Volume 113, Issue 13, 01 October 2000
 ARTICLES

 Theoretical Methods and Algorithms

Accurately solving the electronic Schrödinger equation of atoms and molecules by extrapolating to the basis set limit. I. The helium dimer
View Description Hide DescriptionA new formula, to extrapolate energies, (that arise when the basis set is truncated at a finite angular momentum quantum number, L) to the limit, E, is derived and applied to the computation of the pair potential of He. Large basis sets up to daugccpV5Z and 6Z are used, and in addition, a new ccpV7Z set is presented. The fullCI is approximated using the “multireference averaged coupledpair functional” (MRACPF) with 121 references. The calculated molecular constants of are in excellent agreement with those recently obtained with [R. J. Gdanitz, Mol. Phys. 96, 1423 (1999)], but they agree only fairly with the completeCI estimate of van Mourik and Dunning [J. Chem. Phys. 111, 9248 (1999)]. The potential of Komasa [J. Chem. Phys. 110, 7909 (1999)] which has been calculated with the “exponentially correlated Gaussians” method does not give a bound state. The sensitivity of the molecular constants 〈R〉 and to errors of the interaction potential at different distances is estimated by perturbing the potential by Gaussian functions. The region of is found to be most sensitive. From this analysis, doubts arise that recent calculations (including the present one) are accurate enough to allow the molecular constants to be determined to better than ≈10%.

CC2 excitation energy calculations on large molecules using the resolution of the identity approximation
View Description Hide DescriptionA new implementation of the approximate coupled cluster singles and doubles method CC2 is reported, which is suitable for large scale integraldirect calculations. It employs the resolution of the identity (RI) approximation for twoelectron integrals to reduce the CPU time needed for calculation and I/O of these integrals. We use a partitioned form of the CC2 equations which eliminates the need to store double excitation cluster amplitudes. In combination with the RI approximation this formulation of the CC2 equations leads to a reduced scaling of memory and disk space requirements with the number of correlated electrons and basis functions to, respectively, and compared to in previous implementations. The reduced CPU, memory and disk space requirements make it possible to perform CC2 calculations with accurate basis sets on large molecules, which would not be accessible with conventional implementations of the CC2 method. We present an application to vertical excitation energies of alkenes for and report results for the lowest lying dipoleallowed transitions for the TZVPP basis sets, which for contain 1108 basis functions. Comparison with conventional CC2 results for the smaller alkenes show that for CC2 ground stateenergies and for excitation energies of valence states, the error due to the RI approximation is negligible compared to the usual basis set error, if auxiliary basis sets are used, which have been optimized for MP2 energy calculations.

Structural decomposition of the chemical shielding tensor: Contributions to the asymmetry, anisotropy, and orientation
View Description Hide DescriptionThe nine elements of chemical shielding tensors contain important information about local structure, but the extraction of that information is difficult. Here we explore a semiempirical method that has the potential for providing relatively accessible structural correlations. The approach entails approximating the fieldinduced electron current density as entirely perpendicular to the applied field. This has two interesting consequences. (1) The resulting shielding tensor is perfectly symmetric. Thus, asymmetry in a shielding tensor is an indication of current density that is not orthogonal to the applied field. (2) The orientation dependence of the chemical shielding at a point of interest is related explicitly to the isotropic average of the chemical shielding at every point in the surrounding region. This suggests a relatively simple relationship between the orientation dependence of the chemical shielding and the molecular structure. Good correlation with experimental tensors is obtained with just one or two adjustable parameters in several series of compounds, including silicates, phosphates, hydrogen bonds, carboxyls, and amides. As expected, the results indicate that for a given center, the contribution to the shielding anisotropy that is associated with each bonded neighbor increases as the number of electrons at either the center or the neighbors increases.

The quantum vibrational dynamics of clusters
View Description Hide DescriptionThe centroid molecular dynamics technique is applied to the case of chloride–water clusters to estimate their finite temperature quantum vibrational structure. We employ the flexible RWK2 water potential [J. R. Reimers, R. O. Watts, and M. L. Klein, Chem. Phys. 64, 95 (1982)] and the parametrization of a chloride–water interaction potential of Dorsett, Watts and Xantheas [J. Phys. Chem. A 103, 3351 (1999)]. We then investigate the temperaturedependent vibrational structure (infrared spectra). We find that the centroid molecular dynamics technique is capable of recovering a majority of the red shift associated with hydrogen bonding.

Direct calculation of the oneelectron density matrix for closedshell systems
View Description Hide DescriptionIt has been found that independent parameters in the variation of a oneelectron density matrix (DM) for closedshell systems are elements of its unitary transformed matrix and, in a special case, reduce to the rotation parameters that connect the occupied and virtual orbital spaces in the exponential transformed selfconsistent field method. To obtain the unitary matrix of transformation, a simpler method of orthogonalizing the column vectors of the DM has been proposed instead of its diagonalization. An iterative method has been formulated to determine these independent parameters. Several test calculations using this method reproduced the results using the Hartree–Fock–Roothaan method.

Kohn–Sham calculations using hybrid exchangecorrelation functionals with asymptotically corrected potentials
View Description Hide DescriptionThe theory is presented for asymptotically correcting the potentials of hybrid exchangecorrelation functionals, i.e., those that include a fraction of orbital exchange. The Kohn–Sham equations involve a multiplicative potential due to the continuum part of the hybrid functional and a nonmultiplicative term due to the orbital exchange. In asymptotic regions the multiplicative spin potential is corrected to take the form where is the fraction of orbital exchange; is the spin selfconsistent highest occupied Kohn–Sham eigenvalue; and is an approximate ionization energy. For the hydrogen atom, the asymptotic correction leads to a potential that closely resembles the exact potential; the eigenvaluespectrum is intermediate between the Schrödinger and Hartree–Fock eigenvalues, reflecting the presence of orbital exchange. Kohn–Sham orbitals and eigenvalues determined from this procedure have been used to calculate singlet vertical excitation energies for CO, and The correction significantly improves excitation energies to Rydberg states, with mean absolute errors below 0.2 eV. However, despite including orbital exchange, the results do not represent an improvement over the results obtained by asymptotically correcting a recently developed GGA functional. The asymptotic correction is also shown to reduce static isotropic polarizabilities.

Quaternion formulation of diffusion quantum Monte Carlo for the rotation of rigid molecules in clusters
View Description Hide DescriptionA quaternion formulation is used to derive an algorithm for performing calculations on molecular clusters using the quantum diffusionMonte Carlo method. It is assumed that the monomers in the cluster rotate and translate as rigid bodies. The algorithm is tested on the water dimer and the benzene–water cluster. Comparison with dissociation energies and rotational constants obtained with other methods illustrates the accuracy of the algorithm.

Determination of vibrational polarizabilities and hyperpolarizabilities using fieldinduced coordinates
View Description Hide DescriptionAn analytical set of fieldinduced coordinates (FICs) is defined. It is shown that, instead of normal coordinates, a relatively small number of FICs is sufficient to describe the vibrational polarizability and hyperpolarizabilities due to nuclear relaxation. The fact that the number of FICs does not depend upon the size of the molecule leads to computational advantages. A method is provided for separating anharmonic contributions from harmonic contributions as well as effective mechanical from electrical anharmonicity. Hartree–Fock calculations on a dozen representative conjugated molecules illustrate the procedures and indicate that anharmonicity can be very important. Other potential applications including the determination of zeropoint vibrational averaging corrections are noted.

Fourier grid Hamiltonian multiconfigurational selfconsistentfield: A method to calculate multidimensional hydrogen vibrational wavefunctions
View Description Hide DescriptionThe Fourier Grid Hamiltonian Multiconfigurational SelfConsistentField (FGHMCSCF) method for calculating vibrational wavefunctions is presented. This method is designed to calculate multidimensional hydrogen nuclear wavefunctions for use in mixed quantum/classical molecular dynamics simulations of hydrogen transfer reactions. The FGHMCSCF approach combines a MCSCF variational method, which describes the vibrational wavefunctions as linear combinations of configurations that are products of onedimensional wavefunctions, with a Fourier grid method that represents the onedimensional wavefunctions directly on a grid. In this method a full configuration interaction calculation is carried out in a truncated onedimensional wavefunction space [analogous to complete active space selfconsistentfield (CASSCF) in electronic structure theory]. A stateaveraged approach is implemented to obtain a set of orthogonal multidimensional vibrational wavefunctions. The advantages of the FGHMCSCF method are that it eliminates the costly calculation of multidimensional integrals, treats the entire range of the hydrogen coordinates without bias, avoids the expensive diagonalization of large matrices, and accurately describes ground and excited state hydrogen vibrational wavefunctions. This paper presents the derivation of the FGHMCSCF method, as well as a series of test calculations on systems comparing its performance with exact diagonalization schemes.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Large amplitude vibrations in the state of
View Description Hide DescriptionA threedimensional potential energy function (PEF) of the electronic ground state of has been generated by electronic structure calculations. The PEF possesses a minimum in an isosceles triangular structure which lies 2204 cm^{−1} below two equivalent minima having linear equilibrium geometry. The barrier height between the minima relative to the triangular structure has been calculated to the 2383 cm^{−1}. The nuclear motion problem has been solved variationally in Jacobi coordinates for and 1. Ten vibrational states of and nine of symmetry are calculated to lie below the linear minima. The permutational splitting between the and states in the linear has been calculated to be 0.064 cm^{−1}, in this is 0.530 cm^{−1}. Above the energy of the barrier to linearity there are large amplitude vibrations with triangular structure character. In the dense stack of such states vibrational modes of the linear structure are discernible, including their permutational splittings.

Evidence for fluorescence from jetcooled 3methylindolepolar solvent complexes
View Description Hide DescriptionThe ratio of nonresonant twophoton induced fluorescence excitation spectra using circularly and linearly polarized light for jetcooled 3methylindole complexed with a series of increasingly basic hydrogen bond acceptors (water, methanol, ethanol, diethylether, diethylamine and triethylamine) is consistent with an avoided crossing of the two lowest excited singlet states, and The dispersed fluorescence of these from this series also reflects the crossing, providing a definitive jetcooled fluorescencespectrum. The jetcooled fluorescencespectrum is not broad and redshifted, but has vibronic structure that agrees well with ab initio predictions and is similar to that of phosphorescence.

Electronic excitation and ionization spectra of cyclopentadiene: Revisit by the symmetryadapted cluster–configuration interaction method
View Description Hide DescriptionElectronic excitation and ionizationspectra of cyclopentadiene (CP) were reinvestigated by the symmetryadapted cluster (SAC) and SAC–configuration interaction (SACCI) method with an extended basis set and a wide active orbital space. To give a satisfactory interpretation of the general profile of the observed excitation spectrum, 40 lowlying excited singlet and triplet states (with excitation energies of up to 9.5 eV) were computed. The calculated excitation energies were greatly improved compared to those reported previously. All of the peaks in the experimental spectrum were reassigned theoretically with small deviations. The natures of the lowlying valence and Rydbergexcited states were discussed in detail, and the results were also compared with those of some other recent theoretical studies. The ionization energies calculated by the SACCI generalR method agree well with the experimental peaks in the photoelectron spectrum. A number of twoelectron shakeup states were calculated below 23 eV.

Theoretical characterization of the structures and properties of phenol complexes
View Description Hide DescriptionExtensive ab initio calculations at different levels of theory have been performed with the basis set. Three minimum energy structures of (a), (b), and (c) were found on the ground and excited state surfaces of the phenol– complex, with cyclic structure (a) being the most stable. Experimentally inferred very low frequencies for intermolecular vibrations in were reproduced using the present calculations. The high vibrational mode density resulting from very low frequency vibrations of the structure (b) may be responsible for a broad electronic origin in the spectra of the phenol– complex. The intermolecular interaction has little influence on the structures of phenol and water, but a significant change is found in the properties upon complexation. The intramolecular vibrations, which have frequencies of the magnitude of the intermolecular vibrations or involve the OH group of phenol, are significantly affected by formation of complex. All of these have been discussed in detail.

Comparative ab initio study of the structures, energetics and spectra of clusters
View Description Hide Descriptionhave been studied using high level ab initio calculations. This extensive work compares the structures of the different halide water clusters and has found that the predicted minimum energy geometries for different cluster are accompanied by several other structures close to these global minima. Hence the most highly populated structures can change depending on temperature due to the entropy effect. As the potential surfaces are flat, the wideranging zero point vibrational effects are important at 0 K, and not only a number of lowlying energy conformers but also large amplitude motions can be important in determining structures, energies, and spectra at finite temperatures. The binding energies, ionization potentials, chargetransfertosolvent (CTTS) energies, and the O–H stretching frequencies are reported, and compared with the experimental data available. A distinctive difference between and is noted, as the former tends to favor internal structures with negligible hydrogen bonding between water molecules, while the latter favors surface structures with significant hydrogen bonding between water molecules. These characteristics are well featured in their O–H spectra of the clusters. However, the spectra are forced to be very sensitive to the temperature, which explains some differences between different spectra. In case of a significant charge transfer is noted in the ground state, which results in much less significant charge transfer in the excited state compared with other hydrated halide clusters which show near full charge transfers in the excited states. Finally, the nature of the stabilization interactions operative in these clusters has been explained in terms of manybody interaction energies.

Vibrational spectra and electron detachment energy of the anionic water hexamer
View Description Hide DescriptionA number of experimental and theoretical studies have been carried out on the anionic water hexamer in the last decade. However, none of these studies have reported the adiabatic electron detachment energy. The present study employing extensive highlevel ab initio calculations report the adiabatic electron detachment energy, which explains the unusual stability of the anionic water hexamer. This stability can be correlated to the unusually intense peak observed in the photoelectrondetachment spectra. It is also shown that our previously predicted pyramid structure reproduces the important characteristics of the experimental O–H vibrational spectra.

Rotational spectroscopy of and the systematics of intermolecular electron transfer in the series B⋯BrCl, where B=CO, HCN, and
View Description Hide DescriptionGroundstate rotational spectra of the isotopomers and of the phosphine–bromine monochloride complex were observed by the pulsedjet, Fouriertransform method, incorporating a mixing nozzle to preclude reaction among the component gases. Each isotopomer exhibited a symmetrictoptype spectrum which yielded accurate values of the spectroscopic constants and on analysis. Interpretations of the changes in the values with isotopomer showed that the intermolecular bond involves P and Br, with and that the BrCl bond increases in length by ∼0.04 Å on complex formation. Changes in the halogen nuclear quadrupole coupling constants when is formed lead, with the aid of the Townes–Dailey model, to the conclusion that a fraction of an electron is transferred from P to Br on complex formation, while the polarization of BrCl by can be viewed as the transfer of from Br to Cl, leading to a net change of in the population of the orbital of Br. The complex is only of moderate strength, with an intermolecular stretching force constant Values of similarly determined, for the series B⋯BrCl, where B=CO, HCN, or are presented. It is shown that the variation of with the ionization energy of the Lewis base B can be described by an expression This behavior is compared with that for the corresponding series B⋯ICl.

Multiple dynamical pathways in the reaction: A comprehensive crossed beam study
View Description Hide DescriptionIn this report, the reaction has been reinvestigated using universal crossed molecular beam methods. Angular resolved timeofflight spectra have been measured for various reaction channels of the title reaction: and Different product angular distributions have been observed for these product channels, indicating that these reaction channels occur via distinctive dynamical pathways. This study provides an excellent example of multiple dynamical pathways in a single chemical reaction, which opens enormous opportunities in investigating the dynamics of complicated chemical reactions that are important in combustion and atmospheric chemistry, and also provides a link between kinetics studies and dynamical research.

Reaction dynamics of with Harpoontype mechanism for highly excited states
View Description Hide DescriptionUsing a pump–probe technique, the reactions of with have been measured to yield similar rotational distributions of as that obtained for the reaction of the state with A series of measurements is conducted to clarify that the reactions are initiated directly by these higher states, rather than occurring from the lower state following radiative and collisional relaxation. The reactivity of the Mg state with is found to be comparable to that of the state, but about three times larger than that of the state. The reactions proceed via a harpoontype process, and are closely associated with the reaction coordinate through evolution of a series of surface crossings. To support our suggestion that the harpoon mechanism is involved, the cross sections of collisional deactivation by for various excited states are measured. The ratios of cross sections observed for the and state, equal to 1:2.85:4.3, are consistent with the calculated prediction of 1:2.62:4.24. The calculated cross sections are based on a simple hard sphere model with effective radii evaluated differently. Here, the effective radii for the higher states are determined from the crossing of ionic and covalent curves, while the radius is estimated from the nonadiabatic crossing between the reactive state and the ground state. Consistency between observation and prediction confirms that the harpoon mechanism proposed in this work is plausible.

Structures of the linear silicon carbides and Isotopic substitution and Ab Initio theory
View Description Hide DescriptionThe structures of two linear siliconcarbides, and have been determined by a combination of isotopic substitution and largescale coupledclusterab initio calculations, following detection of all of the singly substituted isotopic species in a supersonic molecular beam with a Fourier transformmicrowave spectrometer.Rotational constants obtained by leastsquares fitting transition frequencies were used to derive experimental structures; except for those nearest the center of mass, individual bond lengths for both chains have an error of less than 0.008 Å. Accurate equilibrium structures were derived by converting the experimental rotational constants to equilibrium constants using the vibration–rotation coupling constants from coupledcluster calculations, including connected triple substitutions. Equilibrium dipole moments and harmonic vibrational frequencies were also calculated for both chains. On the basis of the calculated vibration–rotation and ltype doubling constants, weak rotational satellites from a lowlying vibrational state of were assigned to a bending mode calculated to lie about 205 cm^{−1} above the ground state. A recommended ab initio equilibrium structure for has also been established.

Structure and vibrational spectra of Is the excess proton in a symmetrical hydrogen bond?
View Description Hide DescriptionThe energetics, structure, and vibrational spectra of a wide variety of structures are calculated using density functional theory and secondorder Møller–Plesset ab initio methods. In these isomers of the local environment of the excess proton sometimes resembles a symmetric structure and sometimes but many structures are intermediate between these two limits. We introduce a quantitative measure of the degree to which the excess proton resembles or Other bond lengths and, perhaps most useful, the position of certain vibrational bands track this measure of the symmetry in the local structure surrounding the excess proton. The general trend is for the most compact structures to have the lowest energy. However, adding zeropoint energy counteracts this trend, making prediction of the most stable isomer impossible at this time. At elevated temperatures corresponding to recent experiments and atmospheric conditions (150–200 K), calculated Gibbs free energies clearly favor the least compact structures, in agreement with recent thermal simulations [Singer, McDonald, and Ojamäe, J. Chem. Phys. 112, 710 (2000)]. © 2000 American Institute of Physics.