Showing papers in "Journal of Chemical Physics in 1995"

A smooth particle mesh Ewald method

Abstract: The previously developed particle mesh Ewald method is reformulated in terms of efficient B‐spline interpolation of the structure factors This reformulation allows a natural extension of the method to potentials of the form 1/rp with p≥1 Furthermore, efficient calculation of the virial tensor follows Use of B‐splines in place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy We demonstrate that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N) For biomolecular systems with many thousands of atoms this method permits the use of Ewald summation at a computational cost comparable to that of a simple truncation method of 10 A or less

Constant pressure molecular dynamics simulation: The Langevin piston method

Abstract: A new method for performing molecular dynamics simulations under constant pressure is presented. In the method, which is based on the extended system formalism introduced by Andersen, the deterministic equations of motion for the piston degree of freedom are replaced by a Langevin equation; a suitable choice of collision frequency then eliminates the unphysical ‘‘ringing’’ of the volume associated with the piston mass. In this way it is similar to the ‘‘weak coupling algorithm’’ developed by Berendsen and co‐workers to perform molecular dynamics simulation without piston mass effects. It is shown, however, that the weak coupling algorithm induces artifacts into the simulation which can be quite severe for inhomogeneous systems such as aqueous biopolymers or liquid/liquid interfaces.

Gaussian basis sets for use in correlated molecular calculations. V. Core-valence basis sets for boron through neon

Abstract: The correlation‐consistent polarized valence basis sets (cc‐pVXZ) for the atoms boron through neon have been extended to treat core and core‐valence correlation effects. Basis functions were added to the existing cc‐pVXZ sets to form correlation‐consistent polarized core‐valence sets (cc‐pCVXZ) in the usual pattern: Double zeta added (1s1p), triple zeta added (2s2p1d), quadruple zeta added (3s3p2d1f), and quintuple zeta added (4s4p3d2f1g). The exponents of the core functions were determined by minimizing the difference between all‐electron and valence‐only correlation energies obtained from HF+1+2 calculations on the ground states of the atoms. With the cc‐pCVXZ sets, core, core‐valence, and valence correlation energies all converge exponentially toward apparent complete basis set (CBS) limits, as do the corresponding all‐electron singles and doubles CI energies. Several test applications of the new sets are presented: The first two ionization potentials of boron, the 3P–5S separation in carbon, and the X...

Efficient molecular numerical integration schemes

Abstract: New grids for three‐dimensional numerical integration are introduced. They include a new mapping for radial integration of the Gauss–Chebyshev type which seems to surpass in accuracy the existing integration schemes as proposed by Becke [J. Chem. Phys. 88, 2547 (1988)], Murray et al. [Mol. Phys. 78, 997 (1993)], or Gill et al. [Chem. Phys. Lett. 209, 506 (1993)]. Lebedev grids are employed for spherical integration. Open ended quadrature schemes are presented using the efficient Lobatto formula for the θ integration. These grids are employed for self‐consistent density functional calculations using local approximation and nonlocal corrections and are implemented into the program package turbomole. The results of grid tests and demonstrative applications of energy and especially analytical gradient calculations are given.

Heteronuclear decoupling in rotating solids

Abstract: A simple two pulse phase modulation (TPPM) scheme greatly reduces the residual linewidths arising from insufficient proton decoupling power in double resonance magic angle spinning (MAS) experiments. Optimization of pulse lengths and phases in the sequence produces substantial improvements in both the resolution and sensitivity of dilute spins (e.g., 13C) over a broad range of spinning speeds at high magnetic field. The theoretical complications introduced by large homo‐ and heteronuclear interactions among the spins, as well as the amplitude modulation imposed by MAS, are explored analytically and numerically. To our knowledge, this method is the first phase‐switched sequence to exhibit improvement over continuous‐wave (cw) decoupling in a strongly coupled homogeneous spin system undergoing sample spinning.

A generalized reaction field method for molecular dynamics simulations

Abstract: Molecular dynamics simulations of ionic systems require the inclusion of long‐range electrostatic forces. We propose an expression for the long‐range electrostatic forces based on an analytical solution of the Poisson–Boltzmann equation outside a spherical cutoff, which can easily be implemented in molecular simulation programs. An analytical solution of the linearized Poisson–Boltzmann (PB) equation valid in a spherical region is obtained. From this general solution special expressions are derived for evaluating the electrostatic potential and its derivative at the origin of the sphere. These expressions have been implemented for molecular dynamics (MD) simulations, such that the surface of the cutoff sphere around a charged particle is identified with the spherical boundary of the Poisson–Boltzmann problem. The analytical solution of the Poisson–Boltzmann equation is valid for the cutoff sphere and can be used for calculating the reaction field forces on the central charge, assuming a uniform continuum of given ionic strength beyond the cutoff. MD simulations are performed for a periodic system consisting of 2127 SPC water molecules with 40 NaCl ions (1 molar). We compare the structural and dynamical results obtained from MD simulations in which the long range electrostatic interactions are treated differently; using a cutoff radius, using a cutoff radius and a Poisson–Boltzmann generalized reaction field force, and using the Ewald summation. Application of the Poisson–Boltzmann generalized reaction field gives a dramatic improvement of the structure of the solution compared to a simple cutoff treatment, at no extra computational cost.

Extension of Gaussian-2 (G2) theory to molecules containing third-row atoms K and Ca

Abstract: Gaussian-3 (G3) theory is extended to molecules containing the third-row nontransition elements K, Ca, Ga–Kr. Basis sets compatible with those used in G3 theory for molecules containing first- and second-row atoms have been derived. The G3 average absolute deviation from experiment for a set of 47 test reactions containing these elements is 0.94 kcal/mol. This is a substantial improvement over Gaussian-2 theory, which has an average absolute deviation of 1.43 kcal/mol for the same set. Variations of G3 theory are also presented that are based on reduced orders of perturbation theory. These variations also show similar improvement over the corresponding G2 methods. The use of scaling parameters in G3 theory for the third row was investigated and found to perform nearly as well as use of the higher level correction. In addition, these methods are evaluated on a set of molecules containing K and Ca for which the experimental data are not accurate enough for them to be included in the test set. Results for this set indicate that G3 theory performs significantly better than G2 for molecules containing Ca. When the 47 third-row systems are added to the G3/99 database the complete G3 average absolute deviation becomes 1.06 kcal/mol for 423 energies.

Ab initio molecular dynamics simulation of the solvation and transport of hydronium and hydroxyl ions in water

Abstract: Charge defects in water created by excess or missing protons appear in the form of solvated hydronium H3O+ and hydroxyl OH− ions. Using the method of ab initio molecular dynamics, we have investigated the structure and proton transfer dynamics of the solvation complexes, which embed the ions in the network of hydrogen bonds in the liquid. In our ab initio molecular dynamics approach, the interatomic forces are calculated each time step from the instantaneous electronic structure using density functional methods. All hydrogen atoms, including the excess proton, are treated as classical particles with the mass of a deuterium atom. For the H3O+ ion we find a dynamic solvation complex, which continuously fluctuates between a (H5O2)+ and a (H9O4)+ structure as a result of proton transfer. The OH− has a predominantly planar fourfold coordination forming a (H9O5)− complex. Occasionally this complex is transformed in a more open tetrahedral (H7O4)− structure. Proton transfer is observed only for the more waterlike (H7O4)− complex. Transport of the charge defects is a concerted dynamical process coupling proton transfer along hydrogen bonds and reorganization of the local environment. The simulation results strongly support the structural diffusion mechanism for charge transport. In this model, the entire structure—and not the constituent particles—of the charged complex migrates through the hydrogen bond network. For H3O+, we propose that transport of the excess proton is driven by coordination fluctuations in the first solvation shell (i.e., second solvation shell dynamics). The rate‐limiting step for OH− diffusion is the formation of the (H7O4)− structure, which is the solvation state showing proton transfer activity.

Incorporation of solvent effects into density functional calculations of molecular energies and geometries

Abstract: In this paper, we present the implementation of the ‘‘conductorlike screening model’’ (COSMO) into the density functional program DMol. The electronic structure and geometry of the solute are described by a density functional method (DFT). The solute is placed into a cavity which has the shape of the solute molecule. Outside of the cavity, the solvent is represented by a homogeneous dielectric medium. The electrostatic interaction between solute and solvent is modeled through cavity surface charges induced by the solvent. The COSMO theory, based on the screening in conductors, allows for the direct determination of the surface charges within the SCF procedure using only the electrostatic potentials. This represents the major computational advantage over many of other reaction field methods. Since the DMol/COSMO energy is fully variational, accurate gradients with respect to the solute coordinates can be calculated for the first time, without any restriction on the shape of the cavity. The solvation energies and optimized molecular structures are calculated for several polar solutes. In addition, the trends in basicity of amines and the relative stabilities of molecular conformers are studied. Our results suggest that for neutral solutes, agreement between calculated and experimental solvation energies of better than about 2 kcal/mol can be achieved.

Molecular dynamics simulation of the orthobaric densities and surface tension of water

Abstract: Molecular dynamics simulations have been performed to study the liquid–vapor equilibrium of water as a function of temperature. The orthobaric densities and the surface tension of water are reported for temperatures from 316 K until 573 K. The extended simple point charge (SPC/E) interaction potential for water molecules is used with full Ewald summation. The normal and tangential components of the pressure tensor were calculated and are presented at 328 K. The nature of the long‐range contribution to the surface tension has been studied in detail. At 328 K the calculated surface tension is 66.0±3.0 mN m−1 in comparison with the experimental value of 67 mN m−1. The simulated surface tensions between 316 K and 573 K are in good agreement with experiment. The orthobaric densities are in better agreement with experimental values than those obtained from the Gibbs ensemble calculation for the SPC model of water.

Tensor propagator for iterative quantum time evolution of reduced density matrices. i: theory

Abstract: For common condensed phase problems described by a low‐dimensional system coupled to a harmonic bath, Feynman’s path integral formulation of time‐dependent quantum mechanics leads to expressions for the reduced density matrix of the system where the effects of the harmonic environment enter through an influence functional that is nonlocal in time. In a recent Letter [Chem. Phys. Lett. 221, 482 (1994)], we demonstrated that the range of the nonlocal interactions is finite even at zero temperature, such that the nonlocal kernel extends over only a few time steps if the path integral is expressed in terms of accurate quasiadiabatic propagators. This feature arises from disruption of phase coherence in macroscopic environments and leads to Markovian dynamics for an augmented reduced density tensor, permitting iterative time evolution schemes. In the present paper we analyze the structure and properties of the relevant tensor propagator. Specifically, we show that the tensor multiplication scheme rigorously conserves the trace of the reduced density matrix, and that in cases of short‐range nonlocality it leads to Redfield‐type equations which are correct to all orders in perturbation theory and which take into account memory effects. We also argue that a simple eigenvector analysis reveals (without actual iteration) the nature of the dynamics and of the equilibrium state, and directly yields quantum reaction or relaxation rates.

Response functions in the CC3 iterative triple excitation model

Abstract: The derivation of response functions for coupled cluster models is discussed in a context where approximations can be introduced in the coupled cluster equations. The linear response function is derived for the approximate coupled cluster singles, doubles, and triples model CC3. The linear response functions for the approximate triples models, CCSDT‐1a and CCSDT‐1b, are obtained as simplifications to the CC3 linear response function. The consequences of these simplifications are discussed for the evaluation of molecular properties, in particular, for excitation energies. Excitation energies obtained from the linear response eigenvalue equation are analyzed in orders of the fluctuation potential. Double replacement dominated excitations are correct through second order in all the triples models mentioned, whereas they are only correct to first order in the coupled cluster singles and doubles model (CCSD). Single replacement dominated excitation energies are correct through third order in CC3, while in CCSD...

Equation of motion coupled cluster method for electron attachment

Abstract: The electron attachment equation of motion coupled cluster (EA‐EOMCC) method is derived which enables determination of the various bound states of an (N+1)‐electron system and the corresponding energy eigenvalues relative to the energy of an N‐electron CCSD reference state Detailed working equations for the EA‐EOMCC method are derived using diagrammatic techniques for both closed‐shell and open‐shell CCSD reference states based upon a single determinant The EA‐EOMCC method is applied to a variety of different problems, the main purpose being to establish its prospects and limitations The results from EA‐EOMCC calculations are compared to other EOMCC approaches, starting from different reference states, as well as other theoretical methods and experimental values, where available We have investigated electron affinities for a wide selection of both closed‐shell and open‐shell systems Excitation spectra of atoms and molecules with an odd number of electrons are obtained, taking the closed‐shell ground state of the ion as a reference in the EA‐EOMCC calculation Finally we consider excitation spectra of some closed‐shell systems, and find in particular that the electron attachment approach is capable of yielding accurate triplet excitation energies in an efficient way

Extraction, through filter‐diagonalization, of general quantum eigenvalues or classical normal mode frequencies from a small number of residues or a short‐time segment of a signal. I. Theory and application to a quantum‐dynamics model

Abstract: In a previous paper we developed a method, Filter‐Diagonalization, for extracting eigenvalues and eigenstates of a given operator at any desired energy range. In essence, the method eliminates correlation between distant eigenstates through a short‐time filter while correlations between closely lying states are eliminated by diagonalization. Here we extend Filter‐Diagonalization. When used to extract eigenvalues for a given operator H, we show that all eigenvalue information is directly extracted from a short segment of the correlation functionC(t)=(ψ(0)‖e −iHt ‖ψ(0)), or alternately from a small number of residues (ψ(0)‖R n (H)‖ψ(0)), where ψ(0) is a random initial function and R n (H) is any desired polynomial expansion in H. The implications of this feature are twofold. First, in contrast to the previous version the wave packet needs only to be propagated once (to prepare C(t)), and eigenstates at all desired energy windows can then be extracted with negligible extra computation time (and negligible storage requirements). In a simulation presented here, accurate eigenvalues are extracted using propagation times which are only a 0.0041 fraction of the ‘‘natural’’ time, i.e., the time by which the relative phase of the two closest eigenstates reaches 2π. The second and more important feature is that the method is automatically suitable for extracting eigenvalues (or normal modes) using a short‐time segment of any signal C(t) which is a sum of (unknown) Fourier components (C(t)=∑ nd ne −ie nt ) regardless of its origin. In addition to its use for determining eigenvalues of known operators, the method may also be utilized to extract normal modes from classical‐dynamics simulations, eigenstates from real‐time Quantum Monte‐Carlo studies, frequencies from experimental optical or electrical signals, or be utilized in any other circumstance where a correlation function or general signal is only known for short times (or expensive to generate at long times).

Computer simulations of vapor-liquid phase equilibria of n-alkanes

Abstract: For petrochemical applications knowledge of the critical properties of the n‐alkanes is of interest even at temperatures where these molecules are thermally unstable. Computer simulations can determine the vapor–liquid coexistence curve of a large number of n‐alkanes ranging from pentane (C5) through octatetracontane (C48). We have compared the predicted phase diagrams of various models with experimental data. Models which give nearly identical properties of liquid alkanes at standard conditions may have critical temperatures that differ by more than 100 K. A new n‐alkane model has been developed by us that gives a good description of the phase behavior over a large temperature range. For modeling vapor–liquid coexistence a relatively simple united atom model was sufficient to obtain a very good agreement with experimental data; thus it appears not necessary to take the hydrogen atoms explicitly into account. The model developed in this work has been used to determine the critical properties of the long‐chain alkanes for which experiments turned out to be difficult and contradictory. We found that for the long‐chain alkanes (C8–C48) the critical density decreases as a function of the carbon number. These simulations were made possible by the use of a recently developed simulation technique, which is a combination of the Gibbs‐ensemble technique and the configurational‐bias Monte Carlo method. Compared with the conventional Gibbs‐ensemble technique, this method is several orders of magnitude more efficient for pentane and up to a hundred orders of magnitude for octatetracontane. This recent development makes it possible to perform routinely phase equilibrium calculations of complex molecules.

Dynamics of glass-forming liquids. i: temperature-derivative analysis of dielectric relaxation data

Abstract: We have measured the dielectric relaxation times of the α process of phenyl salicylate (salol) covering 11 decades in frequency. Being representative for the class of low molecular weight organic glass forming materials, the highly resolved temperature dependence of the dynamics in salol does not follow a particular function like the Vogel–Fulcher–Tammann (VFT) law over the entire accessible range of temperatures. In order to conduct a detailed and unambiguous analysis of the temperature dependence, we take advantage of the derivatives of the experimental log(fmax) values with respect to temperature, which allow us to either linearize the frequently used temperature laws or to resolve subtle changes in fmax(T) by decreasing the number of free parameters. In this manner we observe that none of the common routes for rationalizing the dynamics like Arrhenius, VFT, Souletie scaling, and idealized mode‐coupling theory account for the experimental findings properly. However, we do observe a VFT behavior within the limits 265 K≤T≤320 K, i.e., for temperatures ranging from significantly above the glass transition at Tg=220 K to far above the melting point.

Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitrary shapes

Abstract: We present a discrete dipole approximation (DDA) method to determine extinction and Raman intensities for small metal particles of arbitrary shape. The Raman intensity calculation involves evaluation of surface electromagnetic fields, and thus is relevant to surface enhanced Raman scattering (SERS) intensities. We demonstrate convergence of the method by considering light absorption and scattering from an isolated spheroid, from an isolated tetrahedron, from two coupled spheroids, and from a spheroid on a flat surface. We also examine comparisons with traditional T‐matrix methods. Extensions and simplifications of the method in studies of clusters and arrays of particles are presented.

A density‐matrix divide‐and‐conquer approach for electronic structure calculations of large molecules

Abstract: A density matrix divide‐and‐conquer method is proposed for electronic structure calculation of large molecules. It is based on partition of density matrix and thus applicable to both density‐functional and Hartree–Fock method. Compared to the original formulation with electron density, the present method is more efficient and as accurate.

Extension of Gaussian‐2 (G2) theory to bromine‐ and iodine‐containing molecules: Use of effective core potentials

Abstract: Basis sets have been developed for carrying out G2 calculations on bromine‐ and iodine‐containing molecules using all‐electron (AE) calculations and quasirelativistic energy‐adjusted spin–orbit‐averaged seven‐valence–electron effective core potentials (ECPs). Our recommended procedure for calculating G2[ECP] energies for such systems involves the standard G2 steps introduced by Pople and co‐workers, together with the following modifications: (i) second‐order Mo/ller–Plesset (MP2) geometry optimizations use polarized split‐valence [31,31,1] basis sets for bromine and iodine together with 6‐31G(d) for first‐ and second‐row atoms; (ii) single‐point higher‐level energies are calculated for these geometries using our new supplemented bromine and iodine valence basis sets along with supplemented 6‐311G and McLean–Chandler 6‐311G bases for first‐ and second‐row atoms, respectively; and (iii) first‐order spin–orbit corrections are explicitly taken into account. An assessment of the results obtained using such a procedure is presented. The results are also compared with corresponding all‐electron calculations. We find that the G2[ECP] calculations give results which are generally comparable in accuracy to those of the G2[AE] calculations but which involve considerably lower computational cost. They are therefore potentially useful for larger bromine‐ and iodine‐containing molecules for which G2[AE] calculations would not be feasible.

Relaxation in filled polymers: A fractional calculus approach

Abstract: In recent years the fractional calculus approach to describing dynamic processes in disordered or complex systems such as relaxation or dielectric behavior in polymers or photo bleaching recovery in biologic membranes has proved to be an extraordinarily successful tool. In this paper we apply fractional relaxation to filled polymer networks and investigate the dependence of the decisive occurring parameters on the filler content. As a result, the dynamics of such complex systems may be well–described by our fractional model whereby the parameters agree with known phenomenological models.

Cavity ring-down spectroscopy for quantitative absorption measurements

Abstract: We examine under what conditions cavity ring-down spectroscopy ~CRDS! can be used for quantitative diagnostics of molecular species. We show that CRDS is appropriate for diagnostics of species whose absorption features are wider than the spacing between longitudinal modes of the optical cavity. For these species, the absorption coefficient can be measured by CRDS without a knowledge of the pulse characteristics provided that the cavity ring-down decay is exponential. We find that the exponential ring-down decay is obeyed when the linewidth of the absorption feature is much broader than the linewidth of the light circulating in the cavity. This requirement for exponential decay may be relaxed when the sample absorption constitutes only a small fraction of the cavity loss and, consequently, the sample absorbance is less than unity during the decay time. Under this condition the integrated area of a CRDS spectral line approximates well the integrated absolute absorption coefficient, which allows CRDS to determine absolute number densities ~concentrations!. We determine conditions useful for CRDS diagnostics by analyzing how the absorption loss varies with the sample absorbance for various ratios of the laser pulse linewidth to the absorption linewidth for either a Gaussian or a Lorentzian absorption line shape. © 1995 American Institute of Physics.

Ab initio energy‐adjusted pseudopotentials for the noble gases Ne through Xe: Calculation of atomic dipole and quadrupole polarizabilities

Abstract: Nonrelativistic and one‐component relativistic energy‐adjusted ab initio pseudopotentials for the noble gases neon through xenon are presented together with corresponding optimized valence basis sets. To account for nonscalar relativistic effects the relativistic pseudopotentials are supplemented with effective spin–orbit potentials. The reliability of the presented pseudopotentials is demonstrated in atomic test calculations on ionization potentials and spin–orbit splittings in comparison with nonrelativistic and relativistic all‐electron calculations as well as experimental data. Together with extended valence basis sets the pseudopotentials are applied in calculations on the static dipole and quadrupole polarizabilities of the noble gas atoms. The best values, computed at the coupled‐cluster level of theory [CCSD(T)], for the dipole and quadrupole polarizabilities of the noble gases are 2.69a30 and 7.52a50 for Ne, 11.07a30 and 52.25a50 for Ar, 17.06a30 and 97.39a50 for Kr, and 27.66a30 and 209.85a50 fo...

Modification of the gaussian-2 theoretical model : the use of coupled-cluster energies, density-functional geometries, and frequencies

Abstract: A family of modified GAUSSIAN−2 (G2M) calculational schemes have been proposed, based on geometry optimization and vibrational frequency calculations using the hybrid density‐functional approach, and electron correlation evaluation using the coupled‐cluster methods. The most accurate model, called G2M(RCC), gives the average absolute deviation of calculated atomization energies from experiment for 32 first‐row compounds of 0.88 kcal/mol. The other two methods, called G2M(RCC,MP2) and G2M(rcc,MP2), exhibit the average absolute deviations of 1.15 and 1.28 kcal/mol, respectively, and can be used for the calculations of molecules and radicals of larger sizes containing up to six to seven heavy atoms. The G2M(rcc,MP2) model demonstrates an accuracy comparable to that of G2(MP2) and requires less intensive computations than the latter. The preference of the G2M(RCC) methods over the original G2 is expected to be particularly significant for the open shell systems with large spin contamination.

Tensor propagator for iterative quantum time evolution of reduced density matrices. II. Numerical methodology

Abstract: In a recent Letter [Chem. Phys. Lett. 221, 482 (1994)], we demonstrated that the dynamics of reduced density matrices for systems in contact with dissipative harmonic environments can be obtained in an iterative fashion by multiplication of a propagator tensor. The feasibility of iterative procedures in reduced dimension spaces arises from intrinsic features of the dissipative influence functional in Feynman’s path integral formulation of quantum dynamics. Specifically, the continuum of frequencies characteristic of broad condensed phase spectra disrupts phase coherence to a large extent, such that the dynamics of an augmented reduced density tensor becomes Markovian. In a preceding article [J. Chem. Phys. 102, 4600 (1995)] we examined in detail the formal properties of the tensor propagator. In the present paper we show that the tensor propagator can be further decomposed into a product of small rank tensors, resulting in an extremely simple and efficient numerical scheme that scales almost linearly with...

The nature of flexible linear polyelectrolytes in salt free solution: A molecular dynamics study

Abstract: We present results of molecular dynamics simulations of linear polyelectrolytes in solution. The fundamental model for polyelectrolytes in solution is studied. Specifically, simulations are performed for multichain systems of a flexible chain model of charged polymers. The full Coulomb interactions of the monomers and counterions are treated explicitly. Experimental measurements of the osmotic pressure and the structure factor are reproduced. The simulations reveal a new picture of the chain structure based on calculations of the structure factor, persistence length, end‐to‐end distance, etc. We present a detailed discussion of the chain structure and a comparison with present theories. In contrast to the predicted dilute limit of rodlike chains, we find that the chains have significant bending at very low densities. Furthermore, the chains contract significantly before they overlap. We also show that counterion condensation dramatically alters the chain structure.

Accuracy and efficiency of the particle mesh Ewald method

Abstract: In this article, a recently proposed method called the particle mesh Ewald (PME) method for computing the long ranged Coulomb interactions in for example molecular dynamics simulations is studied. The PME method has a complexity O(N log N), where N is the total number of charges. This complexity should in particular be compared with the complexity O(N3/2) for the well known Ewald method and O(N) for the rather new (but already famous) fast multipole method (FMM). However, these complexities say nothing about which method is fastest at some finite N. The purpose of this article is thus to study the PME method and compare its efficiency with the Ewald method and the fast multipole method. To enable this, a theoretical estimate for the accuracy of the PME method as function of its truncation parameters is derived. It is shown that this estimate is very precise by comparing it with results obtained from molecular dynamics simulations of a molten NaCl. Based on this estimate and very careful time experiments, ...

A modification of the Gaussian‐2 approach using density functional theory

Abstract: The quadratic configuration interaction calculation in the Gaussian‐2 second‐order Mo/ller–Plesset perturbation theory approach, G2(MP2), is replaced by a coupled‐cluster (CC) singles and doubles calculation including a perturbational estimate of the triples excitations. In addition, the self‐consistent‐field (SCF) and MP2 geometry optimizations and SCF frequency calculation in the G2(MP2) approach are replaced by a density functional theory geometry optimization and frequency calculation [using the Becke three parameter hybrid functional with the Lee–Yang–Parr non‐local correlation functional (B3LYP)] in the proposed G2(B3LYP/MP2/CC) approach. This simplification does not affect the average absolute deviation from experiment, but decreases the maximum error compared with the G2(MP2) approach. The G2(B3LYP/MP2/CC) atomization energies are compared with those obtained using the B3LYP approach, and the G2(B3LYP/MP2/CC) model is found to be more reliable, even if the B3LYP calculations are performed using a large basis set.

Theoretical study of the vibrational spectra of the transition metal carbonyls M(CO)6 [M=Cr, Mo, W], M(CO)5 [M=Fe, Ru, Os], and M(CO)4 [M=Ni, Pd, Pt]

Abstract: The harmonic force fields of the title compounds have been calculated at the level of Hartree–Fock (HF) theory, Mo/ller–Plesset second‐order perturbation theory (MP2), and gradient‐corrected density functional theory (DFT) using all‐electron and effective core potential wave functions in conjunction with polarized double‐ and triple‐zeta basis sets. The DFT results are in very good agreement with the available experimental data, whereas the HF results are inadequate and the MP2 results are satisfactory only for the 5d and (partly) the 4d transition metal complexes, but not for the 3d transition metal complexes. The calculated DFT frequencies are accurate enough to suggest reassignments in the vibrational spectrum of Fe(CO)5. In the case of Ru(CO)5, Os(CO)5, Pd(CO)4, and Pt(CO)4 where experimental data are scarce, the DFT predictions may guide future experimental work.

Ab initio studies of cyclic water clusters (h2o)n, n=1-6. iii: comparison of density functional with mp2 results

Abstract: The optimal structures and harmonic vibrational frequencies of ring water clusters (H2O)n, n=1–6 are computed using density functional theory (DFT). The exchange functionals of Slater (S), Becke (B), the correlation functionals of Lee–Yang–Parr (LYP), Vosko–Wilk–Nusair (VWN), Perdew’s local (PL), and gradient‐corrected (P86) as well as their combinations are used to perform benchmark calculations on the water monomer and dimer. We use the augmented correlation‐consistent polarized valence orbital basis set of double (aug‐cc‐pVDZ) and triple zeta quality (aug‐cc‐pVTZ) in order to compare the DFT with earlier MP2 results [J. Chem. Phys. 99, 8774 (1993); 100, 7523 (1994)]. Better overall agreement with the MP2 and experimental results for the water monomer and dimer is observed for the B–LYP and B–P86 functional combinations. The optimal structures, harmonic vibrational frequencies, and energetics of the clusters trimer through hexamer are computed at the B–LYP/aug‐cc‐pVDZ level of theory. This functional co...

The anharmonic force field of ethylene, C2H4, by means of accurate ab initio calculations

Abstract: The quartic force field of ethylene, C2H4, has been calculated ab initio using augmented coupled cluster, CCSD(T), methods and correlation consistent basis sets of spdf quality. For the C-12 isotopomers C2H4, C2H3D, H2CCD2, cis-C2H2D2, trans-C2H2D2, C2HD3, and C2D4, all fundamentals could be reproduced to better than 10 per centimeter, except for three cases of severe Fermi type 1 resonance. The problem with these three bands is identified as a systematic overestimate of the Kiij Fermi resonance constants by a factor of two or more; if this is corrected for, the predicted fundamentals come into excellent agreement with experiment. No such systematic overestimate is seen for Fermi type 2 resonances. Our computed harmonic frequencies suggest a thorough revision of the accepted experimentally derived values. Our computed and empirically corrected re geometry differs substantially from experimentally derived values: both the predicted rz geometry and the ground-state rotational constants are, however, in excellent agreement with experiment, suggesting revision of the older values. Anharmonicity constants agree well with experiment for stretches, but differ substantially for stretch-bend interaction constants, due to equality constraints in the experimental analysis that do not hold. Improved criteria for detecting Fermi and Coriolis resonances are proposed and found to work well, contrary to the established method based on harmonic frequency differences that fails to detect several important resonances for C2H4 and its isotopomers. Surprisingly good results are obtained with a small spd basis at the CCSD(T) level. The well-documented strong basis set effect on the v8 out-of-plane motion is present to a much lesser extent when correlation-optimized polarization functions are used. Complete sets of anharmonic, rovibrational coupling, and centrifugal distortion constants for the isotopomers are available as supplementary material to the paper.