Showing papers in "Journal of Chemical Physics in 1988"

An efficient internally contracted multiconfiguration–reference configuration interaction method

Abstract: A new internally contracted direct multiconfiguration–reference configuration interaction (MRCI) method is described which allows the use of much larger reference spaces than any previous MRCI method. The configurations with two electrons in the external orbital space are generated by applying pair excitation operators to the reference wave function as a whole, while the singly external and internal configurations are standard uncontracted spin eigenfunctions. A new efficient and simple method for the calculation of the coupling coefficients is used, which is well suited for vector machines, and allows the recalculation of all coupling coefficients each time they are needed. The vector H⋅c is computed partly in a nonorthogonal configuration basis. In order to test the accuracy of the internally contracted wave functions, benchmark calculations have been performed for F−, H2O, NH2, CH2, CH3, OH, NO, N2, and O2 at various geometries. The deviations of the energies obtained with internally contracted and uncontracted MRCI wave functions are mostly smaller than 1 mH and typically 3–5 times smaller than the deviations between the uncontracted MRCI and the full CI. Dipole moments, electric dipole polarizabilities, and electronic dipole transition moments calculated with uncontracted and contracted MRCI wave functions also are found to be in close agreement. The efficiency of the method is demonstrated in large scale calculations for the CN, NH3, CO2, and Cr2 molecules. In these calculations up to 3088 reference configurations and up to 154 orbitals were employed. The biggest calculation is equivalent to an uncontracted MRCI with more than 78 million configurations.

A complete basis set model chemistry. I. The total energies of closed‐shell atoms and hydrides of the first‐row elements

Abstract: The major source of errror in most ab initio calculations of molecular energies is the truncation of the one‐electron basis set. A complete basis set model chemistry is defined to include corrections for basis set truncation errors. This model uses double zeta plus polarization level atomic pair natural orbital basis sets to calculate molecular self‐consistent‐field (SCF) energies and correlation energies. The small corrections to give the complete basis set SCF energies are then estimated using the l−6 asymptotic convergence of the multicenter angular momentum expansion. The calculated correlation energies of the atoms He, Be, and Ne, and of the hydrides LiH, BH3, CH4, NH3, H2O, and HF, using the double zeta plus polarization basis sets vary from 83.0% to 91.2% of the experimental correlation energies. However, extrapolation of each of the pair energies and pair‐coupling terms to the complete basis set values using the asymptotic convergence of pair natural orbital expansions retrieves from 99.5±0.7% to ...

A multicenter numerical integration scheme for polyatomic molecules

Abstract: We propose a simple scheme for decomposition of molecular functions into single‐center components The problem of three‐dimensional integration in molecular systems thus reduces to a sum of one‐center, atomic‐like integrations which are treated using standard numerical techniques in spherical polar coordinates The resulting method is tested on representative diatomic and polyatomic systems for which we obtain five‐ or six‐figure accuracy using a few thousand integration points per atom

An efficient reformulation of the closed‐shell coupled cluster single and double excitation (CCSD) equations

Abstract: The closed‐shell CCSD equations are reformulated in order to achieve superior computational efficiency Using a spin adaptation scheme based on the unitary group approach (UGA), we have obtained a new set of equations that greatly improves our previous formulation Based on this scheme we have also derived equations for the closed‐shell configuration interaction including all single and double excitations (CISD) case Both methods have been implemented and tested For a range of test cases the new CCSD method is more efficient than the earlier CCSD method The new closed‐shell CISD procedure is faster than the shape‐driven (SD)GUGA algorithm and the new CCSD scheme is less than two times more computation intensive than SDGUGA CISD per iteration

The determination of molecular structures by density functional theory. The evaluation of analytical energy gradients by numerical integration

Abstract: An algorithm, based on numerical integration, has been proposed for the evaluation of analytical energy gradients within the Hartree–Fock–Slater (HFS) method. The utility of this algorithm in connection with molecular structure optimization is demonstrated by calculations on organics, main group molecules, and transition metal complexes. The structural parameters obtained from HFS calculations are in at least as good agreement with experiment as structures obtained from ab initio HF calculations. The time required to evaluate the energy gradient by numerical integration constitutes only a fraction (40%–25%) of the elapsed time in a full HFS‐SCF calculation. The algorithm is also suitable for density functional methods with exchange‐correlation potential different from that employed in the HFS method.

Determinant based configuration interaction algorithms for complete and restricted configuration interaction spaces

Abstract: A restricted active space (RAS) wave function is introduced, which encompasses many commonly used restricted CI expansions. A highly vectorized algorithm is developed for full CI and other RAS calculations. The algorithm is based on Slater determinants expressed as products of alphastrings and betastrings and lends itself to a matrix indexing C(Iα, Iβ ) of the CI vector. The major features are: (1) The intermediate summation over determinants is replaced by two intermediate summations over strings, the number of which is only the square root of the number of determinants. (2) Intermediate summations over strings outside the RAS CI space is avoided and RAS calculations are therefore almost as efficient as full CI calculations with the same number of determinants. (3) An additional simplification is devised for MS =0 states, halving the number of operations. For a case with all single and double replacements out from 415 206 Slater determinants yielding 1 136 838 Slater determinants each CI iteration takes ...

Correlation energy of an inhomogeneous electron gas: A coordinate‐space model

Abstract: We develop a coordinate‐space model for dynamical correlations in an inhomogeneous electron gas. The model treats opposite‐spin and same‐spin pairs separately, and it also accounts properly for correlation contributions to the kinetic energy. Furthermore, it gives identically zero correlation energy in the case of one‐electron systems. Applications to the uniform electron gas and to the atoms H through Ar are reported.

On evaluating the reaction path Hamiltonian

Abstract: This paper examines a number of aspects of evaluating the reaction path Hamiltonian (RPH) of Miller, Handy, and Adams. The reaction path is represented as a Taylor series expansion of mass weighted Cartesian coordinates as a function of arc length. The second (path tangent) and third (path curvature) coefficients in the Taylor series are important in the RPH. General analytical formulas for all the coefficients as explicit functions of energy derivatives are derived. If the Taylor series is expanded about the saddle point, special limiting formulas for the coefficients are required. These are obtained using L’Hospital’s rule. In a local quadratic approximation (LQA) third and higher energy derivatives are ignored. Within this approximation all but the first two coefficients in the Taylor series expansion of the path are zero when the expansion point is the saddle point. At nonstationary points on the path the first three Taylor series coefficients are evaluated exactly within the LQA while the others have...

Phase diagram and dynamics of Yukawa systems

Abstract: The phase diagram and dynamical properties of systems of particles interacting through a repulsive screened Coulomb (Yukawa) potential have been calculated using molecular and lattice dynamics techniques. The phase diagram contains both a melting transition and a transition from fcc to bcc crystalline phases. These phase transitions have been studied as a function of potential shape (screening length) and compared to phenomenological criteria for transition temperatures such as those of Lindemann and of Hansen and Verlet. The transition from fcc to bcc with increasing temperature is shown to result from a higher entropy in the bcc phase because of its softer shear modes. Even when the stable solid phase below the melting temperature is fcc, bcc‐like local order is found in the liquid phase. This may substantially slow crystallization. The calculated phase diagram and shear modulus are in good agreement with experiments on colloidal suspensions of polystyrene spheres. The single particle dynamics of Yukawa systems show several unusual features. There is a pronounced subdiffusive regime in liquids near and below the melting temperature. This regime reflects the existence of two time scales: a typical phonon period, and the time for a particle to feel a new environment. The second time scale becomes longer as the temperature is lowered or the range of interaction (screening length) increases.

Kinetics of discontinuous volume-phase transition of gels

Abstract: Kinetics of the first order volume–phase transition of submillimeter gels is investigated for various initial and final states of the transition. Characteristic times for swelling and shrinking critically depend on the final state, but are much less influenced by the intial state. The transition becomes infinitely slow when the final temperature is near the transition threshold. The study of the dependence of the transition time on the gel size reveals that the overall volume change is described approximately as a collective diffusion process, but not precisely. The exponent for time–radius relation is smaller than 2. The transitions having large volume change are accompanied by formation and evolution of transient patterns which appear on the surface of a gel. The patterns for swelling and shrinking are quite different, but both play an important role in the kinetic processes.

Free energy of ionic hydration: Analysis of a thermodynamic integration technique to evaluate free energy differences by molecular dynamics simulations

Abstract: The thermodynamic integration technique to evaluate free energy differences by molecular dynamics simulations is analyzed. The hydration of the ions Na+ , K+ , Ca++ , F−, Cl−, and Br− is used as the process to illustrate the potential utility of the method. A neon–water system is used as a reference system. The parameters that influence the performance and accuracy of the thermodynamic integration, in which the potential interaction parameters are gradually and continuously changed, are studied. These parameters include the total simulation time, the magnitude of the time step for the numerical integration of the equations of motion, the system size, and the cutoff radii for the intermolecular interactions. Fast convergence is found for the Gibbs free energy difference between Ne and Na+ with respect to total simulation time. The time step and system size are relatively unimportant. The use of cutoff radii, for the ion–water but especially unfortunately also the water–water intermolecular interactions, seriously influences the results obtained. A simple correction for the use of cutoff radii cannot be made. Results are compared to experimental values.

Computer simulation of the dynamics of aqueous solvation

Abstract: Equilibrium and nonequilibrium molecular dynamics computer simulations have been used to study the time dependence of solvation in water. The systems investigated consisted of monatomic ions immersed in large spherical clusters of ST2 water. Relaxation of the solvation energy following step junction jumps in the solute’s charge, dipole moment, and quadrupole moment have been determined from equilibrium molecular dynamics (MD) simulations under the assumption of a linear solvation response. The relaxation times observed differ substantially depending on the type of multipole jump and the charge/size ratio of the solute. These results could not be quantitatively understood on the basis either of continuum or molecular theories of solvation dynamics currently available. Even the qualitative picture of a distribution of relaxation times which monatonically increases with distance away from the solute is not correct for the systems studied. This lack of agreement is partially explained in terms of the structur...

A polarizable model for water using distributed charge sites

Abstract: An algorithm is proposed for treating many‐body polarization effects that is suitable for molecular dynamics simulations of polar fluids. As an application of the procedure we have augmented an existing point charge model for water. Using reasonable parameters, the characteristic water structure and liquid binding energy can be reproduced. The resulting effective dipole moment of a water molecule in water is found to be 2.85 D.

Ab initio analytic polarizability, first and second hyperpolarizabilities of large conjugated organic molecules: Applications to polyenes C4H6 to C22H24

Abstract: The static dipole polarizability and second hyperpolarizability tensors are calculated for polyene systems via ab initio coupled‐perturbed Hartree–Fock theory. The effect of basis set augmentation on the calculated properties is explored for C4H6 and example basis sets are used to calculate the polarizability and second hyperpolarizability for the longer polyenes: C6H8, C8H10, C10H12, C12H14, C14H16,C16H18, C18H20, C20H22, C22H24. Results for the finite polyenes are extrapolated to predict the unit‐cell polarizability and second hyperpolarizability of infinite polyacetylene. The working equations which take advantage of the 2n+1 theorem of perturbation theory for calculating up to the second hyperpolarizability are given, and their implementation is briefly discussed. In particular it is shown that the implementation is readily amenable to parallel processing.

Photophysics of buckminsterfullerene and other carbon cluster ions

Abstract: The laser-induced fragmentation behavior of positive carbon cluster ions has been investigated by tandem time-of-flight techniques for the jet-cooled clusters up to 80 atoms in size. Two distinct photophysical regimes were found. The first applies to clusters with 34 atoms or more, all of which dissociate to produce even numbered fragments. Large even clusters fragment by the loss of the high energy species C2, odd ones lose a C atom. The second regime applies to clusters composed of 31 or less atoms, all of which fragment by the loss of C3. These two regimes are sharply separated by C + 32 which fragments to produce small cluster ions in the 10–19 atom size range. Fragmentation of the large clusters occurs on a microsecond or faster time scale only at very high levels of excitation (>12.8 eV). These photophysical results are interpreted as consequences of the large even clusters having edgeless, spheroidal cage structures while the small ones have linear chain or ring structures.

Molecular model for aqueous ferrous–ferric electron transfer

Abstract: We present a molecular model for studying the prototypical ferric–ferrous electron transfer process in liquid water, and we discuss its structural implications. Treatment of the nonequilibrium dynamics will be the subject of future work. The elementary constituents in the model are classical water molecules, classical ferric ions (i.e., Fe3+ particles), and a quantal electron. Pair potentials and pseudopotentials describing the interactions between these constituents are presented. These interactions lead to ligand structures of the ferric and ferrous ions that are in good agreement with those observed in nature. The validity of the tight binding model is examined. With umbrella sampling, we have computed the diabatic free energy of activation for electron transfer. The number obtained, roughly 20 kcal/mol, is in reasonable accord with the aqueous ferric–ferrous transfer activation energy of about 15 to 20 kcal/mol estimated from experiment. The Marcus relation for intersecting parabolic diabatic free ene...

Intramolecular vibrational excitations accompanying solvent‐controlled electron transfer reactions

Abstract: The theory of dynamic solvent effects on outer‐sphere electron transfer (ET) was extended to incorporate the modification of the high‐frequency quantum modes, which is manifested by the reduction of the electronic coupling by nuclear Franck–Condon factors and by the change of the energy gap Explicit expressions for the ET rates were obtained in terms of a sum over parallel vibronic channels, each involving a distinct intramolecular vibrational excitation of the final state In the solvent‐controlled adiabatic limit, the effects of intramolecular vibrational excitation are exhibited by the modification of the (partial) activation energies, while the frequency factor is dominated by the longitudinal dielectric relaxation rate of the solvent

Optimal control of selective vibrational excitation in harmonic linear chain molecules

Abstract: A formalism for designing an optical field for selective vibrational excitation in linear harmonic chain molecules is presented based on optimal control theory. The optimizing functional producing the field designs is flexible to allow for the imposition of desirable laboratory and theoretical constraints. The designed optimal fields, which successfully lead to local bond excitations, exhibit complex structure on the time scale of 10 fs. Analysis of the optimal fields shows a high degree of cooperativety between the temporal structure of the fields and the dynamical capabilities of the molecules. It is generally impossible using only spectral information to devise the optical field needed to selectively excite a local bond in a polyatomic molecule. These results explain why the previous intuitively based laboratory attempts at site specific chemistry have yielded disappointing results.

Empirical three‐body potential for vitreous silica

Abstract: A three‐body potential suitable for molecular dynamics (MD) simulations has been developed for vitreous silica by adding three‐body interactions to the Born–Mayer–Huggins (BMH) pair potential. Previous MD simulations with the BMH potential have formed glassy SiO2 through the melt‐quench method with some success. Though bond lengths were found to be in fair agreement with experiment, the distribution of tetrahedral angles was too broad and the model glass contained 6%–8% bond defects. This is indicative of a lack of the local order that is present in the laboratory glass. The nature of the short range order is expected to play an important role when investigating defect formation, surface reconstruction, or surface reactivities. An attempt has been made to increase the local order in the simulated glass by including a directional dependent term in the effective potential to model the partial covalency of the Si–O bond. The vitreous state obtained through MD simulation with this modified BMH potential shows an increase in the short range order with a narrow O–Si–O angle distribution peaked about the tetrahedral angle and a low concentration of bond defects, typically ∼1%–2%. The static structure factor S(q) is calculated and found to be in good agreement with neutron scattering results. Intermediate range order is also discussed in reference to the distribution of ring sizes.

A method for two-electron Gaussian integral and integral derivative evaluation using recurrence relations

Abstract: An efficient method is presented for evaluating two‐electron Cartesian Gaussian integrals, and their first derivatives with respect to nuclear coordinates. It is based on the recurrence relation (RR) of Obara and Saika [J. Chem. Phys. 84, 3963 (1986)], and an additional new RR, which are combined together in a general algorithm applicable to any angular momenta. This algorithm exploits the fact that the new RR can be applied outside contraction loops. It is shown, by floating point operation counts and comparative timings, to be generally superior to existing methods, particularly for basis sets containing d functions.

Bonding and stabilities of small silicon clusters: A theoretical study of Si7–Si10

Abstract: Ab initio calculations have been performed to study the structures and energies of intermediate‐sized silicon clusters (Sin, n=7–10). All geometries have been optimized at the Hartree–Fock (HF) level of theory with the polarized 6‐31G* basis set. The harmonic vibrational frequencies have been evaluated at the HF/6‐31G* level of theory. Electron correlation effects have been included by means of fourth order Mo/ller–Plesset perturbation theory. The most stable structure for Si7 is a pentagonal bipyramid and the lowest energy calculated structures for Si8–Si10 correspond to capped octahedral or prismatic geometrical arrangements. The evolution of the cluster geometries with increasing size is discussed. Clusters containing four, six, seven, and ten atoms have been identified as ‘‘magic numbers’’ for small silicon clusters, both theoretically and experimentally. The hybridization and bonding in small silicon clusters is discussed. Our results are used to interpret the recent photoelectron spectra of negative...

Nonclassical nucleation theory for the gas-liquid transition

Abstract: We use density functional methods to develop a new nonclassical theory for the homogeneous nucleation of the gas to liquid phase transition. The extent of agreement between our results and the classical prediction of Becker, Doring, and Zeldovich is strongly dependent on the range of the attractive potential which we employ. We show that our predictions are consistent with experimental data using cloud chambers, and we suggest several directions in which experimentalists might look in order to find nonclassical effects. In particular, we suggest that cavitation (gas bubble formation in a liquid subjected to tensile stress) should nucleate at a significantly greater rate than that predicted by classical theory.

Rotary resonance recoupling of dipolar interactions in solid‐state nuclear magnetic resonance spectroscopy

Abstract: A new resonance effect in solid‐state nuclear magnetic resonance (NMR) is described. The effect involves a combination of magic‐angle sample rotation with irradiation of a heteronuclear spin system at the Larmor frequency of one of the spin species. If the irradiation intensity is such as to establish a match between spin nutation and sample rotation, it is shown that the heteronuclear dipolar spin interaction is selectively reintroduced into the spectrum. This allows small dipolar coupling constants to be measured in the presence of large shielding anisotropies. Applications are anticipated for determination of internuclear distances in materials lacking long‐range order, such as polycrystalline materials, polymers, and surfaces.

Molecular hardness and softness, local hardness and softness, hardness and softness kernels, and relations among these quantities

Abstract: Hardness and softness kernels η(r,r’) and s(r,r’) are defined for the ground state of an atomic or molecular electronic system, and the previously defined local hardness and softness η(r) and s(r) and global hardness and softness η and S are obtained from them. The physical meaning of s(r), as a charge capacitance, is discussed (following Huheey and Politzer), and two alternative ‘‘hardness’’ indices are identified and briefly discussed.

Supercooled liquids, glass transitions, and the Kauzmann paradox

Abstract: Many liquids have heat capacities that substantially exceed those of the corresponding crystal, and this discrepancy magnifies in the supercooled regime. Thus, liquid entropy declines more rapidly with temperature than does crystal entropy, and the former paradoxically seems to fall below the latter for temperatures below the Kauzmann point TK. Although laboratory glass transitions inevitably intervene to prevent observation of this entropy crossing, it has often been argued that a second‐order ‘‘ideal glass transition’’ in principle should occur at TK. The inherent structure theory of condensed phases has been modified to describe supercooled liquids, and has been applied to this Kauzmann paradox. The conclusion is that an ideal glass transition of the type normally associated with the Kauzmann phenomenon cannot occur for substances of limited molecular weight and with conventional intermolecular interactions. This result also subverts theoretical expressions for shear viscosity (such as the Tamman–Vogel...

The ab initio model potential representation of the crystalline environment. Theoretical study of the local distortion on NaCl:Cu+

Abstract: In this paper we formulate a model potential approach to take into account the crystalline environment within the Hartree–Fock–Roothaan formalism. The formulation is based on the assumption that the theory of separability of many‐electron systems may be applicable to the group of electrons within a reference cluster and the groups of electrons on a set of external lattice sites which, in turn, can be represented according to the ab initio model potential method. The characteristics of the model potentials permit to analyze the contributions to the cluster energies and wave functions of different environmental effects, such as point‐charge and charge‐density Coulomb interactions and quantum interactions (exchange and orthogonality). The formalism is applied to the SCF calculation on the ground state of the octahedaral CuCl5−6 cluster (all‐electron calculation) embedded in a NaCl lattice which is represented by 118 model‐potential ions and 604 point‐charge ions. The calculation reveals that (i) the quantum ...

Local modes of benzene and benzene dimer, studied by infrared–ultraviolet double resonance in a supersonic beam

Abstract: We used rotational cooling of molecules to ∼5 K by supersonic expansion and state‐selective, multilevel saturation spectroscopy to obtain high‐resolution spectra of the fundamental and first and second overtone transitions of C–H stretching modes in ground‐electronic‐state benzene and its dimer. Greatly reduced linewidths (<3 cm−1 FWHM) in the rich spectra show that previously reported spectra have suffered from inhomogeneous congestion. Our observed spectral widths indicate that the vibrational lifetimes of the C–H stretches are at least a few ps, even at the energy of the second overtone (8800 cm−1). The ‘‘local mode’’ picture appears to apply when at least three quanta of C–H stretching motion are present. Spectra of the dimer are similar to those of the monomer but show a red shift of a few cm−1, the appearance of combination bands involving van der Waals vibrational modes, some intensity changes, and a broadening of spectral features that increases with the vibrational energy. The dimer’s predissociation lifetime at ∼3000 cm−1 vibrational energy exceeds ∼3 ps.

Geminate recombination in excited-state proton-transfer reactions: Numerical solution of the Debye-Smoluchowski equation with backreaction and comparison with experimental results

Abstract: The well‐known phenomenon of proton dissociation from excited‐state hydroxy‐arenes is analyzed by the Debye–Smoluchowski equation which is solved numerically with boundary conditions which account for the reversibility of the reaction. The numerical solution is then compared with the measured dissociation profiles which were obtained by picosecond time‐resolved fluorescence spectroscopy. The intrinsic rate constants thus determined are used to predict steady‐state rates, yields, and pK values, in agreement with experiment.

A thermodynamic analysis of solvation

Abstract: The free energy, energy, and entropy of solvation, relative to the pure liquid, are analyzed. By a coupling parameter integration it is shown that only averages over the solute–solvent interaction energy contribute to the free energy and that the solvent–solvent interaction term, which contributes the so‐called cavity (solvent reorganization) term to the energy, is cancelled exactly by a corresponding term in the entropy. These terms exist even in the infinite dilution limit since they arise from the derivative of the free energy with respect to the solute density. Following the approach of Garisto et al. [J. Chem. Phys. 79, 6294 (1983)], the site–site Ornstein–Zernike integral equations and HNC closures are used to determine the derivatives of the distribution functions with respect to the density. This makes it possible to calculate the energetic and entropic contributions to the solvation free energy in the infinite dilution limit. The method is applied to pure solvent and to infinitely dilute aqueous ...