An ab initio intermolecular potential energy surface for the F(2) dimer

Two analytical representations for the potential energy surface of the F(2) dimer were constructed on the basis of ab initio calculations up to the fourth-order of M?ller-Plesset (MP) perturbation theory. The best estimate of the complete basis set limit of interaction energy was derived for analysis of basis set incompleteness errors. At the MP4/aug-cc-pVTZ level of theory, the most stable structure of the dimer was obtained at R = 6.82 au, theta(a) = 12.9 degrees , theta(b) = 76.0 degrees , and phi = 180 degrees , with a well depth of 716 microE(h). Two other minima were found for canted and X-shaped configurations with potential energies around -596 and -629 microE(h), respectively. Hexadecapole moments of monomers play an important role in the anisotropy of interaction energy that is highly R-dependent at intermediate intermolecular distances. The quality of potentials was tested by computing values of the second virial coefficient. The fitted MP4 potential has a more reasonable agreement with experimental values.     

An accurate analytic representation of the water pair potential

The ab initio water dimer interaction energies obtained from coupled cluster calculations and used in the CC-pol water pair potential (Bukowski et al., Science, 2007, 315, 1249) have been refitted to a site-site form containing eight symmetry-independent sites in each monomer and denoted as CC-pol-8s. Initially, the site-site functions were assumed in a B-spline form, which allowed a precise optimization of the positions of the sites. Next, these functions were assumed in the standard exponential plus inverse powers form. The root mean square error of the CC-pol-8s fit with respect to the 2510 ab initio points is 0.10 kcal mol(-1), compared to 0.42 kcal mol(-1) of the CC-pol fit (0.010 kcal mol(-1) compared to 0.089 kcal mol(-1) for points with negative interaction energies). The energies of the stationary points in the CC-pol-8s potential are considerably more accurate than in the case of CC-pol. The water dimer vibration-rotation-tunneling spectrum predicted by the CC-pol-8s potential agrees substantially and systematically better with experiment than the already very accurate spectrum predicted by CC-pol, while specific features that could not be accurately predicted previously now agree very well with experiment. This shows that the uncertainties of the fit were the largest source of error in the previous predictions and that the present potential sets a new standard of accuracy in investigations of the water dimer.     

A six-dimensional H(2)-H(2) potential energy surface for bound state spectroscopy

We present a six-dimensional potential energy surface for the (H(2))(2) dimer based on coupled-cluster electronic structure calculations employing large atom-centered Gaussian basis sets and a small set of midbond functions at the dimer's center of mass. The surface is intended to describe accurately the bound and quasibound states of the dimers (H(2))(2), (D(2))(2), and H(2)-D(2) that correlate with H(2) or D(2) monomers in the rovibrational levels (v,j)=(0,0), (0,2), (1,0), and (1,2). We employ a close-coupled approach to compute the energies of these bound and quasibound dimer states using our potential energy surface, and compare the computed energies for infrared and Raman transitions involving these states with experimentally measured transition energies. We use four of the experimentally measured dimer transition energies to make two empirical adjustments to the ab initio potential energy surface; the adjusted surface gives computed transition energies for 56 experimentally observed transitions that agree with experiment to within 0.036 cm(-1). For 26 of the 56 transitions, the agreement between the computed and measured transition energies is within the quoted experimental uncertainty. Finally, we use our potential energy surface to predict the energies of another 34 not-yet-observed infrared and Raman transitions for the three dimers.     

An interaction potential between an alanine zwitterion and a water molecule based on ab initio calculations

Interaction energies between an alanine zwitterion and a water molecule at 150 different positions and orientations have been calculated using the ab initio method with the minimal basis set and employing the counterpoise method to eliminate the basis set superposition error. Dispersion energies are estimated using the Slater–Kirkwood formula. Out of a total of 150 computed interaction energies, 140 whose SCF interaction energies are below 5 kcal/mol have been fitted with a summation of atom-atom pair potentials in the form of the Lennard–Jones potential plus an electrostatic term. The standard deviation for this fitting is 0.49 kcal/mol. A sampling scheme regarding geometrical configurations is presented. Twenty rays are uniformly drawn from the origin of coordinates, a floatable division with equal ratios is made along each ray, and one of 60 orientations is randomly taken as the orientation of a water molecule. A nonlinear fitting method is used with a restriction on the sign change of fitting coefficients.     

Nitrous oxide dimer: a new potential energy surface and rovibrational spectrum of the nonpolar isomer

The spectrum of nitrous oxide dimer was investigated by constructing new potential energy surfaces using coupled-cluster theory and solving the rovibrational Schro?dinger equation with a Lanczos algorithm. Two four-dimensional (rigid monomer) global ab initio potential energy surfaces (PESs) were made using an interpolating moving least-squares (IMLS) fitting procedure specialized to describe the interaction of two linear fragments. The first exploratory fit was made from 1646 CCSD(T)/3ZaP energies. Isomeric minima and connecting transition structures were located on the fitted surface, and the energies of those geometries were benchmarked using complete basis set (CBS) extrapolations, counterpoise (CP) corrections, and explicitly correlated (F12b) methods. At the geometries tested, the explicitly correlated F12b method produced energies in close agreement with the estimated CBS limit. A second fit to 1757 data at the CCSD(T)-F12b/VTZ-F12 level was constructed with an estimated fitting error of less than 1.5?cm(-1). The second surface has a global nonpolar O-in minimum, two T-shaped N-in minima, and two polar minima. Barriers between these minima are small and some wave functions have amplitudes in several wells. Low-lying rovibrational wave functions and energy levels up to about 150?cm(-1) were computed on the F12b PES using a discrete variable representation/finite basis representation method. Calculated rotational constants and intermolecular frequencies are in very close agreement with experiment.     

Intermolecular electrostatic energies using density fitting

A method is presented to calculate the electron-electron and nuclear-electron intermolecular Coulomb interaction energy between two molecules by separately fitting the unperturbed molecular electron density of each monomer. This method is based on the variational Coulomb fitting method which relies on the expansion of the ab initio molecular electron density in site-centered auxiliary basis sets. By expanding the electron density of each monomer in this way the integral expressions for the intermolecular electrostatic calculations are simplified, lowering the operation count as well as the memory usage. Furthermore, this method allows the calculation of intermolecular Coulomb interactions with any level of theory from which a one-electron density matrix can be obtained. Our implementation is initially tested by calculating molecular properties with the density fitting method using three different auxiliary basis sets and comparing them to results obtained from ab initio calculations. These properties include dipoles for a series of molecules, as well as the molecular electrostatic potential and electric field for water. Subsequently, the intermolecular electrostatic energy is tested by calculating ten stationary points on the water dimer potential-energy surface. Results are presented for electron densities obtained at four different levels of theory using two different basis sets, fitted with three auxiliary basis sets. Additionally, a one-dimensional electrostatic energy surface scan is performed for four different systems (H2O dimer, Mg2+-H2O, Cu+-H2O, and n-methyl-formamide dimer). Our results show a very good agreement with ab initio calculations for all properties as well as interaction energies.     

A systematic ab initio study of the water dimer in hierarchies of basis sets and correlation models

A systematic, high-level ab initio investigation of the water dimer has been performed. The oxygen-oxygen bond distance has been estimated to be around 2.90 ?, about 0.05 ? shorter than the experimentally estimated distance, challenging the accuracy of the latter. The interaction energy has been obtained at −5.0±0.1 kcal/mol, which compares favourably with the experimentally estimated value of −5.4±0.7 kcal/mol. The importance of employing basis sets that include diffuse functions in correlated calculations on hydrogen-bonded systems is confirmed. In correlated calculations on the water dimer and the hydrogen fluoride dimer, the counterpoise-corrected interaction energies converge considerably slower towards the basis set limit than do the uncorrected energies, provided that the correlation-consistent basis sets are augmented with diffuse functions. Received: 12 February 1997 / Accepted: 5 June 1997     

Towards a force field based on density fitting

Total intermolecular interaction energies are determined with a first version of the Gaussian electrostatic model (GEM-0), a force field based on a density fitting approach using s-type Gaussian functions. The total interaction energy is computed in the spirit of the sum of interacting fragment ab initio (SIBFA) force field by separately evaluating each one of its components: electrostatic (Coulomb), exchange repulsion, polarization, and charge transfer intermolecular interaction energies, in order to reproduce reference constrained space orbital variation (CSOV) energy decomposition calculations at the B3LYP/aug-cc-pVTZ level. The use of an auxiliary basis set restricted to spherical Gaussian functions facilitates the rotation of the fitted densities of rigid fragments and enables a fast and accurate density fitting evaluation of Coulomb and exchange-repulsion energy, the latter using the overlap model introduced by Wheatley and Price [Mol. Phys. 69, 50718 (1990)]. The SIBFA energy scheme for polarization and charge transfer has been implemented using the electric fields and electrostatic potentials generated by the fitted densities. GEM-0 has been tested on ten stationary points of the water dimer potential energy surface and on three water clusters (n = 16,20,64). The results show very good agreement with density functional theory calculations, reproducing the individual CSOV energy contributions for a given interaction as well as the B3LYP total interaction energies with errors below kBT at room temperature. Preliminary results for Coulomb and exchange-repulsion energies of metal cation complexes and coupled cluster singles doubles electron densities are discussed.     

Mapping the interaction energy surfaces of cyclic alkanes: evaluating the transferability of an ab initio based potential model

Detailed interaction energy maps are computed for symmetric cyclopropane and tetrahedrane dimer systems using ab initio methods. Interaction energies of cubane and cyclohexane dimers are also reported. The global minimum energy structures of cyclopropane and tetrahedrane systems are both D(3d) structures with energies of -1.850 and -2.171 kcal mol(-1). The ability of NIPE potential model, based on ab initio nonbonding data of neopentane (N), isobutane (I), propane (P), ethane (E) and all their combinations to predict the pair interaction energies of these strained cyclic hydrocarbons is also investigated. The difference between the energies predicted by NIPE and those obtained from the ab initio calculations increases with ring strain In general, NIPE values are in close agreement with the ab initio results for alkane ring structures having low ring strain.     

Interpolating moving least-squares methods for fitting potential energy surfaces: an application to the H2CN unimolecular reaction

Classical trajectories have been used to compute rates for the unimolecular reaction H2CN-->H+HCN on a fitted ab initio potential energy surface (PES). The ab initio energies were obtained from CCSD(T)/aug-cc-pvtz electronic structure calculations. The ab initio energies were fitted by the interpolating moving least-squares (IMLS) method. This work continues the development of the IMLS method for producing ab initio PESs for use in molecular dynamics simulations of many-atom systems. A dual-level scheme was used in which the preliminary selection of data points was done using a low-level theory and the points used for fitting the final PES were obtained at the desired higher level of theory. Classical trajectories were used on various low-level IMLS fits to tune the fit to the unimolecular reaction under study. Procedures for efficiently picking data points, selecting basis functions, and defining cutoff limits to exclude distant points were investigated. The accuracy of the fitted PES was assessed by comparing interpolated values of quantities to the corresponding ab initio values. With as little as 330 ab initio points classical trajectory rate constants were converged to 5%-10% and the rms error over the six-dimensional region sampled by the trajectories was a few tenths of a kcal/mol.     

Interaction of CO with Kr: Potential energy surface and bound states

The first ab initio potential energy surface of the Kr-CO complex is developed using single and double excitation coupled-cluster theory with noniterative treatment of triple excitations. Mixed basis sets, aug-cc-pVQZ for the C and O atoms and aug-cc-pVQZ-PP for the Kr atom, with an additional (3s3p2d2f1g) set of midbond functions are used. The computed interaction energies in 336 configurations are analytically fitted to a two-dimensional potential model by a least squares fit. The potential has a minimum of -119.68 cm(-1) with Re=7.35a 0 at an approximate T-shaped geometry (theta e=98.5 degrees ). Bound state energies are calculated up to J=12, thus enabling a comprehensive comparison between theory and available experimental data as well as providing detailed guidance for future spectroscopic investigations of higher-lying states. The predicted transition frequencies and spectroscopic constants are in good agreement with the experimental results.     

Ab initio potential energy surface and bound states for the Kr-OCS complex

The first ab initio potential energy surface of the Kr-OCS complex is developed using the coupled-cluster singles and doubles with noniterative inclusion of connected triples [CCSD(T)]. The mixed basis sets, aug-cc-pVTZ for the O, C, and S atom, and aug-cc-pVQZ-PP for the Kr atom, with an additional (3s3p2d1f) set of midbond functions are used. A potential model is represented by an analytical function whose parameters are fitted numerically to the single point energies computed at 228 configurations. The potential has a T-shaped global minimum and a local linear minimum. The global minimum occurs at R = 7.146 a(0), θ = 105.0° with energy of -270.73 cm(-1). Bound state energies up to J = 9 are calculated for three isotopomers (82)Kr-OCS, (84)Kr-OCS, and (86)Kr-OCS. Analysis of the vibrational wavefunctions and energies suggests the complex can exist in two isomeric forms: T-shaped and quasi-linear. The calculated transition frequencies and spectroscopic constants of the three isotopomers are in good agreement with the experimental values.     

Ab initio intermolecular potential energy surface and second pressure virial coefficients of methane

A six-dimensional potential energy hypersurface (PES) for two interacting rigid methane molecules was determined from high-level quantum-mechanical ab initio computations. A total of 272 points for 17 different angular orientations on the PES were calculated utilizing the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory with basis sets of aug-cc-pVTZ and aug-cc-pVQZ qualities. The calculated interaction energies were extrapolated to the complete basis set limit. An analytical site-site potential function with nine sites per methane molecule was fitted to the interaction energies. In addition, a semiempirical correction to the analytical potential function was introduced to take into account the effects of zero-point vibrations. This correction includes adjustments of the dispersion coefficients and of a single-parameter within the fit to the measured values of the second virial coefficient B(T) at room temperature. Quantitative agreement was then obtained with the measured B values over the whole temperature range of the measurements. The calculated B values should definitely be more reliable at very low temperatures (T<150 K) than values extrapolated using the currently recommended equation of state.     

Theoretical investigation of the He-I2(E3Πg) ion-pair state: ab initio intermolecular potential and vibrational levels

We present a theoretical study on the potential energy surface and vibrational bound states of the E electronic excited state of the HeI(2) van der Waals system. The interaction energies are computed using accurate ab initio methods and large basis sets. Relativistic small-core effective core potentials in conjunction with a quintuple-zeta quality basis set are employed for the heavy iodine atoms in multireference configuration interaction calculations for the (3)A' and (3)A" states. For the representation of the potential energy surface we used a general interpolation technique for constructing potential surfaces from ab initio data based on the reproducing kernel Hilbert space method. The surface presents global and local minima for T-shaped configurations with well-depths of 33.2 and 4.6 cm(-1), respectively. Vibrational energies and states are computed through variational quantum mechanical calculations. We found that the binding energy of the HeI(2)(E) T-shaped isomer is 16.85 cm(-1), in excellent agreement with recent experimental measurements. In lieu of more experimental data we also report our predictions on higher vibrational levels and we analyze the influence of the underlying surface on them. This is the first attempt to represent the potential surface of such a highly excited electronic state of a van der Waals complex, and it demonstrates the capability of the ab initio technology to provide accurate results for carrying out reliable studies to model experimental data.     

Ab initio potential energy surface and spectrum of the B(3Pi) state of the HeI2 complex

The three-dimensional interaction potential for I2(B 3Pi0u+)+He is computed using accurate ab initio methods and a large basis set. Scalar relativistic effects are accounted for by large-core relativistic pseudopotentials for the iodine atoms. Using multireference configuration interaction calculations with subsequent treatment of spin-orbit coupling, it is shown for linear and perpendicular structures of the complex that the interaction potential for I2(B 3Pi0u+)+He is very well approximated by the average of the 3A' and 3A" interaction potentials obtained without spin-orbit coupling. The three-dimensional 3A' and 3A" interaction potentials are computed at the unrestricted open-shell coupled-cluster level of theory using large basis sets. Bound state calculations based on the averaged surface are carried out and binding energies, vibrationally averaged structures, and frequencies are determined. These results are found to be in excellent accord with recent experimental measurements from laser-induced fluorescence and action spectra of HeI2. Furthermore, in combination with a recent X-state potential, the spectral blueshift is obtained and compared with available experimental values.     

硝酸甲酯分子间相互作用的DFT和ab initio比较

用密度泛函理论(DFT)和从头算(ab initio)方法,分别在B3LYP/6 31G和HF/6 31G水平上求得硝酸甲酯三种二聚体的全优化几何构型和电子结构,并用6 311G和6 311＋＋G基组进行总能量计算.对HF/6 31G计算结果进行MP4SDTQ电子相关校正.在各基组下均进行基组叠加误差(BSSE)和零点能(ZPE)校正求得结合能.对6 31G优化构型作振动分析并基于统计热力学求得200～600 K温度下单体和二聚体的热力学性质.详细比较两种方法的相应计算结果,发现DFT求得的分子间距离较短,分子内键长较长,所得结合能均小于相应ab initio计算值.     

Potential-energy surface for the electronic ground state of NH3 up to 20,000 cm-1 above equilibrium

Ab initio coupled cluster calculations with single and double substitutions and a perturbative treatment of connected triple excitations [CCSD(T)] with the augmented correlation-consistent polarized valence triple-zeta aug-cc-pVTZ basis at 51 816 geometries provide a six-dimensional potential-energy surface for the electronic ground state of NH3. At 3814 selected geometries, CBS+ energies are obtained by extrapolating the CCSD(T) results for the aug-cc-pVXZ(X=T,Q,5) basis sets to the complete basis set (CBS) limit and adding corrections for core-valence correlation and relativistic effects. CBS** ab initio energies are generated at 51,816 geometries by an empirical extrapolation of the CCSD(T)/aug-cc-pVTZ results to the CBS+ limit. They cover the energy region up to 20,000 cm-1 above equilibrium. Parametrized analytical functions are fitted through the ab initio points. For these analytical surfaces, vibrational term values and transition moments are calculated by means of a variational program employing a kinetic-energy operator expressed in the Eckart-Sayvetz frame. Comparisons against experiment are used to assess the quality of the generated potential-energy surfaces. A "spectroscopic" potential-energy surface of NH3 is determined by a slight empirical adjustment of the ab initio potential to the experimental vibrational term values. Variational calculations on this refined surface yield rms deviations from experiment of 0.8 cm-1 for 24 inversion splittings and 0.4 (3.0) cm-1 for 34 (51) vibrational term values up to 6100 (10,300) cm-1.