Breakdown of the pseudopotential approximation for magnetizabilities and electric multipole moments. II. The importance of gauge invariance for large-core semi-local pseudopotentials

In a previous paper we pointed out that core contributions to the static magnetizability are non-negligible, and can therefore lead to erroneous results within the pseudopotential approximation [P. Schwerdtfeger, B. Assadollahzadeh, U. Rohrmann, R. Scha?fer, and J. R. Cheeseman, J. Chem. Phys. 134, 204102 (2011)]. In a recent paper van Wu?llen showed that additional terms arising from the gauge-invariant condition for the semi-local part of a pseudopotential operator can lead to non-negligible contributions to the magnetizability tensor, which are sensitive to the gauge origin and basis set chosen [C. van Wu?llen, J. Chem. Phys. 136, 114110 (2012)]. These terms were neglected in previous calculations as they were assumed to be small. In this paper we analyze the importance of the gauge-dependent semi-local pseudopotential correction term in detail for AuF and clusters of Sn showing that it leads indeed to very large corrections to the paramagnetic term for large-core pseudopotentials. Without this correction the results become very sensitive to the basis set applied. This now resolves some of the unusual large paramagnetic contributions reported before for both AuF and Sn(2).     

Gel mechanics: a comparison of the theories of Biot and Tanaka, Hocker, and Benedek

This article compares the Biot [J. Appl. Phys. 12, 155 (1941)] and Tanaka, Hocker, and Benedek (THB) [J. Chem. Phys. 59, 5151 (1973)] theories of gel deformation. Biot's theory treats the gel as a continuum with the pore pressure as a state variable whereas the THB theory treats the gel as a mixture of solid and liquid phases. We revisit the problem of gel deswelling and use this example to show that there can be substantial differences between the two theories. The THB theory is not a complete mixture theory since the displacements of the liquid are assumed to be negligibly small in comparison with the displacements of the network. We propose a simple extension of the THB model, which takes into account the momentum transfer of the liquid phase. We show that with this simple addition and some very reasonable assumptions, the extended THB theory is identical to the Biot theory.     

Isotope effects in the CO dimer: millimeter wave spectrum and rovibrational calculations of (12C18O)2

The millimeter wave spectrum of the isotopically substituted CO dimer, (12C18O)2, was studied with the Orotron jet spectrometer, confirming and extending a previous infrared study [A. R. W. McKellar, J. Mol. Spectrosc. 226, 190 (2004)]. A very dilute gas mixture of CO in Ne was used, which resulted in small consumption of 12C18O sample gas and produced cold and simple spectra. Using the technique of combination differences together with the data from the infrared work, six transitions in the 84-127 GHz region have been assigned. They belong to two branches, which connect four low levels of A+ symmetry to three previously unknown levels of A- symmetry. The discovery of the lowest state of A- symmetry, which corresponds to the projection K=0 of the total angular momentum J onto the intermolecular axis, identifies the geared bending mode of the 12C18O dimer at 3.607 cm(-1). Accompanying rovibrational calculations using a recently developed hybrid potential from ab initio coupled cluster [CCSD(T)] and symmetry-adapted perturbation theory calculations [G. W. M. Vissers et al., J. Chem. Phys. 122, 054306 (2005)] gave very good agreement with experiment. The isotopic dependence of the A+/A- energy splitting, the intermolecular separation R, and the energy difference of two ground state isomers, which change significantly when 18O or 13C are substituted into the normal (12C16O)2 isotopolog [L. A. Surin et al., J. Mol. Spectrosc. 223, 132 (2004)], was explained by these calculations. It turns out that the change in anisotropy of the intermolecular potential with respect to the shifted monomer centers of mass is particularly significant.     

Comparison of different methods for calculating the paramagnetic relaxation enhancement of nuclear spins as a function of the magnetic field

The enhancement of the spin-lattice relaxation rate for nuclear spins in a ligand bound to a paramagnetic metal ion [known as the paramagnetic relaxation enhancement (PRE)] arises primarily through the dipole-dipole (DD) interaction between the nuclear spins and the electron spins. In solution, the DD interaction is modulated mostly by reorientation of the nuclear spin-electron spin axis and by electron spin relaxation. Calculations of the PRE are in general complicated, mainly because the electron spin interacts so strongly with the other degrees of freedom that its relaxation cannot be described by second-order perturbation theory or the Redfield theory. Three approaches to resolve this problem exist in the literature: The so-called slow-motion theory, originating from Swedish groups [Benetis et al., Mol. Phys. 48, 329 (1983); Kowalewski et al., Adv. Inorg. Chem. 57, (2005); Larsson et al., J. Chem. Phys. 101, 1116 (1994); T. Nilsson et al., J. Magn. Reson. 154, 269 (2002)] and two different methods based on simulations of the dynamics of electron spin in time domain, developed in Grenoble [Fries and Belorizky, J. Chem. Phys. 126, 204503 (2007); Rast et al., ibid. 115, 7554 (2001)] and Ann Arbor [Abernathy and Sharp, J. Chem. Phys. 106, 9032 (1997); Schaefle and Sharp, ibid. 121, 5387 (2004); Schaefle and Sharp, J. Magn. Reson. 176, 160 (2005)], respectively. In this paper, we report a numerical comparison of the three methods for a large variety of parameter sets, meant to correspond to large and small complexes of gadolinium(III) and of nickel(II). It is found that the agreement between the Swedish and the Grenoble approaches is very good for practically all parameter sets, while the predictions of the Ann Arbor model are similar in a number of the calculations but deviate significantly in others, reflecting in part differences in the treatment of electron spin relaxation. The origins of the discrepancies are discussed briefly.     

Simplified derivation of a one-range addition theorem of the Yukawa potential

The one-range addition theorem [J. Fernández Rico, R. López, and G. Ramírez, Int. J. Quantum Chem. 34 , 121 (1988)] for the Yukawa potential is rederived in a very simple manner using weakly convergent expansions [E. J. Weniger, J. Math. Phys. 26 , 276 (1985)] of plane waves in the Fourier representation. It is discussed in which sense the addition theorem converges. The relation to Sturmian expansions of Coulomb Green functions is pointed out. © 1992 John Wiley & Sons, Inc.     

Analysis and calculation of the 31P and 19F NMR spectra of hexafluorocyclotriphosphazene

The higher order high-resolution (31)P and (19)F NMR spectra of hexafluorocyclotriphosphazene (F(2)PN)(3) were measured at 183 K and interpreted using subspectral analysis and iterative fitting computation. (F(2)PN)(3) forms a rigid nine-spin system [A[X](2)](3) with D(3h) symmetry. Two complete and very similar sets of six experimental spin-spin coupling constants, (1)J(P,F), (2)J(P,P), (2)J(F,F), (3)J(P,F), (4)J(F,F)(cis) and (4)J(F,F)(trans), were determined for the first time. Theoretical DFT calculations of chemical shifts and coupling constants were performed to assess their predictive value. The PP/aug-cc-pVDZ treatment rendered the best agreement with experimental data.     

The I2 dissociation mechanisms in the chemical oxygen-iodine laser revisited

The recently suggested mechanism of I(2) dissociation in the chemical oxygen-iodine laser (COIL) [K. Waichman, B. D. Barmashenko, and S. Rosenwaks, J. Appl. Phys. 106, 063108 (2009); and J. Chem. Phys. 133, 084301 (2010)] was largely based on the suggestion of V. N. Azyazov, S. Yu. Pichugin, and M. C. Heaven [J. Chem. Phys. 130, 104306 (2009)] that the vibrational population of O(2)(a) produced in the chemical generator is high enough to play an essential role in the dissociation. The results of model calculations based on this mechanism agreed very well with measurements of the small signal gain g, I(2) dissociation fraction F, and temperature T in the COIL. This mechanism is here revisited, following the recent experiments of M. V. Zagidullin [Quantum Electron. 40, 794 (2010)] where the observed low population of O(2)(b, v = 1) led to the conclusion that the vibrational population of O(2)(a) at the outlet of the generator is close to thermal equilibrium value. This value corresponds to a very small probability, ～0.05, of O(2)(a) energy pooling to the states O(2)(X,a,b, v > 0). We show that the dissociation mechanism can reproduce the experimentally observed values of g, F, and T in the COIL only if most of the energy released in the processes of O(2)(a) energy pooling and O(2)(b) quenching by H(2)O ends up as vibrational energy of the products, O(2)(X,a,b), where the vibrational states v = 2 and 3 are significantly populated. We discuss possible reasons for the differences in the suggested vibrational population and explain how these differences can be reconciled.     

State-to-state reactive differential cross sections for the H+H2-->H2+H reaction on five different potential energy surfaces employing a new quantum wavepacket computer code: DIFFREALWAVE

State-to-state differential cross sections have been calculated for the hydrogen exchange reaction, H+H2-->H2+H, using five different high quality potential energy surfaces with the objective of examining the sensitivity of these detailed cross sections to the underlying potential energy surfaces. The calculations were performed using a new parallel computer code, DIFFREALWAVE. The code is based on the real wavepacket approach of Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)]. The calculations are parallelized over the helicity quantum number Omega' (i.e., the quantum number for the body-fixed z component of the total angular momentum) and wavepackets for each J,Omega' set are assigned to different processors, similar in spirit to the Coriolis-coupled processors approach of Goldfield and Gray [Comput. Phys. Commun. 84, 1 (1996)]. Calculations for J=0-24 have been performed to obtain converged state-to-state differential cross sections in the energy range from 0.4 to 1.2 eV. The calculations employ five different potential energy surfaces, the BKMP2 surface and a hierarchical family of four new ab initio surfaces [S. L. Mielke, et al., J. Chem. Phys. 116, 4142 (2002)]. This family of four surfaces has been calculated using three different hierarchical sets of basis functions and also an extrapolation to the complete basis set limit, the so called CCI surface. The CCI surface is the most accurate surface for the H3 system reported to date. Our calculations of differential cross sections are the first to be reported for the A2, A3, A4, and CCI surfaces. They show that there are some small differences in the cross sections obtained from the five different surfaces, particularly at higher energies. The calculations also show that the BKMP2 performs well and gives cross sections in very good agreement with the results from the CCI surface, displaying only small divergences at higher energies.     

Vibrational effects on the dynamic electric properties of hydrogen peroxide

In this work we present a method based on the perturbation theoretic approach of Bishop and co-workers [J. Chem. Phys. 95, 2646 (1991); 97, 5255 (1992); 108, 10013 (1998)] to calculate the effect of torsional motion on the polarizability and hyperpolarizabilities of hydrogen peroxide. The frequency dependence has been evaluated using the time-dependent Hartree-Fock method. The results obtained show that the zero-point vibrational averaging contributions are small compared to the corresponding electronic contributions. In the static limit the pure vibrational contributions are very large, specially for beta and gamma. These contributions are significant for the hyperpolarizabilities even in the visible region, except for the second harmonic generation and third harmonic generation processes.     

A family of ferro- and antiferromagnetically coupled decametallic chromium(III) wheels

The synthesis and crystal structures of a family of decametallic Cr(III) "molecular wheels" are reported, namely [Cr10(OR)20(O2CR')10] [R' = Me, R = Me (1), Et (2); R' = Et, R = Me (3), Et (4); R' = CMe3, R = Me (5), Et (6)]. Magnetic studies on 1-6 reveal a remarkable dependence of the magnetic behaviour on the nature of R. In each pair of complexes with a common carboxylate (R') the nearest neighbour CrCr magnetic exchange coupling is more antiferromagnetic for the ethoxide-bridged (R = Et) cluster than for the methoxide analogue. In complexes 2, 4 and 6 the overall coupling is weakly antiferromagnetic resulting in diamagnetic (S = 0) ground states for the cluster, whilst in 1 and 5 it is weakly ferromagnetic thus resulting in very high-spin ground states. This ground state has been probed directly in the perdeuterated version of 1 ([D]1) by inelastic neutron scattering experiments, and these support the S = 15 ground state expected for ferromagnetic coupling of ten Cr(III) ions, and they also indicate that a single J-value model is inadequate. The ground state of 5 is large but not well defined. The trends in J on changing R are further supported by density functional calculations on 1-6, which are in excellent agreement with experiment. The very large changes in the nature of the ground state between 1 and 2, and 5 and 6 are the result of relatively small changes in J that happen to cross J = 0, hence changing the sign of J.     

Resolution of identity Dirac-Kohn-Sham method using the large component only: Calculations of g-tensor and hyperfine tensor

A new relativistic two-component density functional approach, based on the Dirac-Kohn-Sham method and an extensive use of the technique of resolution of identity (RI), has been developed and is termed the DKS2-RI method. It has been applied to relativistic calculations of g and hyperfine tensors of coinage-metal atoms and some mercury complexes. The DKS2-RI method solves the Dirac-Kohn-Sham equations in a two-component framework using explicitly a basis for the large component only, but it retains all contributions coming from the small component. The DKS2-RI results converge to those of the four-component Dirac-Kohn-Sham with an increasing basis set since the error associated with the use of RI will approach zero. The RI approximation provides a basis for a very efficient implementation by avoiding problems associated with complicated integrals otherwise arising from the elimination of the small component. The approach has been implemented in an unrestricted noncollinear two-component density functional framework. DKS2-RI is related to Dyall's [J. Chem. Phys. 106, 9618 (1997)] unnormalized elimination of the small component method (which was formulated at the Hartree-Fock level and applied to one-electron systems only), but it takes advantage of the local Kohn-Sham exchange-correlation operators (as, e.g., arising from local or gradient-corrected functionals). The DKS2-RI method provides an attractive alternative to existing approximate two-component methods with transformed Hamiltonians (such as Douglas-Kroll-Hess [Ann. Phys. 82, 89 (1974); Phys. Rev. A 33, 3742 (1986)] method, zero-order regular approximation, or related approaches) for relativistic calculations of the structure and properties of heavy-atom systems. In particular, no picture-change effects arise in the property calculations.     

Stochastic Liouville equation treatment of the electron paramagnetic resonance line shape of an S-state ion in solution

The current approaches used for the analysis of electron paramagnetic resonance spectra of Gd3+ complexes suffer from a number of drawbacks. Even the elaborate model of [Rast et al., J. Chem. Phys. 113, 8724 (2000)] where the electron spin relaxation is explained by the modulation of the zero-field splitting (ZFS), by molecular tumbling (the so called static contribution), and deformations (transient contribution), is only readily applicable within the validity range of the Redfield theory [Advances in Magnetic Resonance, edited by J.-S. Waugh (Academic, New York, 1965), Vol. 1, p. 1], that is, when the ZFS is small compared to the Zeeman energy and the rotational and vibrational modulations are fast compared to the relaxation time. Spin labels (nitroxides and transition metal complexes) have been studied for years in systems that violate these conditions. The theoretical framework commonly used in such studies is the stochastic Liouville equation (SLE). The authors shall show how the physical model of Rast et al. can be cast into the SLE formalism, paying special attention to the specific problems introduced by the [Uhlenbeck and Ornstein, Phys. Rev. 36, 823 (1930)] process used to model the transient ZFS. The resulting equations are very general and valid for arbitrary correlation times, magnetic field strength, electron spin S, or symmetry. The authors demonstrate the equivalence of the SLE approach with the Redfield approximation for two well-known Gd3+ complexes.     

Quantum dynamics of H2, D2, and HD in the small dodecahedral cage of clathrate hydrate: evaluating H2-water nanocage interaction potentials by comparison of theory with inelastic neutron scattering experiments

We have performed rigorous quantum five-dimensional (5D) calculations and analysis of the translation-rotation (T-R) energy levels of one H(2), D(2), and HD molecule inside the small dodecahedral (H(2)O)(20) cage of the structure II clathrate hydrate, which was treated as rigid. The H(2)- cage intermolecular potential energy surface (PES) used previously in the molecular dynamics simulations of the hydrogen hydrates [Alavi et al., J. Chem. Phys. 123, 024507 (2005)] was employed. This PES, denoted here as SPC/E, combines an effective, empirical water-water pair potential [Berendsen et al., J. Phys. Chem. 91, 6269 (1987)] and electrostatic interactions between the partial charges placed on H(2)O and H(2). The 5D T-R eigenstates of HD were calculated also on another 5D H(2)-cage PES denoted PA-D, used by us earlier to investigate the quantum T-R dynamics of H(2) and D(2) in the small cage [Xu et al., J. Phys. Chem. B 110, 24806 (2006)]. In the PA-D PES, the hydrogen-water pair potential is described by the ab initio 5D PES of the isolated H(2)-H(2)O dimer. The quality of the SPC/E and the PA-D H(2)-cage PESs was tested by direct comparison of the T-R excitation energies calculated on them to the results of two recent inelastic neutron scattering (INS) studies of H(2) and HD inside the small clathrate cage. The translational fundamental and overtone excitations, as well as the triplet splittings of the j=0-->j=1 rotational transitions, of H(2) and HD in the small cage calculated on the SPC/E PES agree very well with the INS results and represent a significant improvement over the results computed on the PA-D PES. Our calculations on the SPC/E PES also make predictions about several spectroscopic observables for the encapsulated H(2), D(2), and HD, which have not been measured yet.     

Calculation of the crystal-melt interfacial free energy of succinonitrile from molecular simulation

The crystal-metal interfacial free energy for a six-site model of succinonitrile [N triple bond C-(CH(2))(2)-C triple bond N] has been calculated using molecular-dynamics simulation from the power spectrum of capillary fluctuations in interface position. The orientationally averaged magnitude of the interfacial free energy is determined to be (7.0+/-0.4)x10(-3) J m(-2). This value is in agreement (within the error bars) with the experimental value [(7.9+/-0.8)x10(-3) J m(-2)] of Marasli et al. [J. Cryst. Growth 247, 613 (2003)], but is about 20% lower than the earlier experimental value [(8.9+/-0.5)x10(-3) J m(-2)] obtained by Schaefer et al. [Philos. Mag. 32, 725 (1975)]. In agreement with the experiment, the calculated anisotropy of the interfacial free energy of this body-centered-cubic material is small. In addition, the Turnbull coefficient from our simulation is also in agreement with the experiment. This work demonstrates that the capillary fluctuation method of Hoyt et al. [Phys. Rev. Lett. 86, 5530 (2001)] can be successfully applied to determine the crystal-melt interfacial free energy of molecular materials.     

Calculation of the transport and relaxation properties of methane. I. Shear viscosity, viscomagnetic effects, and self-diffusion

Transport properties of pure methane gas have been calculated in the rigid-rotor approximation using the recently proposed intermolecular potential energy hypersurface [R. Hellmann et al., J. Chem. Phys. 128, 214303 (2008)] and the classical-trajectory method. Results are reported in the dilute-gas limit for shear viscosity, viscomagnetic coefficients, and self-diffusion in the temperature range of 80-1500 K. Compared with the best measurements, the calculated viscosity values are about 0.5% too high at room temperature, although the temperature dependence of the calculated values is in very good agreement with experiment between 210 and 390 K. For the shear viscosity, the calculations indicate that the corrections in the second-order approximation and those due to the angular-momentum polarization are small, less than 0.7%, in the temperature range considered. The very good agreement of the calculated values with the experimental viscosity data suggests that the rigid-rotor approximation should be very reasonable for the three properties considered. In general, the agreement for the other measured properties is within the experimental error.     

Ab initio equation of state of an organic molecular crystal: 1,1-diamino-2,2-dinitroethylene

A complete equation of state for the molecular crystal 1,1-diamino-2,2-dinitroethylene has been calculated from first principles for temperatures between 0 and 400 K, and for specific volumes from 61 to 83 cm3/mol, corresponding to relative volumes from 0.78 to 1.06. The calculated 300 K isotherm agrees very well with the experimentally measured pressure-volume relation reported by Peiris et al. (Peiris, S. M.; Wong, C. P.; Zerilli, F. J. J. Chem. Phys. 2004, 120, 8060). The volumetric thermal expansion coefficient is calculated to be 140 ppm/K at 300 K and atmospheric pressure and varies considerably with specific volume as well as temperature. The Grüneisen parameter varies significantly with temperature, but its variation with specific volume is small. The calculated specific heat (160 J/mol/K at 300 K and atmospheric pressure) has only a very small dependence on specific volume.     

The He-LiH potential energy surface revisited. II. Rovibrational energy transfer on a three-dimensional surface

We use our rigid rotor He-LiH potential energy surface [B. K. Taylor and R. J. Hinde, J. Phys. Chem. 111, 973 (1999)] as a starting point to develop a three-dimensional potential surface that describes the interaction between He and a rotating and vibrating LiH molecule. We use a fully quantum treatment of the collision dynamics on the current potential surface to compute rovibrational state-to-state cross sections. We compute excitation and relaxation vibrational rate constants as a function of temperature by integrating these cross sections over a Maxwell-Boltzmann translational energy distribution and summing over Boltzmann-weighted initial rotational levels. The rate constants for vibrational excitation of LiH are very small for temperatures below 300 K. Rate constants for vibrational relaxation of excited LiH molecules, however, are several orders of magnitude larger and show very little temperature dependence, suggesting that the collisions that result in vibrational relaxation are governed by long-range attractive interactions.     

Two-component heterogeneous nucleation kinetics and an application to Mars

We develop a two-component heterogeneous nucleation model that includes exact calculation of the Stauffer-type [D. Stauffer, J. Aerosol Sci. 7, 319 (1976)] steady-state kinetic prefactor using the correct heterogeneous Zeldovich factor for a heterogeneous two-component system. The model, and a simplified version of it, is tested by comparing its predictions to experimental data for water-n-propanol nucleating on silver particles. The model is then applied to water-carbon dioxide system in Martian conditions, which has not been modeled before. Using the ideal mixture assumption, the model shows theoretical possibilities for two-component nucleation adjacent to the initial stages of one-component water nucleation, especially with small water vapor amounts. The numbers of carbon dioxide molecules in the critical cluster are small in the case of large water amounts (up to 300 ppm) in the gas phase, but larger when there is very little water vapor (1 ppm).     

Analytical determination of the [Ln-aminoxyl radical] exchange interaction taking into account both the ligand-field effect and the spin-orbit coupling of the lanthanide ion (Ln = DyIII and HoIII)

Numerous compounds in which a paramagnetic LnIII ion is in an exchange interaction with a second spin carrier, such as a transition metal ion or an organic radical, have been described. However, except for GdIII, very little has been reported about the magnitude of the interactions. Indeed, for these ions both the ligand-field effects and the exchange interactions between the magnetic centers become relevant in the same temperature range; this makes the analysis of the magnetic behavior of such compounds more difficult. In this study, quantitative analyses of the thermal variations of the static isothermal initial magnetic susceptibility measured on powdered samples of the [Ln(NO3)3-[organic radical]2] (Ln = DyIII and HoIII) compounds were performed. The ligand-field effects on the Ln ions were taken into account, and the exchange interactions within a molecule were treated exactly within an appropriate Racah formalism. Values of the intramolecular [Ln-aminoxyl radical] exchange parameter have thus been rigorously deduced for both the Dy Kramers and Ho non-Kramers ion-based compounds. Ferromagnetic [Ln-radical] interactions are found for both the Dy and Ho derivatives with J = 8 cm(-1) and J = 4.5 cm(-1), respectively.