interactions of H with isolated animals, it suggests that orientation could only be made visible through cooperativity at the social level. These results are generalized to other physical stimuli and effects, leading to the concept of cooperative sensory response, i.e., a group response to an external physical agent even when its effect on isolated members of the group is undetectable.

Notes: The role of nonadditivity of the interaction energy between three LiH molecules was investigated within the SCF ab initio framework. The nonadditive part of the interaction energy is more important in the case of a cyclic structure than in a linear trimer, and is stabilizing in both cases. The value of the ratio of three-body and two-body terms for different points on the energy hypersurface is discussed.

Notes: The pair-density-analysis method is applied to the study of CNDO/2 wave functions of the water molecule in various configurations. Particular attention is devoted to the modifications introduced by the consideration of environmental effects. The validity of the separated pair approximation is discussed and a detailed analysis of group functions is given.

Notes: A method is proposed that reduces the computational effort of HF calculations considerably by reducing the number of two-electron integrals that have to be calculated. The following concepts are used: (i) approximation of the electron density by only few functions for the Coulomb part of the HF matrix; (ii) modification of this approximate density, to improve its Coulomb field; (iii) in the exchange part, a basis function χ is replaced by a function \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \chi $\end{document} consisting of fewer Gaussian lobes; (iv) the error caused by this replacement is reduced by a modification of the densities \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \chi _i \tilde \chi _j $\end{document} in the exchange integrals. The computation time of the integral part is reduced by a factor 6 for molecules containing five first-row atoms as, e.g., CF4, if one uses a 7S/3P basis set contracted to (5, 1, 1/3). The integral time increases roughly with n3, if n is the number of Gaussian lobes.

Notes: The HF approximation method that was outlined in Paper I is tested with respect to several molecular properties. Three different levels of approximation a, b, and c are considered. Satisfactory results - compared to corresponding “exact” HF calculations - are obtained with the STO-3G basis and the approximation level a. At this level the error in the binding energy is 0.001-0.025 a.u. for all considered molecules which contain up to six first-row atoms as, e.g., cyclopentanone (C5OH8). The error in the reaction energies considered here is about 4 kcal/mol (the maximal error is 9 kcal/mol). Orbital energies, dipole moments, gross charges, equilibrium geometries, and barriers to internal rotation are well reproduced by the approximation method at all three levels.

Notes: A simple two-parameter analytic potential adjusted so as to reproduce the experimental energy levels is used to generate wave functions for the ground and excited states of the lithium atom. Using these wave functions in conjunction with the Born approximation and the Russell-Saunders LS-coupling scheme, we calculate the optical oscillator strengths for various excitations from the 1s22s(2S1/2) ground state. The results are compared to experiment and other calculations.

Notes: A matching measure between two molecular structures based on density functions is described. Some examples related with an alarm pheromone activity are given; the results encourage the possible use of similarity density concepts in molecular engineering.

Notes: This paper is devoted to the interpretation of DNA UDS caused by complexing DNA with Me ions using the correlation between the values of the spectral changes of the DNA absorption bands and the constants of reaction velocities of hydrated electrons with Me2+ and H3O+ ions.

Notes: Various criteria that have been suggested for assessing the accuracy of complex-coordinate eigenvalues are critically tested in an application to the lowest helium 1S resonance, and found to be relatively ineffective. An alternative criterion is described, based on a generalized stabilization procedure, which seems better able to select the “best” resonance eigenvalue and to guide the construction of variational trial functions.

Notes: In the present paper a new model for the transport through membranes, introduced previously by Hosur, is considered. In this model, the membrane is assimilated to a potential barrier, and the material flow through the membrane is determined from the transmission coefficient of the barrier, assuming the existence of an energy difference among the molecules placed at both sides of the membrane. An equation for the transport, in the case of small energy differences, is obtained, which is particularized to the cases that the energy difference is caused by a temperature gradient, a concentration gradient, and both gradients acting together. In all cases, under certain limitations, formally identical equations to those of the thermodynamics of irreversible processes are obtained.

Notes: The nonrigid molecule symmetry group for methylamine is determined as a set of permutations and permutation inversions for two situations. In the first case the internal rotations of the methyl group and NH2 group are included and the second case the transition of a hydrogen atom from the methyl group to NH2 group is also included. In both cases the energy level splitting of the rigid model of the methylamine is found, nuclear statistical weights of the split levels are calculated, and sections rules for the allowed dipole transitions are given.

Notes: A hierarchy of necessary conditions that an exact density matrix of a pure state or an ensemble has to satisfy is derived, namely the hermiticity of certain operators F(k). For k = 1 this reduces to the well-known Hartree-Fock condition. It is then shown that the kth set of conditions is equivalent to stationarity of the energy with respect to unitary k-particle transformations. k-Particle generalizations of Hartree-Fock theory are then discussed both in the spirit of k-particle pseudoeigenvalue equations and in the framework of a Newton-Raphson-type constructive scheme.

Notes: The many-body perturbation theory is reformulated within the dielectric function method presented in the preceding paper [12]. The self-energy effects are explicitly considered. These corrections turn out to be important and are calculated to the same level of approximation as the corresponding local-field terms. The method is at the moment applicable to π-electron systems within the zero differential overlap approximation. Explicit calculations of the excitation energies for the benzene molecule, using different parametrizations, are presented. Comparison is made with the results obtained in the random phase approximation (RPA) and other schemes.

Notes: A new method is presented for the electronic structure calculations with use of Bonifacic and Huzinaga's model potential and Slater's Xα local-statistical-exchange potential. The density of the valence electrons and its cube root are least-square fitted to ls-type Gaussians to evaluate the Coulomb potential and the Xα potential analytically. Preliminary results of the applications of the method to molecules consisting of the second-row atoms are given. Agreement with experimental ionization energies is satisfactory.

Notes: A variational theory is proposed where the distance dependence of two-center integrals is semianalytically given and the outer-shell orbitals are eigenfunctions of the one-particle Schrödinger equations. It is useful in the attempt of unifying the theory of atoms and atomic aggregates such as molecules, microclusters, crystals, etc., especially in the problems of predicting their stable structures. The purpose of this theory is not to derive lower ground-state energies but to obtain some useful wave functions for the explanation of some tendencies of the atomic aggregates in the periodic table.

Notes: One can treat the linear variation calculation by the perturbation expansion; on the other hand, one can also relate the perturbed wave function for the mth state to the mth eigenvector and justify the upper bound nature of the perturbation calculations for excited states. One can also associate a special type linear variation wave function to the SCF calculation. The upper bound nature of the excited-state SCF calculation can then be accessed by the help of this special wave function.

Notes: An advantage of modified virtual orbitals of Hartree-Fock method is discussed in the calculation of the second-order perturbation energy. All the modified virtual orbitals can be fitted for the intermediate virtual states in the perturbation expansion, only if the molecular orbitals are expanded in terms of infinite basis functions and the set of molecular orbitals is infinite and complete. If the molecular orbitals are expanded in terms of finite basis functions, only the modified virtual orbitals with lower energies are appropriate to describe the intermediate virtual states, but the modified virtual orbitals with higher energies become inadequate. To explain the usefulness of the modified virtual orbitals, the calculation by the modified Hartree-Fock method without CI are compared with the calculation by the traditional Hartree-Fock method with complete CI.

Notes: The matrix elements of the transition dipolar momentum IR have been computed between the low-lying states associated to the Lyman-α transition. The orthogonalization of the involved electronic states (obtained by the CIPSI method) has been performed and led to a better value for the asymptotic behavior of the {Ar(3p5, 4s) + H+} configuration. Position of the satellites in the red and blue wing of the line are deduced from the potential-energy curves in the frame of the quasistatic theory.

Notes: Within the presented LCAS MS (linear combination of atomic spinors-molecular spinors) SCF formalism both large and small components of the spinor radial parts have been expanded within the Gaussian basis set. The respective expressions for matrix elements as well as for one- and two-electron integrals are given.

Notes: In this paper, a fresh attempt has been made to discuss dual-symmetry groups by which the supra-antarafacial cycloaddition and the chelatropic reactions can be correctly described, as a direct consequence of which the corresponding energy correlation diagrams are successfully constructed. Furthermore, the energy correlation diagrams of sigmatropic reactions are also established by the use of another kind of single-symmetry group.

Notes: The many-body Green's function method is applied to the vertical ionization potential of the hydrogen molecule. The ionization potential is calculated iteratively by expanding the self-energy part up to third order. The effects of higher-order correlation corrections and nondiagonal self-energy elements on the solutions of the Dyson equation are examined with some techniques and approximations, by means of which a Koopmans' defect of 97.7% of the accurate value is obtained.

Notes: A comparison between the construction of symmetry-correlation diagrams and the perturbation method for studying chemical reactions is carried out. The perturbation method consists of decomposing the system Hamiltonian H into a sum, H = H0 + H′. Various symmetry correlation schemes appearing in the literature may be explained by the nonuniqueness of the decomposition scheme. All symmetry selection rules may be viewed as the varieties. By examining the symmetry-correlation diagrams, processes under investigation may be called “forbidden” or “allowed,” depending on the topological feature. Of particular importance is the topology associated with the “avoided crossing.” By making the comparison, we can establish the correspondence of the two methods and conclude that the perturbation order furnishes the origin of the “forbiddenness” of a process.

Notes: The total dipole moments, molecular energies, and π-electron densities for the linear and orthogonal pyrrole⃛acetonitrile hydrogen-bonded complexes were studied in the ab initio valence bond framework using the minimal STO-3G basis set. That the orthogonal conformation, although slightly less stable than the other, is predominant as observed in carbon tetrachloride, can be explained by its relatively high symmetry number.

Notes: The electronic structures of both the ground and excited states of ozone (O3) are investigated by the ab initio unrestricted Hartree-Fock (UHF) and UHF-natural orbital (NO) CI methods. It is found that the ab initio UHF-NO CI method provides reasonable descriptions of both the states of O3.

Notes: Ab initio molecular-orbital theory has been used to study the 1,3-sigmatropic hydrogen rearrangements: propene → propene, formic acic → formic acid, and vinyl alcohol → acetaldehyde. Fully optimized structures of stable molecules and transition states have been determined using gradient procedures and the 4-31G basis set. Improved energies have been obtained using a variety of techniques with basis sets up to the size of double-ζ plus polarization (DZP) and electron correlation up to the CEPA/DZP level. Although both polarization functions and electron correlation lead to a lowering of the calculated barriers, the values remain substantial for all three rearrangements.

Notes: The Hückel-London theory has been applied to the calculation of the “ring currents” octopole hypersusceptibilities of a series of conjugated compounds. Our calculations have been performed using fourth-order Rayleigh-Schrödinger perturbation technique. This is believed to be the first calculation of this kind. It is found that the values of “ring currents” hypersusceptibilities of fulvene and azulene are larger, in absolute magnitude, than the values corresponding, respectively, to benzene and naphthalene. It is found that, in most cases, the “ring currents” hypersusceptibilities are diamagnetic (negative values) for aromatic molecules and paramagnetic (positive values) for pseudoaromatic or antiaromatic compounds.

Notes: Global features of potential-energy curves are drawn using minimal basis SCF-CI method. Potential-energy surfaces are drawn at points of interest. The mechanism of the chemiluminescence is discussed along with the measurement of a rate constant exploiting the phenomena.

Notes: As is known, the Schrödinger equation for a particle in the ring-shaped potential V(r,v) = ησ2(2a0/r-a02/r2 sin2v)ε0, defined in the whole space, has been solved exactly. Here the eigenfunctions are represented in a form which is advantageous for concrete evaluations. The spin-orbit interaction energy ELS in quasirelativistic approximation is determined analytically, for the first time with a nonspherically symmetric potential. The influence of spin-orbit interaction on the eigenvalues of the spin-free problem and on the selection rules for electrical dipole transitions are investigated as well as the dependence of ELS on the position and depth of the potential minimum. The model can be useful for investigations of axial symmetric subjects like the benzene molecule or related problems and may be easily extended to a many-electron theory.

Notes: Within the framework of the LCAO-MO theory, a novel sign-alternation rule has been found empirically for the lowest excited ππ* triplet state in the alternant aromatic system. This rule can be applied to identify the phosphorescent state.

Notes: The transport of C6H5O- (or similarly charged moieties) through a lipoidal membrane may possibly be facilitated by forming complexes with the neutral compound. Thus, theoretical studies were performed on the model [C6H5OH⃛OC6H5]- molecular complex to obtain some information concerning the possible molecular and electronic structure of such complexes. Ab initio MODPOT/VRDDO SCF calculations were carried out on the neutral-anion dimer [C6H5OH⃛OC6H5] to optimize the equilibrium geometry. Electrostatic molecular potential contour maps have been generated from the ab initio MODPOT/VRDDO results in the molecular plane and in the plane perpendicular to the molecular plane and intersecting the hydrogen bond O⃛H—O. Difference maps have also been generated showing the change of potential on complex formation. There is a decrease of electrostatic interactions of the phenoxide anion upon complex formation with the neutral phenol. Counterpoise corrections for basis set size could not be made since calculation of the phenoxide anions in the basis set of the phenol plus the phenoxide anion led to an excited state for the phenoxide anion. This behavior is somewhat similar to that occurring in the stabilization method for excited states of negative ions as the size of the basis set is increased.

Notes: We present the results obtained within the CNDO/2 method for the diamagnetic susceptibilities of a series of conjugated molecules including benzene, fulvene, pyridine, pyrrole, and furan. The calculations have been carried out, according to Bley's method, in the framework of coupled Hartree-Fock perturbation theory, using gauge invariant atomic orbitals and the London approximation. The two usual CNDO parametrizations, due respectively to Pople, Santry, and Segal and to Del Bene and Jaffe, did not enable one to obtain the principal susceptibilities of the molecules under consideration. We investigated the effect of the CNDO parametrizations on the different contributions to the susceptibility, and gave a first improvement to Bley's method, which permits the calculation of the mean susceptibility of conjugated molecules with less than 9% error.

Notes: The s-p separation model CNDO-MO method has been introduced and developed for both the open- and closed-shell systems since 1975. This method has two chief advantages over most of the other CNDO methods. (1) The ns and np bases of the same atom may be considered independent to infer different bonding behavior. (2) Pariser-Parr and Nishimoto-Mataga approximations are applied to the Coulombic repulsion integrals, which not only simplifies the calculation and saves computer time but also gives reliable computational results. A series of nitrogen fluoride molecules such as NF, NF2, NF3, cis-N2F2, trans-N2F2, and N2F2 have been selected for this MO calculation. In each case, both ionization potential and dipole moment were calculated. The results are closer to the observed values than those reported in other works.

Notes: The equations-of-motion (EOM) method has been parametrized for the evaluation of the “π → π*” transition energies and moments of conjugated hydrocarbons. In this new semiempirical scheme, the effect of the dynamical screening by σ electrons is explicitly included.

Notes: An electron pair in a molecule is a complex entity and is incompletely described by the independent particle picture. Electron pairs are treated as Bose particles to include correlation of intrapair interaction effectively by the use of the Dyson transformation. The use of a Bose-type Hamiltonian permits a straight forward interpretation for geminals and facilitates the calculation of electronic energies. A Bose-type representation method is applied to the calculation of electronic energies of a lithium hydride molecule.

Notes: Multicenter integrals over Slater-type orbitals can be expanded in series with known coefficients if they are considered as elements of appropriate Hilbert spaces. Some test calculations for the three-center nuclear attraction integrals are given.

Notes: A simple transition probability formula is applied to the core hole ionization in CO, satisfactorily predicting the ratio between the intensity of the two inner-shell peaks. The formula is also applied to the full ESCA spectra of water and methane; the theoretical results agree reasonably well with the experiment.

Notes: Calculations of molecular-orbital energies and x-ray photoelectron spectra have been carried out for the third-row oxyanions, transition-metal oxyanions, SiO2 and TiO2, by the discrete variational-Xα cluster method. The calculated orbital energies are consistent with those determined from the XPS experiments. Theoretical XPS line shapes with Gaussian are generally in good agreement with the observed spectra. However, underestimation has been found for the photopeak intensities in the low-binding-energy region of TiO2. The discrepancy is partially attributed to the use of inaccurate photoionization cross-section for the Ti3d orbital.

Notes: A general way for drawing the state correlation diagram and seeking the reaction path is presented. If a high-symmetry reacting system is given, its least-motion path that maintains the symmetry is primarily examined. For a given state, it is judged whether the least-motion path is symmetry allowed or forbidden. If allowed, it is called the direct process. If forbidden, the symmetry imposed on the system should be relaxed, resulting in the mixing of MO's. Then, the energy barrier of the avoided crossing for some excited states is removed and the possible reaction path is found. After this procedure, the symmetry-allowed paths may be sought by the geometry optimization with a suitable wave function. By the use of such a procedure, the dissociation of diazomethane and (3H-)diazirine is found to proceed via the Cs and C2 symmetries.

Notes: A new theoretical method to calculate the photoionization cross sections of complex molecules and solids is derived in the framework of the dynamical theory by using the Green's function method. The approximations applicable to treat the photoionization by x-rays are also discussed.

Notes: The emission spectra and lifetimes of the vapor-phase exciplexes of four cyano-substituted anthracenes with N,N-dimethylaniline (DMA) as a donor are examined over a wide temperature range. The activation energies associated with the exciplex dissociation are calculated to be of the order of 10 kcal/mol. The entropy change in forming the exciplexes is discussed in relation to the efficiency of the exciplex formation. For various donors other than DMA, preliminary results on how they interact with excited 9,10-dicyanoanthracene are also given.

Notes: The binding energy spectra for the valence orbitals of hydrogen chloride have been obtained using the binary (e,2e) method at 1200 eV. The strength of the innermost valence orbital (4σ) is severely split among several ion states in the energy range 25 to 41 eV. The measured cross sections are compared with results of calculations using contracted Gaussian basis sets of double-zeta quality, and with a one-particle Green's function calculation.

Notes: The differential cross-sections for high-energy electrons scattered from water have been measured over a wide range of momentum transfers. The effect of chemical binding was seen from the comparison between the experiment and the calculation for an independent-atom model. The ab initio calculation using SCF MO was carried out with respect to the elastic scattering. It was in a good agreement with the experiment and thus a reliable electron distribution in water was obtained.

Notes: Traditionally, the calculation of the vibrational spectra of molecules involves at one point or another a numerical differentiation procedure. Such a method has some serious drawbacks both in efficiency and in accuracy. In this paper, an alternative method based on linear response theory is presented. The second derivative of the ground-state energy is expressed in terms of the electron density response matrix by means of perturbation theory. The unperturbed wave functions are obtained from the Hartree-Fock equation. First-order perturbation theory applied to this equation leads to the Hartree-Fock linear response. As an illustration of this method the vibrational frequency of a H2 molecule is calculated. The result is 1.348 × 1014 Hz as compared to the experimental value of 1.319 × 1014 Hz. This method is also applicable in the calculation of the phonon dispersion curves of solids.

Notes: A new approach to evaluate the determinant of the adjacency matrix is presented in this paper.

Notes: Normal-mode vibrational frequencies were obtained for uracil and 4-hydroxyuracil with the MINDO/3 SCF method. MINDO/3 vibrational frequencies and the moments of inertia for STO-3G optimized geometries yielded a ΔST0 for U ⇄ U* of 1.06 e.u./mol by standard statistical thermodynamic equations. ΔGT0 is then 6.29 kcal/mol in the gas phase for U ⇄ U*. The reaction field continuum model of solvent effect lowers ΔGT0 to 5.3 kcal/mol in aqueous solution. The tautomeric equilibrium constant in solution is then 1.3 × 10-4, in good agreement with experimental values.

Notes: A new algorithm for calculating characteristic coefficients is proposed.

Notes: No. Abstract.

Notes: A brief account of a quantum chemistry literature data base (QCLDB) is described, which contains the key information of about 2000 papers of ab initio calculations of atoms and molecules published in 1977-1979. The QCLDB is stored in a computer and can be sorted and rearranged into author and substance indices. Selection of the items for each paper in a computer-readable data base is discussed.

Notes: A new parameterization for the first transition metal has been proposed in the framework of CNDO/2 method. We carried out CNDO/2 calculation of hexamine complexes [M(NH3)6]2+ and hexa-aquo complexes [M(OH2)6]2+ in the high spin state where M = Mn, Fe, Co, Ni, and Cu, using new parameters. It is shown that the calculated order of binding energy is Mn—L 〈 Fe—L 〈 Co—L 〈 Ni—L ≈ Cu—L (where L means the ligand), and is in good agreement with experiment. We discussed how the orbital nodes affect the nature of bonding between metal and ligand.

Notes: Molecules exposing considerable microsurface areas to the surrounding solvent such as amino acids, nucleotide bases in biopolymers, or various drug molecules, antigens, and substrates, tend to be pulled apart or pushed together as the case may be by the surrounding solvent medium. These solvophobic forces and their quantitative theory were introduced sometime earlier [O. Sinanoğlu, in Molecular Associations in Biology, B. Pullman, Ed. (Academic, New York, 1968), pp. 427-445; and references therein]. The forces involve both enthalpy and entropy effects. The case in water had been shown to involve particularly strong forces but not differing in kind from other solvents. There are still somewhat contradictory views on the aqueous case, referred to in the literature as “hydrophobic bonding” treated as a phenomena unique to water and previously thought to involve only entropic effects. The temperature dependence and volumetric effects on the earlier type of “hydrophobic bonding” are presently not always reconcilable with recent experimental evidence. By contrast, the solvophobic force theory allows the calculation of the full solvent effect on various association or isomerization equilibria using its quite rigorous relations and basic data derived with it from liquids and solutions. [cf., e.g., for an early application to cis-trans azobenzene isomerization, T. Halčǐoǧlu and O. Sinanoğlu, Ann. N.Y. Acad. Sci., 158, 308 (1969)]. The solvophobic force theory had also introduced as a measurable new quantity, “the thermodynamic microsurface area change of a reaction,” which is now finding considerable use in protein chemistry [cf., e.g., F.M. Richards and T. Richmond, in CIBA Symposium Proceedings on Molecular Interaction and Activity in Proteins (CIBA, New York, 1977)]. Solvophobic force theory has been tested and applied recently in detail in high pressure liquid chromatography (HPLC) by C. Horvàth, W. Melander, and I. Molnar [J. Chromatograph. 125, 123 (1976)] who verified the predicted temperature, molecular surface area, and salt concentration dependence. It worked well when applied in detail to the complicated methanol-water mixtures as well. The theory also gave the first a priori derivation of the experimentally well-known protein salting-in-salting-out curve [W. Melander and C. Horvath, Arch. Biochem. Biophys. 183, 200 (1977)]. We have now extended the theory further with new basic derivations which eliminate the need for the direct calculation of some cumbersome effects. The theory has also been recently applied to a number of new areas including drug-receptor interactions, aqueous amino acid interactions, and to multicomponent phase equilibria; the latter also of chemical engineering interest. Solvophobic interactions, although part statistical thermodynamical in nature, were shown to be usable as if they were an ordinary U(R) potential added on to quantum-chemical intrinsic in vacuo potentials for prediction of conformations in solution [O. Sinanoğlu, in The World of Quantum Chemistry, R. Daudel and B. Pullman, Eds. (Reidel, Dordrecht, 1974)]. There have also been some recent applications that illustrate the convenience of our solvophobic theory in correcting for solvent effects once quantum-mechanical molecular electronic structures and potential-energy surfaces are computed.

Notes: Metal chelates [(C2H2X2)2M]n with ligating atoms X = NH, O, S and central atoms M = Be2+, Mg2+, Ni2+, Zn2+ (n = 0, ± 2), and M = Li+, Cu+ (n = ± 1, -3), have been studied in our Laboratory for some years by ab initio calculations. In this article it is shown that certain features of the complexes are the same for all the different metals in our series. These features include a drastic reduction of the energy gap between unoccupied and occupied orbitals, when electrons are added to the positively charged complexes. This change of the energy gap is shown to be an effect of the ligand dimer [(C2H2X2)2]n. But this dimer can only exist when a positive ion, e.g., a metal ion, forms a bridge between the two monomers. The reduced energy gap implies a strong bathochromic shift of the electronic spectrum and low electrical resistivity.

Notes: The intermolecular energy of two conformations of stacked hydrated purine dimers is computed for a varying number of molecules of water around the stacks. The results obtained show that hydration can modify the relative stability of the dimers as calculated in vacuo. In addition, the optimized arrangements of the molecules of water around the dimers depict that purine molecules strongly interact with the solvent and that bridges made of water dimers or trimers are formed between the stacked bases.

Notes: In order to elucidate further details of RNA conformations we have studied base stacking in dinucleoside monophosphates (DNP's) using UV difference spectra and the hypochromic effect. SCF CI MO calculations according to PPP and MIM approximations were carried out for six pyrimidine-containing DNP's in each of several stacking geometries. The calculated and plotted difference spectra were fitted to the experimental spectra. Different DNP's showed distinct geometries in the range of the helix angle of 35°. From our results we conclude that there is a microstructure in the helix. This would imply an additional content of information in this macromolecule, a higher precision in nucleic acid interactions, and make possible the prediction of the conformation of polynucleotides.

Notes: The photoisomerization of imine compounds is studied in terms of an ab initio MO CI calculation. The potential curves of the syn-anti isomerization via the rotation and the inversion are examined for benzaldimine. It is suggested that the photoisomerization is initiated through the rotation around the C—N bond in both singlet and triplet states. The ease of the photoisomerization is found to be determined by both the conformation of phenyl ring in the ground state and the energy difference of vertically excited states between two isomers.

Notes: The reaction mechanism of photoisomerization of isoxazoles to oxazoles through azirine intermediates is investigated theoretically by means of ab initio MO CI calculations. Azirine intermediates in S1 state [(n →*) state of the carbonyl chromophore] cause the C—N bond rupture of azirine ring and transform to isoxazoles via intersystem crossing to T1 state. On the other hand, azirine intermediates in S2 state [(n →*) state of the ketimine chromophore] lead to the C—C bond rupture of azirine ring and convert to oxazoles via intersystem crossing to T1 state.

Notes: Monoalkyl and dialkyl quarternary ammonium salt-type cationic surfactants containing a phenoxy group as aromatic chromophores at different positions of alkyl chains were synthesized. Monoalkyl-type surfactants formed micelles in aqueous solutions. The bilayer structure similar to that found in phospholipid liposomes was obtained in the aqueous dispersions of dialkyl-type surfactants. The phenoxy groups were partially oriented and aligned in these molecular assemblies. The interactions of aligned phenoxy groups in micelles or bilayers resulted in luminescence with lower energy than that of the monomer fluorescence or in a radiationless deactivation of excited states. Such interactions could be effectively prevented in bilayer structures composed of surfactant molecules containing a “spacer chain” between aligned chromophores. Evidence was obtained supporting energy migrations between aligned chromophores that were separated by a dodecyl chain in the bilayer structure.

Notes: The range in ordinary space of a defect in a solid, polymer, or a large molecule is an important parameter in many physical and chemical situations like, e.g., substitutional and interstitial impurities in ionic crystals, deep and shallow energy levels in semiconductors, core holes in systems studied by photoelectron spectroscopy, and hydrogen in metals. Both the electronic structure and the lattice of the host molecule or solid are normally influenced by the defect, and it is desirable to treat, as far as possible, these two aspects together. An explicit procedure for investigating the degree of localization is proposed that is based on the direct calculation of Wannier functions and partitioning technique.

Notes: The ion implantation of oxygen in either n or p-type gallium arsenide results in the formation of a semi-insulating layer that is thermally stable. There still is no reasonable explanation for this phenomenon (except one of us has made a preliminary investigationSee Ref. 1.). In this paper, we simulate the crystal of GaAs by a molecular cluster. As is well known the molecular-cluster model has a shortcoming in introducing “surface states” owing to the dangling of atomic bonds on the surfaces.See Ref. 2. In order to suppress this effect, the dangling bonds were saturated with hydrogen atoms as proposed by Larkins.See Ref. 3. Therefore, in this paper the perfect crystal of GaAs was simulated by a cluster of atoms with a composition Ga4As13H36 (which corresponds to a pseudocluster Ga13As13). In the authors' opinion, this kind of treatment may cause minor changes in the positions of a few energy levels, but the general energy diagram pattern will reflect the main features of the real crystal. The electronic states of the entire system are then computed by an LCAO-MO technique (extended-Hückel theory). The substitutional oxygen OAs, the arsenic vacancy VAs, and the OAs—VAs complex are treated similarly. The results of the calculation show that the substitutional oxygen (OAs) forms deep donor levels in the forbidden gap. The arsenic vacancy also forms donor levels in the forbidden gap. On the other hand, the OAs—VAs complex forms deep acceptor levels in the forbidden gap. Thus we have given a reasonable model for the mechanism of the formation of an insulating layer produced by oxygen ion implantation in GaAs.

Notes: In Phillips' spectroscopic theory of semiconductors, the covalency and ionicity are derived empirically from the average band gap between the highest valence and lowest conduction bands. In this paper an explicit expression for the average band gap is derived based on a continued fraction representation of the polarizability matrix. Results of a calculation for six covalent and polar semiconductors, using the pseudopotential model, are presented and compare favorably with experimental values.

Notes: Exciton transfers in the two-dimensional and spin-canted antiferromagnet (C2H5NH3)2MnCl4 were studied by investigating the absorption spectra 6A1g → 4T2g(4D) of Mn2+. A magnon side band (exciton-magnon simultaneous excitation) which has an anomalous shape with the cutoffs at the low-energy as well as the high-energy sides was observed. This anomalous shape could be reproduced in calculation as magnon side band, considering both the intersublattice and intrasublattice exciton transfers. From the analysis of this band shape, the magnitudes of the intersublattice and intrasublattice exciton transfers are estimated to be 10.2 and 6.8 cm-1, respectively. In the case of simple antiferromagnets without spin canting, the intersublattice exciton transfer process is forbidden because of the spin angular momentum. However, in the case of (C2H5NH3)2MnCl4, the prohibition of the intersublattice exciton transfer is removed by the canted-spin arrangement.

Notes: The occurrence of broken-symmetry Hartree-Fock solutions may indicate instability of the lattice depending on the symmetry of the charge-density wave (CDW). In case of polyacetylene, (CH)x, we have found such solutions having an off-diagonal CDW. It is pointed out that this sort of instability is principally different from the Peierls instability. The importance of correct (symmetrical) cutoff of interactions in direct space (“finite neighbor's approximation”) is emphasized. A basic difference in the potential-energy curve of trans-(CH)x and the isoelectronic (HCN)x around the equidistant configuration is shown.

Notes: A molecular LCAO Hartree-Fock procedure was used to calculate total energies of axially stretched normal paraffins containing up to nine carbon atoms. The results are used to model the mechanical properties of polyethylene.

Notes: The wave function and total energy of ammonia crystal are determined from the results of a totally optimized STO-3G ab initio calculation of the tetramer, pattern of the crystal. The crystal electronic energy is expressed in terms of the interatomic distances and charge density matrix elements. The geometry obtained from optimization of the tetramer energy on geometric parameters is in very good agreement with the experimental data of the crystal.

Notes: Open-shell single-determinantal calculations are reported here for the molecular species H2, Li2+, N2, O2 (triplet), O22-;, O2-, O22+, O2+, and F2; corresponding closed-shell calculations are reported for the species H2, N2, O2 (singlet), O22-, O22+, and F2. The floating spherical Gaussian orbital (FSGO) method was employed. The calculated trend in bond lengths of isonucleic diatomic molecules is in agreement with experiment. For heteronucleic diatomic molecules, however, the experimental trend in bond lengths is not obtained; in this connection, the effect of lone pairs on bond length is discussed. The dissociation energies of H2 and Li2+ are evaluated. The energy gap between the triplet and singlet states of the oxygen molecule is calculated to be 8.96 eV compared to the experimental value of 4.54 eV.

Notes: It is shown that trial functions involving Padé approximants yield satisfactory results for the ground state of the helium atom. In particular, the five-parameter form reproduces the best variational function of the type Ψ = e-zsφ(u) obtained numerically, to a remarkable extent.

Notes: Using a modified form of Sharma's method for the expansion of a Slater-type orbital in spherical harmonics about a displaced center, a general expression for the overlap integral between two orbitals is derived that is equivalent to that given by Sharma. By use of a simple kind of “computer algebra” this expression is developed here into a formula that is equivalent to earlier known ones and may have computational advantages when the generated formula coefficients are stored. This method is capable of extension to more complicated integrals.

Notes: A new method has been proposed for calculating the Gaussian matrix elements of the interaction operator represented by an arbitrary degree of interelectron distance X12ρ. The method is based on the expansion of two-electron integrals as the sum of one-electron integrals which in turn admit compact operator representation in terms of confluent hypergeometric functions. The generating differential operator has been shown to be related to the modified Hermitian polynomials. The standard structure of the special functions encountered in this approach is useful in studying the analytical behavior of the integrals and makes it possible to obtain for these integrals recurrence relations, direct algebraic expressions in the forms of finite sum of confluent hypergeometric functions, integral representations, and asymptotic properties. Unlike the usual methods based on integral transformation of the interaction operator, the proposed approach has a wider field of application, and in addition, leads to compact and convenient analytical expressions. The idea of using differential properties of integrals to simplify the integrand structure gives the proposed approach a certain resemblance to that suggested by Boys but not developed in detail in his pioneer work.