Volume 104, Issue 7, 15 February 1996
Index of content:

Poling behavior of optical absorption spectra in carbazoles with one‐ and two‐dimensional charge‐transfer character
View Description Hide DescriptionSpectral change in optical absorption due to molecular alignment induced by electric poling has been studied experimentally and theoretically, in one‐ and two‐dimensional charge‐transfer carbazole molecules. After poling, an increase in absorbance at λ_{max} was observed in 3,6‐dinitrocarbazoles which present a two‐dimensional charge‐transfer character, while the absorbance at λ_{max} decreased in 3‐monosubstituted carbazoles which possess a one‐dimensional charge‐transfer character. From molecular‐orbital calculations and evaluations of the molecular polarizabilityspectra for random and uniaxial orientations of the molecules, an explanation is provided for the poling behavior in terms of the vector directions of the transition and ground‐state dipole moments of the molecules. Theoretical investigation of various conformers has been made, resulting in the suggestion that the poling behavior of absorption spectra should be strongly affected by the conformation of the acceptor groups in the case of disubstituted carbazoles.

Comparative studies of triplet monocyclic aromatic diazines under pressure
View Description Hide DescriptionWe report a zero‐field optically detected magnetic resonance study under high pressure for triplet pyrimidine in benzene, pyrazine in benzene and in p‐dichlorobenzene, and s‐tetramethylpyrazine in durene. Generally, the pressure sensitivity of the zero‐field splitting (ZFS) parameter D, ∂D/∂P, for these compounds is much higher than that for quinoxaline. This is rationalized in terms of a smaller π‐electron cloud in the monocyclics than in quinoxaline. For pyrazine and pyrimidine, the ^{3} nπ* nature of the lowest triplet leads to a larger spin–orbit contribution to the pressure shift. We observed a larger change in the ZFS parameter E for pyrazine in benzene than in dichlorobenzene. This is explained by the difference in crystalline packing between the two host lattices. There is a large change in D and a multiplet splitting under high pressure for tetramethylpyrazine. These are ascribed to the presence of a pseudo‐Jahn–Teller interaction in this molecule.

Vibrational hyperpolarizabilities and the Kerr effect in CH_{4}, CF_{4}, and SF_{6}
View Description Hide DescriptionThe hyperpolarizabilities γ of CH_{4}, CF_{4}, and SF_{6} were measured by the dc Kerr effect at wavelengths from 457.9 to 1092 nm. Vibrational hyperpolarizabilities γ^{ v } were obtained by combining these measurements with electric‐field‐induced second harmonic generation (ESHG) measurements. The vibrational contribution to the hyperpolarizability ranges from 6% to 35% of the total. At high optical frequency the difference between γ^{ v } for Kerr and γ^{ v } for ESHG is approximately constant, and has values 18, 31, and 51×10^{−63} C^{4} m^{4} J^{−3} for CH_{4}, CF_{4}, and SF_{6}, respectively. The experimental results are in good quantitative agreement with the results of recent ab initio calculations of the frequency dependence of γ^{ v } for CH_{4}, except for a small but non‐negligible discrepancy at high frequency.

Continuous slit‐jet infrared spectrum of the CO–N_{2} complex
View Description Hide DescriptionThe weakly bound complex CO–N_{2} has been studied in the 4.7 μm infrared region of the CO stretching vibration using a continuous slit‐jet supersonic expansion and a tunable diode laserspectrometer. A total of 152 lines were observed and assigned to four connected subbands with K=0←1, 0←0, 1←0, and 2←1, and to one unconnected subband with K=1←1. Analysis of these bands yielded K‐state origins, rotational parameters, and centrifugal distortion parameters. The effective intermolecular separation for the complex in its ground state was found to be 4.025 Å, and predictions of rotational frequencies were made to aid in the search for CO–N_{2}microwave transitions. The spectra observed were surprisingly simple and well behaved, to the extent that they could virtually be ascribed to a (fictitious) complex of CO with a rare gas atom having a mass of 28 a.m.u. This simplicity may be explained by postulating that the N_{2} undergoes relatively free internal rotation in the complex. All but one of the observed bands involve levels which correlate with the rotationless J=0 state of ortho‐N_{2}. Further spectroscopic work in the infrared and microwave regions should be combined with theoretical studies in order to learn more about the orientational structure and intermolecular potential of this atmospherically relevant system.

A comparison of time‐ and frequency‐domain resonance Raman spectroscopy in triiodide
View Description Hide DescriptionA common model for the photodissociative potential surfaces of the triiodide ion in ethanol is used to simulate both the spontaneous resonance Raman (RR) spectra and the femtosecond resonant impulsive stimulated Raman scattering (RISRS) signals for comparison with experimental data. The Fourier transforms of the RISRS signals, while resembling RR spectra, are not the same either theoretically or experimentally, and these differences are only partly due to the finite spectral bandwidth of the pulses in the RISRS experiment. The RISRS signals vary much more strongly with wavelength than do the RR spectra. Direct Fourier transformation of the RISRS signals with a fixed phase tends to diminish the apparent contributions of weaker components due to the different phases of different oscillations. Linear prediction singular value decomposition (LPSVD) is shown to give a more faithful representation of the RISRS power spectra by eliminating the phase problem, but there are still significant differences between the RR and LPSVD‐RISRS spectra. Our model, which includes a large number of combination bands between triiodide vibrations and a low frequency solvent or intermolecular mode, gives a good representation of both the experimental RR profiles and the 308 nm RISRS data of Banin et al. [U. Banin, R. Kosloff, and S. Ruhman, Isr. J. Chem. 33, 141 (1993)].

Polymorphism of a glass forming plastic crystal: A kinetic investigation
View Description Hide DescriptionThe glassy crystalline state designates the frozen state of the rotator phase of some molecular crystals. These systems are very suitable for investigating the vitrification and the crystallization processes as well as the interrelations between these two processes. This paper sheds light on this problem through a kinetic investigation of the glass forming plastic crystal (cyanoadamantane)_{1−x } (chloroadamantane)_{ x } for x=0.25. A careful study of both the equilibrium phase diagram and the mode of transformation upon deep quenching conditions has been performed by time resolved x‐ray diffraction and differential scanning calorimetry in a variety of thermal treatments. The results reveal a complex kinetic behavior corresponding to the imbrication of the kinetics toward two low temperature phases: (IV) and (III). Phase (IV) is found to be metastable with respect to phase (III) and only appears upon specific thermal treatments which are clearly established. The conditions in which the monotropic transition between the transient metastable phase (IV) and the undercooled rotator phase (I) can be seen are described.

The effect of spin decoupling on line shapes in solid‐state nuclear magnetic resonance
View Description Hide DescriptionExperimental and theoretical aspects of carbon‐13 line shapes in static solids are described for on‐resonance spin decoupling conditions. A relatively simple theoretical approach is provided for describing line shapes in static solids based on an operator representation of static second‐order perturbation theory and theoretical line shapes in I _{2} S and I _{ nS } systems are calculated. The line shapes are predicted to comprise a single center line and ‘‘decoupling sidebands’’ on each side of the center line which move outward and diminish in amplitude as the decoupling field is increased. The predicted behavior is confirmed by experiments on an isolated seven spin system, where the decoupling sidebands are observed directly, and some organic solids in which the decoupling sidebands are not observed directly but in which their presence can be deduced from the behavior of the center line. A comparison is made between the theoretical predictions based on a complete quantum mechanical treatment and the predictions made using classical approximations in the model for the line shape. We conclude, based on our experimental results, that the line shape has a character which reflects the quantum nature of the spin system, even in organic solids, and that on‐resonance terms appear to dominate experimental line shapes.

Solvation and solvent effects on the short‐time photodissociation dynamics of CH_{2}I_{2} from resonance Raman spectroscopy
View Description Hide DescriptionResonanceRaman spectra of CH_{2}I_{2} have been obtained at excitation wavelengths of 369, 355, and 342 nm in cyclohexane solution and in methanol solution at excitation wavelengths of 355 and 342 nm. ResonanceRaman spectra were also measured for CH_{2}I_{2} in the vapor phase with an excitation wavelength of 355 nm. The resonanceRaman spectra of CH_{2}I_{2} exhibit most of their intensity in fundamentals, overtones, and combination bands of modes nominally assigned as the I–C–I symmetric stretch, the I–C–I bend, and the I–C–I antisymmetric stretch vibrations. The absorption spectra and resonance Raman intensities of the gas phase and methanol solution phase diiodomethane spectra were simulated using a simple model and time‐dependent wave packet calculations. Normal mode coefficients from normal coordinate calculations were used to convert the motion of the wave packet on the excited electronic statesurface from dimensionless normal coordinates into internal coordinates of the molecule. The short‐time photodissociation dynamics of diiodomethane in the vapor phase shows that the two C–I bonds are lengthening by the same amount, the I–C–I angle becomes smaller, the H–C–I angles become larger, and the H–C–H angle becomes smaller.
The two C–I bonds appear essentially equivalent in the Franck–Condon region of the gas phase photodissociation which implies that the molecule chooses which C–I bond is broken after the wave packet has left the Franck–Condon region of the potential energy surface. Comparison of the gas phase resonanceRaman spectrum with solution phase spectra obtained in cyclohexane and methanol solvents reveals that the short‐time photodissociation dynamics are noticeably changed by solvation with a large solvent‐induced symmetry breaking observed. In the Franck–Condon region of the solution phase diiodomethane photodissociation in methanol solvent the two C–I bond become larger by differing amounts, the I–C–I angle becomes smaller, the H–C–H angle becomes smaller, and the H–C–I angles differ from the corresponding gas phase values. During the initial stages of the solution phase photodissociation (at least in methanol and cyclohexane solvents) the two C–I bonds are not the same and this suggests that the molecule chooses which C–I bond will be broken soon after photoexcitation.

Potential energy surface for interactions between N_{2} and He: Ab initio calculations, analytic fits, and second virial coefficients
View Description Hide DescriptionAn ab initiopotential energy surface (PES) for the interaction of rigid N_{2} with He is calculated by supermolecular fourth‐order Mo/ller–Plesset perturbation theory. The computations involve full counterpoise corrections and large basis sets including bond functions. The 61 ab initio points on the PES are fitted to a 21‐parameter algebraic form with an average absolute error of 0.39% and a maximum error less than 1.2%. The characteristics of the fitted PES are compared with those of previous surfaces. Unlike the older surfaces, our PES has the anisotropy thought to be required for a proper description of experimental data. Pressure second virial coefficients are calculated from our surface and compared with experimental values.

The photoionization of large pure and doped helium droplets
View Description Hide DescriptionThe photoionization of neutral liquid heliumdroplets (mean particle number 〈N〉=10^{2}–10^{7}) was studied using synchrotron radiation at photon energies ranging from 15 to 30 eV. Mass spectra as well as total and mass selective ion yields were measured as a function of the photon energy for different droplet sizes. The experiments indicate that ionization occurs not only by a direct process at photon energies above the atomic ionization potential but also at energies below the threshold by an autoionization process. The latter ionization mechanism proceeds via the electronically excited states of the neutral droplet, which show a strong neutral droplet size dependence. For large neutral droplets He_{ N }(〈N〉≳10^{4}) retarding field measurements established that a predominant part of the total ion yield results from larger cluster ions He^{+} _{ k }(k≳10^{3}). These measurements also show that a decay by fluorescence emission is much more probable than one by ionization following the photoexcitation process. In droplets with embedded SF_{6} molecules these are ionized indirectly by Penning ionization via excitons which leads to a large ion signal on the mass of the embedded species. No evidence for direct photoionization of the impurities was found.

Surface diffusivities and reaction rate constants: Making a quantitative experimental connection
View Description Hide DescriptionFor diffusion‐controlled reactions in three dimensions, continuum mechanics provides a quantitative relation between the steady‐state reaction rate constantk and the diffusion coefficient D. However, this approach fails in two dimensions, where no steady‐state solution exists on an infinite domain. Using both Monte Carlo methods and analytical techniques, we show that previous attempts to circumvent this problem fail under real laboratory conditions, where fractional coverages often exceed 10^{−3}. Instead, we have developed a rigorous and general relation between k and D for all coverages on a square lattice for the reactionA+A→A _{2}. For short times or high coverages, the relation k=πD/γ holds exactly, where γ denotes the two‐dimensional packing fraction. For lower coverages, however, k depends on time in both constant‐coverage (adsorption allowed) and transient‐coverage (adsorption forbidden) regimes. In both cases, k decreases in response to the evolution of nonrandom adsorbate configurations on the surface. These results indicate that diffusion‐limited surface reactions may be identified unambiguously in the laboratory and also provide a quantitative link between diffusion parameters and experimentally determined recombination rate parameters. Practical experimental methods highlighting such effects are outlined.

Ab initio study of electronic, structural, and vibrational properties of the Si_{4}C cluster
View Description Hide DescriptionUsing Möller–Plesset second‐order perturbation theory (MP2) for the geometry optimizations, we have examined various structural possibilities for the Si_{4}C cluster. The energies of the MP2‐optimized structures have been calculated using singles and doubles coupled cluster (CCSD) theory and the CCSD (T) method. The structure of lowest energy is a C _{3V } symmetric trigonal pyramid made from four silicons and one carbon atom in a face capping position. Very close in energy (around 5 kcal/mol) lies an isomer with C _{2V } symmetry, resembling the pyramid of the previous structure but with the carbon atom in an edge capping position this time. Both of these structures are closely related to the Si_{5}ground statestructure. Planar and linear structures analogous to C_{5} and C_{4} lie higher in energy and they are transition states in most of the cases examined. To help future experimental tests of our present results, we have computed, at the MP2‐level, the harmonic frequencies, infrared intensities, and isotopic shifts for the two lowest‐lying isomers. Dipole moments and 1s core electron energy shifts are also given. The building up principle we have recently suggested from a study of the Si_{3}C_{3} clusters is found to be fully operative for the Si_{4}C cluster.

Perturbative treatment of triple excitations in coupled‐cluster calculations of nuclear magnetic shielding constants
View Description Hide DescriptionA theory for the calculation of nuclear magnetic shielding constants at the coupled‐cluster singles and doubles level augmented by a perturbative correction for connected triple excitations (CCSD(T)) has been developed and implemented. The approach, which is based on the gauge‐including atomic orbital (GIAO) ansatz, is illustrated by several numerical examples. These include a comparison of CCSD(T) and other highly correlated methods with full configuration interaction for the BH molecule, and a systematic comparison with experiment for HF, H_{2}O,NH_{3}, CH_{4}, N_{2}, CO, HCN, and F_{2}. The results demonstrate the importance of triple excitations in establishing quantitative accuracy. Finally, the ability of GIAO‐CCSD(T) to make accurate predictions for difficult cases is explored in calculations for formaldehyde (CH_{2}O), diazomethane(CH_{2}NN), and ozone (O_{3}).

A general method for constructing multidimensional molecular potential energy surfaces from ab initio calculations
View Description Hide DescriptionA general interpolation method for constructing smooth molecular potential energy surfaces (PES’s) from ab initio data are proposed within the framework of the reproducing kernel Hilbert space and the inverse problemtheory. The general expression for an a posteriori error bound of the constructed PES is derived. It is shown that the method yields globally smooth potential energy surfaces that are continuous and possess derivatives up to second order or higher. Moreover, the method is amenable to correct symmetry properties and asymptotic behavior of the molecular system. Finally, the method is generic and can be easily extended from low dimensional problems involving two and three atoms to high dimensional problems involving four or more atoms. Basic properties of the method are illustrated by the construction of a one‐dimensional potential energy curve of the He–He van der Waals dimer using the exact quantum Monte Carlo calculations of Anderson et al. [J. Chem. Phys. 99, 345 (1993)], a two‐dimensional potential energy surface of the HeCO van der Waals molecule using recent ab initio calculations by Tao et al. [J. Chem. Phys. 101, 8680 (1994)], and a three‐dimensional potential energy surface of the H^{+} _{3} molecular ion using highly accurate ab initio calculations of Röhse et al. [J. Chem. Phys. 101, 2231 (1994)]. In the first two cases the constructed potentials clearly exhibit the correct asymptotic forms, while in the last case the constructed potential energy surface is in excellent agreement with that constructed by Röhse et al. using a low order polynomial fitting procedure.

A complete basis set model chemistry. V. Extensions to six or more heavy atoms
View Description Hide DescriptionThe major source of error in most ab initio calculations of molecular energies is the truncation of the one‐electron basis set. Extrapolation to the complete basis set second‐order (CBS2) limit using the N ^{−1} asymptotic convergence of N‐configuration pair natural orbital (PNO) expansions can be combined with the use of relatively small basis sets for the higher‐order (i.e., MP3, MP4, and QCI) correlation energy to develop cost effective computational models. Following this strategy, three new computational models denoted CBS‐4, CBS‐q, and CBS‐Q, are introduced. The mean absolute deviations (MAD) from experiment for the 125 energies of the G2 test set are 2.0, 1.7, and 1.0 kcal/mol, respectively. These results compare favorably with the MAD for the more costly G2(MP2), G2, and CBS‐QCI/APNO models (1.6, 1.2, and 0.5 kcal/mol, respectively). The error distributions over the G2 test set are indistinguishable from Gaussian distribution functions for all six models, indicating that the rms errors can be interpreted in the same way that experimental uncertainties are used to assess reliability.
However, a broader range of examples reveals special difficulties presented by spin contamination, high molecular symmetry, and localization problems in molecules with multiple lone pairs on the same atom. These characteristics can occasionally result in errors several times the size expected from the Gaussian distributions. Each of the CBS models has a range of molecular size for which it is the most accurate computational model currently available. The largest calculations reported for these models include: The CBS‐4 heat of formation of tetranitrohydrazine (91.5±5 kcal/mol), the CBS‐4 and CBS‐q isomerization energies for the conversion of azulene to naphthalene (ΔH _{calc}=−35.2±1.0 kcal/mol, ΔH _{exp}=−35.3±2.2 kcal/mol), and the CBS‐Q heat of formation of SF_{6} (ΔH _{calc}=−286.6±1.3 kcal/mol, ΔH _{exp}=−288.3±0.2 kcal/mol). The CBS‐Q value for the dissociation energy of a C–H bond in benzene (113.1±1.3 kcal/mol) is also in agreement with the most recent experimental result (112.0±0.6 kcal/mol). The CBS‐QCI/APNO model is applicable to the prediction of the C–H bond dissociation energies for the primary (100.7±0.7 kcal/mol calc.) and secondary (97.7±0.7 kcal/mol calc., 97.1±0.4 kcal/mol exp.) hydrogens of propane.

A J matrix engine for density functional theory calculations
View Description Hide DescriptionWe introduce a new method for the formation of the J matrix (Coulomb interaction matrix) within a basis of Cartesian Gaussian functions, as needed in density functional theory and Hartree–Fock calculations. By summing the density matrix into the underlying Gaussian integral formulas, we have developed a J matrix ‘‘engine’’ which forms the exact J matrix without explicitly forming the full set of two electron integral intermediates. Several precomputable quantities have been identified, substantially reducing the number of floating point operations and memory accesses needed in a J matrix calculation. Initial timings indicate a speedup of greater than four times for the (pp‖pp) class of integrals with speedups increasing to over ten times for (ff‖ff ) integrals.

Structure and hyperfine parameters of cyclopropyl and bicyclobutyl radicals from post‐Hartree–Fock computations
View Description Hide DescriptionExtensive post‐Hartree–Fock calculations are reported for the geometrical structures and hyperfine parameters of cyclopropyl and bicyclobutyl radicals. Computations for the parent molecules, whose structures are experimentally well characterized, show that reliable geometrical parameters are obtained, especially for bicyclobutane, only when using sufficiently flexible basis sets including f functions on carbon. Isotropic hyperfine splittings obtained by purposely tailored basis sets, proper treatment of correlation, and inclusion of vibrational averaging effects are in remarkable agreement with experiment. Our results suggest a revision of the accepted assignment for bicyclobtyl radical and suggest that long‐range couplings are not governed by the well‐known W rule but rather by a syn rule.

Many‐body similarity transformations generated by normal ordered exponential excitation operators
View Description Hide DescriptionNormal ordered exponential operators have been used extensively in open‐shell formulations of coupled clustertheory. The inverse of such an operator is known to exist, but a closed form explicit expression for the inverse is not available. We will address the evaluation of many‐body similarity transformations generated by normal ordered exponential transformation operators without explicit use of the inverse. The similarity transform can be obtained as the solution of a linear system of equations that can be solved trivially using backward substitution. In addition a closed form diagrammatic expression for the similarity transformed operator is presented. Using the many‐body similarity transformation strategy a simple and more general formulation of Fock space coupled clustertheory is presented which is akin in spirit to the formulation by Stolarczyk and Monkhorst [Phys. Rev. A 32, 725, 743 (1985); 37, 1908, 1926 (1988)], but which on the other hand is completely equivalent to the conventional wave operator formulation of Fock space coupled clustertheory (under suitable conditions). Other possible applications of the many‐body similarity transformation will be briefly discussed.

General spin adaptation of open‐shell coupled cluster theory
View Description Hide DescriptionA general scheme for the spin adaptation of open‐shell coupled‐cluster theory is presented, and the generalization to genuine multireference cases is briefly discussed. In our formulation the wave operator is parameterized such that it automatically commutes with the spin operators, and the correlated wave function is hence a spin eigenfunction provided the reference state is. We employ an exponential form for the wave operator, which is assumed to be normal ordered with respect to a closed‐shell vacuum state. The excitation operators can be expressed in terms of generators of the unitary group, and the number of independent coefficients is only marginally larger than in the closed‐shell case: Open‐shell orbitals occur both as creation and as annihilation operators. Using our formalism we are able to obtain spin–orbital based equations, which are expressed in terms of second quantized matrix elements of the similarity transformed Hamiltonian. The explicit form of the similarity transformed Hamiltonian generated by normal ordered exponential operators is presented in an accompanying paper [M. Nooijen, J. Chem. Phys. 104, 2638 (1996) preceding paper], and is crucial to the present formulation.

Current and condensate distributions in rotational excited states of quantum liquid clusters
View Description Hide DescriptionRecent quantum Monte Carlo calculations of small quantum clusters have shown that it is feasible to study their rotationally excited states directly. [M. A. McMahon, R. N. Barnett, and K. B. Whaley, J. Chem. Phys. 99, 8816 (1993).] We extend this work by sampling, from optimized variational wave functions, the current and Bose condensate distributions in (^{4}He)_{7}, (H_{2})_{7}, and (^{4}He)_{40} clusters. We demonstrate that these distributions are useful tools in identifying the location and nature of rotational excitations. With different constructions of rotational wave functions, the excitations can be either localized (as surface modes), or delocalized throughout the cluster analogous to the bulk superfluid vortex states. Condensate depletions in the excited states are observed, except for the delocalized excitation, where we find a higher condensate fraction than in the ground state.