Showing papers in "Journal of Chemical Physics in 1986"

Density Functional Calculations of Molecular Bond Energies

Abstract: The calculation of molecular spectroscopic properties is an interesting application of the local density approximation (LDA) for the exchange-correlation energy of many-electron systems. LDA bond lengths and vibrational frequencies agree remarkably well with experiment. Dissociation energies are also reasonably good, but tend to overestimate the experimental results. Therefore, we consider in this work the effect of non-local gradient-type correction terms on LDA bond energies. In particular, we consider the gradient-corrected exchange-correlation functional of Langreth and Mehl, and also a semi-empirical exchange approximation recently developed by the present author.

Dynamical effects in electron transfer reactions

Abstract: A theoretical treatment is given for the effect of intramolecular vibrational and diffusive solvent orientational motions on the rate of electron transfer reactions. Four limiting cases are considered for the two‐electronic state problem: slow reaction, wide and narrow reaction window, and nondiffusing limits. With the aid of a decoupling approximation, an expression is derived for the reaction rate which reduces to the appropriate expression for each limiting case when the latter is approached. Under certain conditions the time dependence of the survival probability is multiexponential rather than single exponential. Because of this behavior two average survival times are defined and expressions for each are obtained. Experimental data are considered with the present treatment in mind. One feature of the present work is a more general analysis for the case that both vibrational and solvent diffusive motion contribute to the activation process. The relation to previous works in the literature is described.

Unitary quantum time evolution by iterative Lanczos reduction

Abstract: A general unitary time evolution method for wave packets defined on a fixed L2 basis is developed. It is based on the Lanczos reduction of the full N×N Hamiltonian to a p‐dimensional subspace defined by the application of H p−1 times to the initial vector. Unitary time evolution in the subspace is determined by exp{−iHpt}, retaining accuracy for a time interval τ, which can be estimated from the Lanczos reduced Hamiltonian Hp. The process is then iterated for additional time intervals. Although accurate results over long times can be obtained, the process is most efficient for large systems over short times. Time evolution employing this method in one‐ (unbounded) and two‐dimensional (bounded) potentials are done as examples using a distributed Gaussian basis. The one‐dimensional application is to direct evaluation of a thermal rate constant for the one‐dimensional Eckart barrier.

Potential energy curves using unrestricted Mo/ller–Plesset perturbation theory with spin annihilation

Abstract: Unrestricted Hartree–Fock and unrestricted Mo/ller–Plesset perturbation theory are convenient methods to compute potential energy curves for bond dissociation, since these methods approach the correct dissociation limit. Unfortunately, a spin unrestricted wave function can contain large contributions from unwanted spin states that can distort the potential energy surface significantly. The spin contamination can be removed by projection or annihilation operators. As is well known, the spin project unrestricted Hartree–Fock bond dissociation curves have a large kink at the onset of the UHF/RHF instability, and a spurious minimum just beyond. However, the spurious minimum disappears and the kink is very much less pronounced at the unrestricted Mo/ller–Plesset level with spin projection. Bond dissociation potentials for LiH and CH4 were computed at the fourth order Mo/ller–Plesset level plus spin projection,4 and good agreement was found with full CI and MR‐CISD calculations.

Charge‐transfer theory of surface enhanced Raman spectroscopy: Herzberg–Teller contributions

Abstract: A comprehensive development of the charge‐transfer theory of surface enhanced Raman scattering (SERS) is presented. We incorporate the Herzberg–Teller mixing of zero‐order Born–Oppenheimer electronic states by means of vibronic interaction terms in the Hamiltonian. This is similar to the theory of Tang and Albrecht12 except that we include metal states as part of a molecule–metal system. When this is done we may no longer discard a term involving mixing of ground‐state vibrations. The theory is comprehensive in that both molecule‐to‐metal and metal‐to‐molecule transfer is considered. Furthermore, both Franck–Condon and Herzberg–Teller contributions to the intensity are obtained. The former, however, contribute only to the intensity of totally symmetric vibrations, while the latter contribute to nontotally symmetric vibrations as well. Since overtones are observed in SERS only weakly if at all, the Herzberg–Teller terms are most consistent with experimental findings. The resulting formulas may be interpreted as a type of resonance Raman effect in which intensity for the charge transfer transitions is borrowed from an allowed molecular transition. We may also carry out the sum over metal states. This procedure predicts a logarithmic resonance at the Fermi level of the metal. We thus predict intensity vs voltage profiles such as I ∝ ‖ln(ωFI−ω+iΓ)‖2 which fits the experimental curves quite well.

Extensive theoretical studies of the hydrogen‐bonded complexes (H2O)2, (H2O)2H+, (HF)2, (HF)2H+, F2H−, and (NH3)2

Abstract: The structures and binding energies of the complexes (H2O)2, (H2O)2H+, (HF)2, (HF)2H+, F2H−, and (NH3)2 have been examined using much higher levels of theory than has been previously applied to these systems. These methods including large basis sets and full optimization of structures with the effects of electron correlation included, are known to give single bond energies to an accuracy of about 2 kcal mol−1 and are found in this study to give excellent agreement with the extensive experimental data available for the hydrogen fluoride and water dimers. The Cs openform of ammonia dimer remains a very shallow minimum energy structure at these levels, in agreement with previous theoretical results but seemingly in disagreement with experiment. The theoretical enthalpy of association of H5O+2 is found to be −35.0 kcal mol−1, in slight disagreement with the most recent experimental results, but in accord with earlier ones, which suggests that these experiments should be reexamined. The enthalpy of association...

Efficient recursive computation of molecular integrals over Cartesian Gaussian functions

Abstract: Recurrence expressions are derived for various types of molecular integrals over Cartesian Gaussian functions by the use of the recurrence formula for three‐center overlap integrals. A number of characteristics inherent in the recursive formalism allow an efficient scheme to be developed for molecular integral computations. With respect to electron repulsion integrals and their derivatives, the present scheme with a significant saving of computer time is found superior to other currently available methods. A long innermost loop incorporated in the present scheme facilitates a fast computation on a vector processing computer.

Coherent pulse sequence induced control of selectivity of reactions: Exact quantum mechanical calculations

Abstract: We present a novel approach to the control of selectivity of reaction products The central idea is that in a two‐photon or multiphoton process that is resonant with an excited electronic state, the resonant excited state potential energy surface can be used to assist chemistry on the ground state potential energy surface By controlling the delay between a pair of ultrashort (femtosecond) laser pulses, it is possible to control the propagation time on the excited state potential energy surface Different propagation times, in turn, can be used to generate different chemical products There are many cases for which selectivity of product formation should be possible using this scheme We illustrate the methodology with numerical application to a variety of model two degree of freedom systems with two inequivalent exit channels Branching ratios obtained using a swarm of classical trajectories are in good qualitative agreement with full quantum mechanical calculations

An improved log derivative method for inelastic scattering

Abstract: A new method for solving the close coupled equations of inelastic scattering is presented. The method is based on Johnson’s log derivative algorithm, and uses the same quadrature for the solution of the corresponding integral equations. However it differs from the original method in the use of a piecewise constant diagonal reference potential. This results in a reduction in matrix operations at subsequent energies, and an improved convergence of the solution with respect to the number of grid points. These advantages are clearly demonstrated when our method is applied to an atom–diatom rotational excitation problem.

Abinitio relativistic effective potentials with spin‐orbit operators. II. K through Kr

Abstract: A refined version of the ‘‘shape consistent’’ effective potential procedure of Christiansen, Lee, and Pitzer was used to compute averaged relativistic effective potentials (AREP) and spin‐orbit operators for the atoms K through Kr. Particular attention was given to the partitioning of the core and valence space, and where appropriate more than one set of potentials is provided. These are tabulated in analytic form. Gaussian basis sets with expansion coefficients for the lowest energy state of each atom are given. The reliability of the transition metal AREPs was determined by comparing computed atomic excitation energies with accurate all‐electron relativistic values. In all cases the maximum error was found to be less than 0.1 eV. The reliability of the spin‐orbit operators was also considered.

Temperature dependence of the low‐ and high‐frequency Raman scattering from liquid water

Abstract: Low frequency Δν=0–350 cm−1, Raman intensity data were obtained from liquid water between 3.5 and 89.3 °C using holographic grating double and triple monochromators. The spectra were Bose–Einstein (BE) corrected, I/(1+n), and the total integrated (absolute) contour intensities were treated by an elaboration of the Young–Westerdahl (YW) thermodynamic method, assuming conservation of hydrogen‐bonded (HB) and nonhydrogen‐bonded (NHB=bent and/or stretched, O–H O) nearest‐neighbor O–O pairs. A ΔH°1 value of 2.6±0.1 kcal/mol O–H ⋅⋅⋅ O or 5.2±0.2 kcal/mol H2O (11 kJ/mol O–H ⋅⋅⋅ O, or 22 kJ/mol H2O) resulted for the HB→NHB process. This intermolecular value agrees quantitatively with Raman and infrared ΔH° values from the one‐ and two‐phonon OH‐stretching regions, and from molecular dynamics, depolarized light scattering, neutron scattering, and ultrasonic absorption, thus indicating a common process. A population involving partial covalency of, i.e., charge transfer into, the H ⋅⋅⋅ O units of linear and/or weak...

Alkali halides in water: Ion–solvent correlations and ion–ion potentials of mean force at infinite dilution

Abstract: Using the specialization of the extended RISM equation to infinitely dilute systems, we have calculated correlation functions and interionic potentials of mean force for a set of models corresponding to the first few alkali halides in water. From the results obtained at infinite dilution we calculate the lowest order corrections to the solution properties of the ions. Higher concentrations are explored by using the interionic potentials of mean force at infinite dilution as effective solvent mediated pair potentials. Our results indicate that certain thermodynamic properties, such as the mean activity coefficients and osmotic pressures, are quite sensitive to the details of both the theory and the potential models.

Fluids in narrow pores: adsorption, capillary condensation, and critical points

Abstract: By means of a density functional approach the phase equilibria of a simple fluid confined by two adsorbing walls have been investigated as a function of wall separation H and chemical potential μ for temperature T corresponding to both partial and complete wetting situations. For large values of H and small undersaturations Δμ ≡ μsat−μ, we recover the macroscopic formulas for the undersaturation at which a first‐ order phase transition (capillary condensation) from dilute ‘‘gas’’ to a dense ‘‘liquid’’ occurs in a single, infinitely long slit. For smaller H we compute the lines of coexistence between gas and liquid in the (Δμ, 1/H) plane at fixed values of T. The adsorption Γ(Δμ), at fixed T and H, is characterized by a loop. At the first order transition Γ jumps discontinuously by a finite amount; however metastable states exist and these could give rise to hysteresis of the adsorption isotherms obtained for the single slit. The loop disappears at a capillary critical point (Δμc, 1/Hc) at each T. For H

Natural bond orbital analysis of molecular interactions: Theoretical studies of binary complexes of HF, H2O, NH3, N2, O2, F2, CO, and CO2 with HF, H2O, and NH3

Abstract: The binary complexes of HF, H2O, NH3, N2, O2, F2, CO, and CO2 with HF, H2O, and NH3 have been studied by ab initio molecular orbital theory and natural bond orbital (NBO) analysis. Most of the complexes involving N2, O2, F2, CO, and CO2 are found to have both hydrogen‐bonded and non‐hydrogen‐bonded structures. The NBO analysis provides a consistent picture of the bonding in this entire family of complexes in terms of charge transfer (CT) interactions, showing the close correlation of these interactions with the van der Waals penetration distance and dissociation energy of the complex. Contrary to previous studies based on the Kitaura–Morokuma analysis, we find a clear theoretical distinction between H‐bonded and non‐H‐bonded complexes based on the strength of CT interactions. Charge transfer is generally stronger in H‐bonded than in non‐H‐bonded complexes. It plays an intermediate role in non‐H‐bonded CO2 complexes which have been studied experimentally. However, the internal rotation barrier (1 kcal mol−...

Fluids of dimerizing hard spheres, and fluid mixtures of hard spheres and dispheres

Abstract: We continue the study of a fluid of hard spheres which contain an off‐center attraction site, with the range of attraction restricted so that dimers, but no higher s‐mers can be formed. Two approximations, an integral equation and a version of thermodynamic perturbation theory, were previously found to perform well when tested against Monte Carlo simulations. Here, the limit in which the attraction becomes an infinitely strong glue spot of infinitesimal extent is evaluated analytically for the two theories. The resulting equation of state may be identified with the equation of state of a mixture of hard spheres and hard dispheres. In the limit of complete dimerization the system is equivalent to a one‐component fluid of hard dispheres. The equation of state of hard dispheres, known from Monte Carlo simulations, is accurately represented by the Tildesley–Streett (TS) fitting function. In the pure disphere limit, our version of thermodynamic perturbation theory predicts an equation of state which is numerically almost indistinguishable from the TS fitting function. For the integral equation, the disphere limit of the compressibility equation of state is also very good, showing a maximum deviation from the TS fitting function of 2% over the density range of the simulations. The virial equation of state is much less satisfactory, with the deviation rising to 15% at the highest density.

Self‐consistent integral equations for fluid pair distribution functions: Another attempt

Abstract: We propose a new mixed integral equation for the pair distribution function of classical fluids, which interpolates continuously between the soft core mean spherical closure at short distances, and the hypernetted chain closure at large distances. Thermodynamic consistency between the virial and compressibility equations of state is achieved by varying a single parameter in a suitably chosen switching function. The new integral equation generalizes a recent suggestion by Rogers and Young to the case of realistic pair potentials containing an attractive part. When compared to available computer simulation data, the new equation is found to yield excellent results for the thermodynamics and pair structure of a wide variety of potential models (including atomic and ionic fluids and mixtures) over an extensive range of temperatures and densities. The equation can also be used to invert structural data to extract effective pair potentials, with reasonable success.

The diagonal correction to the Born–Oppenheimer approximation: Its effect on the singlet–triplet splitting of CH2 and other molecular effects

Abstract: The prediction of the diagonal correction to the Born–Oppenheimer approximation is now possible by ab initio analytic methods, as has recently been shown by Yarkony and Lengsfield. At the general restricted Hartree–Fock (GRHF) level of approximation, the procedure is straightforward: solutions of the coupled perturbed Hartree–Fock equations (CPHF) and some overlap integrals are all that are required. This correction is evaluated for a series of small molecules with various basis sets: H2O, H2O+, CH2, HCF, H+5, and F2. It is interesting to observe that the value of this correction (0.11 kcal) for the singlet–triplet splitting of CH2 is larger than the relativistic correction, and that the theoretical value for Tnre (BO)≡9.23±0.20 kcal has come even closer to the best ab initio prediction of 9.4 kcal.

Solid–liquid phase changes in simulated isoenergetic Ar13

Abstract: Simulations by molecular dynamics of 13‐particle clusters of argon display distinct nonrigid, liquid‐like and near‐rigid, solid‐like ‘‘phases.’’ The simulations, conducted at constant total energy, display a low‐energy region in which only the solid‐like form appears, a high‐energy region in which only the liquid‐like form appears, and an intermediate band of energy—a ‘‘coexistence region’’— in which clusters exhibit both forms. The intervals of time spent in each phase in the two‐form coexistence region are long compared with the intervals required to establish equilibrium‐like properties distinctive of each form, such as mean square displacement and power spectrum, so that well‐defined phases can be said to exist. The fraction of time spent in each phase is a function of the energy. When a long simulation is separated into regions of solid‐like and liquid‐like behavior, the curve of the derived caloric equation of state is double valued in the two‐phase range of energy, forming two well‐defined, smooth branches. When, instead, the caloric curve is constructed from averages over all of a long run, its form is smooth and monotonic showing no trace of the ‘‘loop’’ that had been reported for earlier treatments with much shorter molecular dynamics runs, and which we could also reproduce with short runs.

Theoretical study of small silicon clusters: Equilibrium geometries and electronic structures of Sin (n=2–7,10)

Abstract: The geometries and energies of small silicon clusters have been investigated in a systematic manner by means of accurate ab initio calculations. The effects of polarization functions and electron correlation have been included in these calculations. Several geometrical arrangements and electronic states have been considered for each cluster. All the geometries considered have been completely optimized within the given symmetry constraints with several basis sets at the Hartree–Fock level of theory. Single point calculations have been performed at these geometries using complete fourth‐order perturbation theory with the polarized 6‐31G* basis set. The effects of larger basis sets including multiple sets of polarization functions have been considered for Si2 and Si3. Singlet ground states are found for Si3–Si7 with the associated geometries corresponding to a triangle, a planar rhombus, a trigonal bipyramid, an edge‐capped trigonal bipyramid, and a tricapped tetrahedron, respectively. The best calculated structure for Si10 corresponds to a tetracapped octahedral arrangement where alternate faces of the octahedron have been capped to yield a structure with overall tetrahedral symmetry. All the geometries are considerably different from those derived from microcrystal fragments. Binding energies have been computed for all clusters and used to interpret the distribution and fragmentation patterns of small silicon cluster ions observed recently.

Noncrystalline structure of argon clusters. II. Multilayer icosahedral structure of ArN clusters 50<N<750

Abstract: In a preceding paper, we have described the polyicosahedral structure of small argon clusters containing less than about 50 atoms which were produced in a free jet expansion. Going on with this study, we describe presently the multilayer icosahedral structure of larger argon clusters containing up to about 750 atoms, a value for which the transition to the fcc crystalline bulk structure is found to occur. Cluster models are used in order to study the third icosahedral layer construction, and the transition from a twin to a regular surface arrangement, which is expected to take place around 75 atoms, is observed on experimental patterns. The good agreement between experimental and calculated diffraction functions leads to an estimate of mean cluster sizes, cluster size distributions, and temperature (32±2 K) of clusters containing several hundreds of atoms.

Highly excited vibrational levels of "floppy" triatomic molecules: A discrete variable representation - Distributed Gaussian basis approach

Abstract: A novel, efficient, and accurate quantum method for the calculation of highly excited vibrational levels of triatomic molecules is presented. The method is particularly well suited for applications to ‘‘floppy’’ molecules, having large amplitude motion, on potential surfaces which may have more than one local minimum. The discrete variable representation (DVR) for the angular, bend coordinate is combined with the distributed (real) Gaussian basis (DGB) for the expansion of other, radial coordinates. The DGB is tailored to the potential, covering only those regions where V(r)

On distributed Gaussian bases for simple model multidimensional vibrational problems

Abstract: Distributed Gaussian bases (DGB) are defined and used to calculate eigenvalues for one and multidimensional potentials. Comparisons are made with calculations using other bases. The DGB is shown to be accurate, flexible, and efficient. In addition, the localized nature of the basis requires only very low order numerical quadrature for the evaluation of potential matrix elements.

The determination of the vector correlation between photofragment rotational and translational motions from the analysis of Doppler‐broadened spectral line profiles

Abstract: A theoretical framework is presented to describe the possible correlation between the translational and rotational motion of a molecular photofragment, and to relate this to experimental observables The correlation is defined by the values of a number of bipolar moments of the translational and rotational angular distributions which reflect the dynamics of the dissociation process Detailed equations are presented for the polarization dependence of the profiles of recoil Doppler–broadened spectral lines of the photoproduct for two distinct classes of system: (i) molecular photodissociation, followed by spontaneous fluorescence by a molecular product with dispersion of its emission spectrum, and (ii) LIF excitation of a photoproduct, with or without dispersion of the resulting emission The application of the theory is illustrated by calculating the line profiles for two model systems, each with several excitation–detection geometries It is pointed out that there may still be detectable correlation between the product motions even for weakly predissociated parent molecule transitions in which the memory of the initial excitation is lost through extensive rotation before dissociation

Theory of activated rate processes: A new derivation of Kramers’ expression

Abstract: The generalized Langevin equation of motion for a particle trapped in a one‐dimensional well with a barrier height V0 and coupled to a dissipative medium is modeled by a harmonic bath. Using the properties of the bath and a normal mode analysis we prove that the reactive frequency defined by Grote and Hynes for averaged motion across the barrier is actually a renormalized effective barrier frequency. We then show that the Kramers–Grote–Hynes expression for the rate of escape over the barrier is just the continuum limit of the usual gas phase harmonic transition state theory expression.

Density functional theory of nonuniform polyatomic systems. I. General formulation

Abstract: We extend the density functional theory of nonuniform fluids to the cases of systems composed of polyatomic species. By the method of Legendre transforms, one demonstrates the existence of a free energy density functional where the densities refer to the locations of interaction sites (not full molecular coordinates). A variational principle for the free energy is derived. The methodology retains nearly all the mathematical simplicity of the traditional theory of atomic fluids. Thus, it may provide a practical route to deriving mean field theories of assembly and phase transitions in complex systems. Certain nonlinearities intrinsic to polyatomic systems and absent in simple fluids become apparent in our analysis. These features are associated with the entropy density functional for systems with bonding constraints. They must be carefully assessed in accurate applications.

Dielectric relaxation in water. Computer simulations with the TIP4P potential

Abstract: In this second paper in a series of systematic investigations seeking to relate the dielectric properties of water to the features of the intermolecular potential, extensive molecular dynamics simulations with the empirical TIP4P effective pair potential are compared with the experimental data for water as well as with the results reported previously for the MCY a b i n i t i omodel. The frequency dependence of the dielectric constant obtained for the two models is contrasted with the predictions of a Mori three‐variable theory and analyzed in detail using a phenomenological description of dielectric relaxation. It is shown that both models are capable of reproducing all reorientational processes observed in the experimental spectrum. However, qualitative agreement with the experimental results for the Debye relaxation time and the static Kirkwood g‐factor g K is only obtained with the TIP4P model, although the values are still too low and ∂g K /∂T has the wrong sign. The differences between the models are interpreted as being due to the different position chosen for the center of negative charge, and it is argued that moving the latter further towards the oxygen would, for simple rigid point charge models, yield considerably improved agreement with experiment.

Frequency dependent nonlinear optical properties of molecules

Abstract: Various nonlinear optical polarizabilities are derived and evaluated by time dependent Hartree–Fock theory (TDHF). The recursive nature of the TDHF theory is exploited to develop formulas that are applicable in any order. The theory is applied to evaluate dispersion effects for the series of molecules CH4, CH3F, CH2F2, CHF3, and CF4. Comparisons are made with results obtained from dc‐induced, second‐Harmonic generation, and third‐Harmonic generation experiments. Additional applications are reported for H2 and HF.

Multiple‐quantum NMR spectroscopy of S=3/2 spins in isotropic phase: A new probe for multiexponential relaxation

Abstract: In nuclear magnetic resonance of quadrupolar spins with S≥3/2, it is shown that excitation and observation of multiple‐quantum coherence is possible in the absence of scalar, dipolar, or quadrupolar splittings, in contrast to the widely accepted view that nonvanishing couplings are a prerequisite for the creation of multiple‐quantum coherence In the absence of splittings, multiple‐quantum coherence can be excited because the longitudinal (‘‘T1’’) or transverse (‘‘T2’’) relaxation is multiexponential, which occurs if the motional correlation times τc are comparable to or larger than the inverse of the Larmor frequency (violation of the extreme narrowing approximation) Two experiments are described, which combine multiple‐quantum filtration with conventional spin‐echo and inversion‐recovery sequences For isotropic motion each experiment allows one to determine the motional correlation time without knowledge of the magnitude of the quadrupolar coupling constant

A modified coupled pair functional approach

Abstract: A modified coupled pair functional (CPF) method is presented for the configuration interaction problem that dramatically improves properties for cases where the Hartree-Fock reference configuration is not a good zeroth-order wave function description. It is shown that the tendency for CPF to overestimate the effect of higher excitations arises from the choice of the geometric mean for the partial normalization denominator. The modified method is demonstrated for ground state dipole moment calculations of the NiH, CuH, and ZnH transition metal hydrides, and compared to singles-plus-doubles configuration interaction and the Ahlrichs et al. (1984) CPF method.

The low‐lying electronic excitations in long polyenes: A PPP‐MRD‐CI study

Abstract: A correct description of the electronic excitations in polyenes demands that electron correlation is accounted for correctly. Very large expansions are necessary including many‐electron configurations with at least one, two, three, and four electrons promoted from the Hartree–Fock ground state. The enormous size of such expansions had prohibited accurate computations of the spectra for polyenes with more than ten π electrons. We present a multireference double excitation configuration interaction method (MRD‐CI) which allows such computations for polyenes with up to 16 π electrons. We employ a Pariser–Parr–Pople (PPP) model Hamiltonian. For short polyenes with up to ten π electrons our calculations reproduce the excitation energies resulting from full‐CI calculations. We extend our calculations to study the low‐lying electronic excitations of the longer polyenes, in particular, the gap between the first optically forbidden and the first optically allowed excited singlet state. The size of this gap is shown to depend strongly on the degree of bond alternation and on the dielectric shielding of the Coulomb repulsion between the π electrons.