Index of content:
Volume 115, Issue 17, 01 November 2001
- Theoretical Methods and Algorithms
115(2001); http://dx.doi.org/10.1063/1.1406536View Description Hide Description
We explore the fundamental connections between certain approximate coupled cluster (CC) and generalized valence bond (GVB) wave functions. We show that the GVB restricted configuration interaction (GVB-RCI) wave function can be associated with a compact CC expansion in the valence space. However, careful analysis reveals that a standard CC expansion contains terms that are not contained in the GVB-RCI wave function. The offending terms violate an effective pairwise exclusion principle (PEP) that is present in the RCI expansion, but is not enforced in the CC analog. These terms do not affect the size separability of either method. Variational calculations show noticeable improvements to the CC wave function when the PEP is enforced, with the most significant improvements coming near the dissociation limit. We modify the standard CC amplitude equations by removing the PEP violating terms and demonstrate remarkably improved results for the dissociation of and the double dissociation of
115(2001); http://dx.doi.org/10.1063/1.1407291View Description Hide Description
This paper is devoted to the development of an operator formulation of the recent extension of the centroid molecular dynamics method [J. Chem. Phys. 110, 3647 (1999); 111, 5303 (1999)] to boson and fermion systems. An operator calculus is used to rederive the basic equations of centroid dynamics. The following generalization to the case of systems of many indistinguishable particles is based on the use of a projection operator. Two different definitions of the quasi-density operator for bosonic and fermionic systems are suggested. The first definition allows an exact evaluation of equilibrium properties for systems with exchange effects using classical-like molecular dynamics calculations. The second one provides a formal justification of Bose–Einstein/Fermi–Dirac centroid dynamics with the same set of approximations as for Boltzmann statistics, and can be used to extract quantum dynamical information. In this case, the corresponding centroid correlation function can be related to a double Kubo transformed quantum mechanical one.
Applications of higher order composite factorization schemes in imaginary time path integral simulations115(2001); http://dx.doi.org/10.1063/1.1410117View Description Hide Description
Suzuki’s higher order composite factorization which involves both the potential and the force is applied to imaginary time path integral simulation. The expression is more general than the original version and involves a free parameter α in the range of [0, 1]. Formal expressions are derived for statistical averages, based on both thermodynamic and quantum operator identities. The derived expressions are then tested for one-dimensional model systems using the numerical matrix multiplication method, which involves no statistical error. When an optimum choice of α is made, the higher order factorization approach is shown to be more efficient than primitive factorization by about a factor of 4 and better than other existing higher order algorithms with similar character. Actual path integral simulation tests are then made for an excess electron in supercritical helium and for bulk water, and these generally demonstrate the efficiency of the higher order factorization approach.
A quantum mechanical method for calculating nonlinear optical properties of condensed phase molecules coupled to a molecular mechanics field: A quadratic multiconfigurational self-consistent-field/molecular mechanics response method115(2001); http://dx.doi.org/10.1063/1.1400138View Description Hide Description
An approach for determining nonlinear optical properties within a quantum mechanics/molecular mechanics method is presented. The response equations in the multiconfigurational self-consistent-field/molecular mechanics approach that includes polarization effects are derived and implemented for second order in response theory. The method is employed to calculate frequency-dependent first hyperpolarizabilities and two-photon absorption properties for in aqueous solution. The results are in close agreement with experimental measurements.
Kerr relaxation of anisotropic dielectric particles and Néel relaxation of anisotropic magnetic particles after a sudden change of field115(2001); http://dx.doi.org/10.1063/1.1405124View Description Hide Description
Kerrrelaxation of anisotropicdielectric particles and Néel relaxation of anisotropic magnetic particles after a sudden change of electric or magnetic field are studied on the basis of the Smoluchowski equation for the orientation distribution function. The equilibrium average of a Legendre moment of any order is evaluated. The time dependence of the relaxation of polarization (first-order Legendre moment) and order parameter (second-order Legendre moment) after a sudden change of field is determined by a fast and accurate numerical method.
115(2001); http://dx.doi.org/10.1063/1.1403689View Description Hide Description
We derive an expression that enables the accurate estimation of equilibrium properties using non-Hamiltonian dynamics. The major advantage of our scheme is that a time average over a single non-Hamiltonian trajectory can be employed instead of an ensemble average. Hence, it can directly be used in standard molecular dynamics simulations. The connection between non-Hamiltonian dynamics and equilibrium properties is established by assigning to the individual frames of the trajectory a weight that is based on the fluctuations of the phase space compression factor. Additionally, a simple scheme that takes into account only fluctuation of a given maximum duration is introduced to reduce the statistical error. By systematically extending the duration of the allowed fluctuations, increasingly accurate results can be obtained. Non-Hamiltonian dynamics schemes that are capable to enhance sampling efficiency are applied to two model systems in order to demonstrate the practical performance of our approach for the calculation of equilibrium free energy differences and probability density profiles.
115(2001); http://dx.doi.org/10.1063/1.1408299View Description Hide Description
A biorthogonal formulation is applied to the non-Hermite transcorrelated Hamiltonian, which treats a large amount of the dynamic correlation effects implicitly. We introduce biorthogonal canonical orbitals diagonalizing the non-Hermitian Fock operator. We also formulate many-body perturbationtheory for the transcorrelated Hamiltonian. The biorthogonal self-consistent field followed by the second order perturbation theory are applied to some pilot calculations including small atoms and molecules.
- Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry
115(2001); http://dx.doi.org/10.1063/1.1409359View Description Hide Description
The elimination from 2,5-dihydrofuran (DHF) was investigated by classical trajectories propagated with the energy and forces taken directly from PM3 semiempirical calculations. The dehydrogenation of DHF was first studied by MP2, B3LYP, and CBS-QB3 calculations and the results were found to be in good agreement with experiment. The CBS-QB3 outcomes were subsequently employed to obtained specific reaction parameters for the PM3 Hamiltonian. Product energy distributions were computed for several ensembles of trajectories initiated at the transition state. Three ensembles based on the quasiclassical barrier sampling (QCBS) technique were used to investigate the problem of zero-point energy (ZPE) leakage in the classical trajectories during the formation of the product molecule. The calculations predict that both the translational energy and vibrational energy distributions may be substantially influenced by nonrandom initial excitations.
115(2001); http://dx.doi.org/10.1063/1.1408914View Description Hide Description
A general numerical method is given to extract angular correlations from photodissociation experiments with ion imaging detection. The angular correlations among the transitiondipole moment of the parent molecule, μ , the photoproduct recoil velocity, v, and its angular momentum,j, are parametrized analytically using the semiclassical bipolar moment scheme due to Dixon. The method is a forward-convolution scheme which allows quantitative extraction of all measurable bipolar moments and can be applied in experiments with both linearly and circularly polarized probe light. It avoids the cylindrical symmetry limitations of the inverse Abel transform method, traditionally used for extracting photoproduct recoil anisotropy and speed distribution from imaging data. The method presented here also takes into account the possibility of multiple photodissociation channels. The features of the method are illustrated in a two-color 1+1′ REMPI-ion imaging study of the NO photoproduct trajectories resulting from the 650 nm photodissociation of 2-chloro-2-nitrosopropane (CNP). A comparison between experimental and synthetic images is presented for selected experimental geometries. The experimental images for CNP and the results from their fit confirm earlier TOF studies showing that the recoil speed distribution is bimodal with the low and high speed components having average values of approximately 500 and 910 m/s. These components have been previously assigned to dissociation from the and electronic states of the parent molecule, respectively. The experimental results from the current study also confirm that for the high-speed component the product NO velocity vector, v, is preferentially perpendicular to its angular momentum,j and that there is no significant correlation between v and the transitiondipole moment μ of the CNP molecule
High-resolution laser spectroscopy of LiAr: Improved interaction potential and spin-rotation-coupling in the ground state115(2001); http://dx.doi.org/10.1063/1.1407275View Description Hide Description
The spin-rotation coupling constant γ has been determined to be for vibrational levels 1, and 2 of the state of by means of an analysis of the high-resolution absorptionspectrum due to the transition in the 670–677 nm region. All rovibrational levels of the state have been observed, and improved values have been obtained for the spectroscopic parameters of vibration and rotation. In addition, the dispersed fluorescence has been recorded by populating selectively a particular rovibrational level of the A state. Using all experimental data, an improved interaction potential has been determined for which is provided in the form of an analytical Hartree-Fock-Dispersion function.
115(2001); http://dx.doi.org/10.1063/1.1409357View Description Hide Description
Collision induced dissociation and four center exchange reaction in are studied by means of time-dependent wave packet calculations and within a three-degree-of-freedom reduced dimensionality model. The role of both—vibrationally excited and vibrationally cold—collision partners is examined varying between 10 and 14 and between 0 and 2, respectively. From the analysis of the results, a clear picture of the main mechanisms of dissociation and reaction has been obtained, and the regions of the potential energy surface most sensitive to the dynamics have been identified. In this way, reaction bottlenecks are found to significantly depend on the initial state, owing to the anharmonicity of these states near dissociation and the different regions of the potential explored by the associated wave packets. The topography of such bottlenecks provide a basis for the existence of tunneling in reactions. Regarding the dissociation process, we find that there are two main mechanisms for dissociation; one where the unbroken diatom recoils with respect to dissociated fragments, and the second, where the diatom passes through the dissociated fragments. These mechanisms are responsible of a double peak observed in some dissociation probabilities. For reagents, new processes appear with non-negligible probabilities: (i) inelastic collision by insertion of the cold diatom into the vibrationally excited one and (ii) dissociation of the initially cold diatom. These features, together with the observation of structures in all channel probabilities, suggest that four-atom complexes are formed during collision.
Barrier recrossing in the vinylidene–acetylene isomerization reaction: A five-dimensional ab initio quantum dynamical investigation115(2001); http://dx.doi.org/10.1063/1.1405120View Description Hide Description
The spectroscopy and dynamics of the vinylidene–acetylene isomerizationreaction are studied theoretically. Based on a new ab initiopotential energy surface, the nuclear dynamics is followed by grid methods and wave packet propagation techniques. All five planar degrees of freedom are included in the calculation, for all three different isotopomers. The experimental photoelectron spectra by Lineberger and co-workers are very well reproduced; upon a small adjustment of the calculated anionic equilibrium geometry the agreement becomes excellent. The vinylidene survival probability for broadband photodetachment exhibits three different time regimes, the longest of which points towards an unusual stability of this reactive intermediate. The latter finding is corroborated by the calculated state-specific lifetimes which exceed previous estimates in the literature by ∼3 orders of magnitude. These findings are found to be reconfirmed when taking the discrete level structure of vibrationally highly excited acetylene into account. They amount to heavy barrier recrossing effects in this isomerizationreaction and lend strong support to the interpretation of CEI experiments on vinylidene by Levin et al. where this species has been identified ∼3 μs after its formation.
Spatial discrimination of Rydberg tagged molecular photofragments in an inhomogeneous electric field115(2001); http://dx.doi.org/10.1063/1.1408286View Description Hide Description
A new approach to detecting the spatial and energetic distribution of photodissociation products is demonstrated, in which an inhomogeneous electric field is used for spatially selective field ionization of Rydberg molecules. State-selected NO fragments from photodissociation in a supersonic beam are excited to high-Rydberg states and allowed to expand through the inhomogeneous field provided by an octopole. The field in the octopole results in the field ionization of those fragments that have moved to large radial distances mm) from the beam axis, and therefore this device transmits only those Rydberg molecules with a low velocity component in the direction perpendicular to the beam. A detailed characterization of the properties of this “steradiancy analyzer” is carried out and factors limiting the energy resolution (currently approximately 100 at an excess energy of 250 along with possible improvements, are discussed in detail.
Electronic structure of chromium oxides, and from photoelectron spectroscopy and density functional theory calculations115(2001); http://dx.doi.org/10.1063/1.1405438View Description Hide Description
The electronic structure of and was investigated using anion photoelectron spectroscopy and density functional theory.Photoelectron spectra of were obtained at several photon energies and yielded electron affinities, vibrational and electronic structure information about the neutral species. Density functional theory calculations were carried out for both the neutrals and anions and were used to interpret the experimental spectra. Several low-lying electronic states of CrO were observed and assigned from photodetachment of the ground state and an excited state which is only 0.1 eV higher. The main spectral features of were interpreted based on a A very weak isomer was also observed with lower electron binding energies. Relatively simple and vibrationally resolved spectra were observed for which was determined to be The neutral was calculated to be with the Cr atom slightly out of the plane of the three O atoms. The spectrum of revealed a very high electron binding energy. Several isomers of were predicted and the ground state has a distorted tetrahedral structure without any O–O bonding. Only one stable structure was predicted for with a superoxo bonded to a
115(2001); http://dx.doi.org/10.1063/1.1407278View Description Hide Description
The photodissociation of and van der Waals complexes is studied using Tully’s fewest-switches surface-hopping and the natural decay of mixing semiclassical trajectory methods for coupled-state dynamics. The lifetimes of the predissociated excited-state complex (exciplex), as well as the branching ratio into reactive and nonreactive arrangements and the internal energy distribution of the products are reported at several excitation energies. The semiclassical trajectory methods agree with each other only qualitatively, and the results are strongly dependent on the choice of electronic representation. In general, the lifetime of the LiFH exciplex is shorter and less dependent on the excitation energy than the lifetime of the NaFH exciplex. The semiclassical dynamics of LiFH and NaFH are interpreted in terms of the features of their coupled potential energy surfaces.
How does the closing of the ring affect the electric properties of sulphur dioxide? A comparison with the open and closed form of ozone115(2001); http://dx.doi.org/10.1063/1.1408297View Description Hide Description
We have calculated the static polarizability and hyperpolarizability of the ring structure of sulphur dioxide. Our best values for the mean dipole polarizability the first and second hyperpolarizability, obtained at the CCSD(T) level of theory with α carefully optimized basis set, are ᾱ=28.94 β̄=110.6 and γ̄=6117 At the same level of theory with a basis set of exactly the same size, the relevant quantities for the open structure are ᾱ=25.84 β̄=30.1 and γ̄=3390 [D. Xenides and G. Maroulis, Chem. Phys. Lett. 319, 618 (2000)]. Thus, the ring structure of sulphur dioxide is significantly more polarizable than the isoelectronic open one. This is in marked contradistinction to ozone, in which case the open system represents the more polarizable form. Electric polarizability and hyperpolarizability increases as
Dipole, dipole–quadrupole, and dipole–octopole polarizability of adamantane, from refractive index measurements, depolarized collision-induced light scattering, conventional ab initio and density functional theory calculations115(2001); http://dx.doi.org/10.1063/1.1410392View Description Hide Description
Refractive index (RI) measurements, depolarized collision-induced light (CILS) scattering and ab initio quantum chemical calculations are used to determine the dipole dipole–quadrupole and dipole–octopole polarizability of adamantane, For this molecule of symmetry group the three polarizabilities can be represented by a single scalar quantity. From experiment we obtain for the static dipole polarizability at K and for the higher polarizabilities and We have performed conventional ab initio and density functional theory calculations with specifically designed basis sets. A very large basis set consisting of 574 basis functions is thought to provide near-Hartree–Fock values for and E: and Our final theoretical estimates for these properties are and Very strong electron correlation effects are found for both the first and second hyperpolarizability. Our estimate for and the mean are and respectively. For the octopole and hexadecapole moments we propose and The basis sets constructed in this work should provide reliable computational tools for the study of intermolecular interactions of adamantane.
115(2001); http://dx.doi.org/10.1063/1.1410973View Description Hide Description
The gallium complexes were produced in pulsed molecular beams and studied with zero electron kinetic energy (ZEKE) photoelectron spectroscopy. Intermolecular vibrational frequencies and adiabatic ionization potentials (IPs) were obtained from ZEKE spectra. Ground electronic states were identified by combining the ZEKE spectra with quantum chemical and Franck–Condon calculations. has an IP of 40 135 cm−1 and metal-ligand stretching frequencies of 270 cm−1 in the ion and 161 cm−1 in the neutral. The IP of is 39 330 cm−1, and the vibrational frequencies are 93 cm−1 for the Ga–N–C bending, 124 cm−1 for the bending, and 299 cm−1 for the stretching. The strength of the gallium–methylamine binding is stronger than that of the gallium–ammonia. The ground state of is and that of is In contrast, has two doublets, and with virtually the same energies, whereas has a ground state.
115(2001); http://dx.doi.org/10.1063/1.1408916View Description Hide Description
Absorption and emission spectra of -doped and -codoped phosphate glasses have been studied within the temperature interval from 10 to 300 K. The analysis of Stark splitting for the excited state and the ground-state multiplets is performed. Simulation of inhomogeneous broadening of Stark levels has shown that all components of both multiplets are split by random distortions of the initial symmetric polyhedron, consisting of the neighboring oxygen ions in phosphate glasses. Inhomogeneous broadening of Stark levels is different for each energy level and reflects the sensitivity of a particular energy level to the variation of crystal field. At least three energy levels participate in shaping the low-energy side of the emission spectra, caused by the transition. The emission linewidth corresponding to the transition to the highest by energy Stark component is assumed to derive from comparable contributions of inhomogeneous and homogeneous broadening, the latter caused by intra-multiplet transitions. The presence of the highest Stark level in the crystal-field splitting of the ground-statemanifold with a high rate of nonradiative relaxation is essential for writing the rate equations which describe the laser operation of erbium glass lasers.
- Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation
115(2001); http://dx.doi.org/10.1063/1.1407292View Description Hide Description
Reaction rates of chemical reactions can be generally well described by classical transition state theory(TST) when considering zero-point energy and tunneling effects. TST is, however, not applicable for small energy barriers comparable in size to the zero-point energy or for cases where even no energy barrier is present. These situations are common for proton transfer in bulk water. Here, energy profiles for proton transfer between water and small organic molecules were computed quantum mechanically and were used as input for solving the time-dependent Schrödinger equation in one dimension. Proton transfer over small barriers occurs very fast and is completed after 10–40 fs. Transition probabilities can reach values as high as 100%. They can easily be fitted by an analytical expression. An interpolation for proton transfer rates is then derived for connecting the low-barrier-regime that should be treated by solving the time-dependent Schrödinger equation with the high-barrier-regime where TST applies.