Index of content:
Volume 129, Issue 1, 07 July 2008
- Theoretical Methods and Algorithms
Inclusion of explicit electron-proton correlation in the nuclear-electronic orbital approach using Gaussian-type geminal functions129(2008); http://dx.doi.org/10.1063/1.2943144View Description Hide Description
The nuclear-electronic orbital explicitly correlated Hartree-Fock (NEO-XCHF) approach for including electron-proton correlation in mixed nuclear-electronic wavefunctions is presented. A general ansatz for the nuclear-electronic wavefunction that includes explicit dependence on the nuclear-electronic distances with Gaussian-type geminal functions is proposed. Based on this ansatz, expressions are derived for the total energy and the electronic and nuclear Fock operators for multielectron systems. The explicit electron-proton correlation is incorporated directly into the self-consistent-field procedure for optimizing the nuclear-electronic wavefunction. This approach is computationally practical for many-electron systems because only a relatively small number of nuclei are treated quantum mechanically, and only electron-proton correlation is treated explicitly. Electron-electron correlation can be included by combining the NEO-XCHF approach with perturbation theory,density functional theory, and multiconfigurational methods. Previous nuclear-electronic orbital-based methods produce nuclear densities that are too localized, resulting in abnormally high stretching frequencies and inaccuracies in other properties relying on these densities. The application of the NEO-XCHF approach to the model system illustrates that this approach includes the significant electron-proton correlation, thereby leading to an accurate description of the nuclear density. The agreement between the proton densities obtained with the NEO-XCHF and grid-based methods validates the underlying theory and the implementation of the NEO-XCHF method.
The influence of thermostats and manostats on reverse nonequilibrium molecular dynamics calculations of fluid viscosities129(2008); http://dx.doi.org/10.1063/1.2943312View Description Hide Description
Reverse nonequilibrium molecular dynamics to calculate the shear viscosity of Lennard-Jones liquids was extended to simulations at constant number of particles, constant volume, and constant pressure using a Berendsen thermostat and a Berendsen manostat. Using additional systems such as water and hexane, we also report on the performance of shear viscosity calculations of systems with electrostatic and nontrivial intramolecular interactions when a manostat is applied. We compare the shear viscosities of simulations using no coupling, only temperature coupling, and temperature and pressure coupling and characterize discrepancies, where observed. From this, we deduce guidelines for when and how manostats can be usefully applied in reverse nonequilibrium simulations.
129(2008); http://dx.doi.org/10.1063/1.2943142View Description Hide Description
Conventional density functional theory(DFT) fails for strongly correlated electron systems due to large intra-atomic self-interaction errors. The method provides a means of overcoming these errors through the use of a parametrized potential that employs an exact treatment of quantum mechanical exchange interactions. The parameters that enter into this potential correspond to the spherically averaged intra-atomic Coulomb and exchange interactions. Recently, we developed an ab initio approach for evaluating these parameters on the basis of unrestricted Hartree–Fock (UHF) theory, which has the advantage of being free of self-interaction errors and does not require experimental input [Mosey and Carter, Phys. Rev. B76, 155123 (2007)]. In this work, we build on that method to develop a more robust and convenient ab initio approach for evaluating and . The new technique employs a relationship between and and the Coulomb and exchange integrals evaluated using the entire set of UHF molecular orbitals (MOs) for the system. Employing the entire set of UHF MOs renders the method rotationally invariant and eliminates the difficulty in selecting unambiguously the MOs that correspond to localized states. These aspects overcome two significant deficiencies of our earlier method. The new technique is used to evaluate and for , FeO, and . The resulting values of are close to empirical estimates of this quantity for each of these materials and are also similar to results of constrained DFT calculations. calculations using the ab initio parameters yield results that are in good agreement with experiment. As such, this method offers a means of performing accurate and fully predictive calculations of strongly correlated electron materials.
129(2008); http://dx.doi.org/10.1063/1.2945900View Description Hide Description
Kato’s cusp condition gives the exact first order dependence of molecular wave functions on interparticle separation near the coalescence of two charged particles. We derive conditions correct to second order in interparticle separation, which concern second order derivatives of the wave function at the coalescence point. For identical particle coalescence, we give equations correct to third order. In addition to a universal, particle dependent term, a system and state dependent term arises in the higher order conditions, which we interpret as an effect of Coulombic screening. We apply our analysis to the standard orbital-based methods of quantum chemistry and discuss the implications for Jastrow- and R12-type correlation factors.
Essential energy space random walks to accelerate molecular dynamics simulations: Convergence improvements via an adaptive-length self-healing strategy129(2008); http://dx.doi.org/10.1063/1.2949815View Description Hide Description
Recently, accelerated molecular dynamics (AMD) technique was generalized to realize essential energy space random walks so that further sampling enhancement and effective localized enhanced sampling could be achieved. This method is especially meaningful when essential coordinates of the target events are not priori known; moreover, the energy space metadynamics method was also introduced so that biasing free energy functions can be robustly generated. Despite the promising features of this method, due to the nonequilibrium nature of the metadynamics recursion, it is challenging to rigorously use the data obtained at the recursion stage to perform equilibrium analysis, such as free energysurface mapping; therefore, a large amount of data ought to be wasted. To resolve such problem so as to further improve simulation convergence, as promised in our original paper, we are reporting an alternate approach: the adaptive-length self-healing (ALSH) strategy for AMD simulations; this development is based on a recent self-healing umbrella sampling method. Here, the unit simulation length for each self-healing recursion is increasingly updated based on the Wang–Landau flattening judgment. When the unit simulation length for each update is long enough, all the following unit simulations naturally run into the equilibrium regime. Thereafter, these unit simulations can serve for the dual purposes of recursion and equilibrium analysis. As demonstrated in our model studies, by applying ALSH, both fast recursion and short nonequilibrium data waste can be compromised. As a result, combining all the data obtained from all the unit simulations that are in the equilibrium regime via the weighted histogram analysis method, efficient convergence can be robustly ensured, especially for the purpose of free energysurface mapping.
Self-consistent implementation of a nonlocal van der Waals density functional with a Gaussian basis set129(2008); http://dx.doi.org/10.1063/1.2948400View Description Hide Description
Nearly all common density functional approximations fail to properly describe dispersion interactions responsible for binding in van der Waals complexes. Empirical corrections can fix some of the failures but cannot fully grasp the complex physics and may not be reliable for systems dissimilar to the fitting set. In contrast, the recently proposed nonlocal van der Waals density functional (vdW-DF) was derived from first principles, describes dispersion interactions in a seamless fashion, and yields the correct asymptotics. Implementation of this functional is somewhat cumbersome: Nonlocal dependence on the electron density requires numerical double integration over the space variables and functional derivatives are nontrivial. This paper shows how vdW-DF can be implemented self-consistently with Gaussian basis functions. The gradients of the energy with respect to nuclear displacements have also been derived and coded, enabling efficient geometry optimizations. We test the vdW-DF correlation functional in combination with several exchange approximations. We also study the sensitivity of the method to the basis set size and to the quality of the numerical quadrature grid. For weakly interacting systems, acceptable accuracy in semilocal exchange is achieved only with fine grids, whereas for nonlocal vdW-DF correlation even rather coarse grids are sufficient. The current version of vdW-DF is not well suited for pairing with Hartree–Fock exchange, leading to considerable overbinding.
Molecular dynamics in the isothermal-isobaric ensemble: The requirement of a “shell” molecule. III. Discontinuous potentials129(2008); http://dx.doi.org/10.1063/1.2949799View Description Hide Description
Based on the approach of Gruhn and Monson [Phys. Rev. E63, 061106 (2001)], we present a new method for deriving the collisions dynamics for particles that interact via discontinuous potentials. By invoking the conservation of the extended Hamiltonian, we generate molecular dynamics (MD) algorithms for simulating the hard-sphere and square-well fluids within the isothermal-isobaric ensemble. Consistent with the recent rigorous reformulation of the ensemble partition function, the equations of motion impose a constant external pressure via the introduction of a shell particle of known mass [M. J. Uline and D. S. Corti, J. Chem. Phys.123, 164101 (2005); 123, 164102 (2005)], which serves to define uniquely the volume of the system. The particles are also connected to a temperature reservoir through the use of a chain of Nosé-Hoover thermostats, the properties of which are not affected by a hard-sphere or square-well collision. By using the Liouville operator formalism and the Trotter expansion theorem to integrate the equations of motion, the update of the thermostat variables can be decoupled from the update of the positions of the particles and the momentum changes upon a collision. Hence, once the appropriate collision dynamics for the isobaric-isenthalpic equations of motion is known, the adaptation of the algorithm to the ensemble is straightforward. Results of MD simulations for the pure component square-well fluid are presented and serve to validate our algorithm. Finally, since the mass of the shell particle is known, the system itself, and not a piston of arbitrary mass, controls the time scales for internal pressure and volume fluctuations. We therefore consider the influence of the shell particle algorithm on the dynamics of the square-well fluid.
129(2008); http://dx.doi.org/10.1063/1.2950094View Description Hide Description
We have investigated the dissociation behavior of the radical helium dimer using the Piris natural orbital functional (PNOF). This system is particularly challenging to be described by standard density functionals. The restricted open formulation of the PNOF-2, as well as the PNOF-2 energy plus the extended Koopmans’ vertical ionization potential calculations of the neutral helium dimer, have been tested for calculating the ground-state energies of as a function of the internuclear distance. For comparison, we present the dissociation curve obtained with the diffusion Monte Carlo method. The dissociation energies, equilibrium bond lengths, and rovibrational levels are reported. The obtained potential energy curves indicate that PNOF-2 yields a correct and accurate dissociation behavior for the helium radical dimer.
129(2008); http://dx.doi.org/10.1063/1.2949547View Description Hide Description
Daubechies wavelets are a powerful systematic basis set for electronic structure calculations because they are orthogonal and localized both in real and Fourier space. We describe in detail how this basis set can be used to obtain a highly efficient and accurate method for density functionalelectronic structure calculations. An implementation of this method is available in the ABINIT free software package. This code shows high systematic convergence properties, very good performances, and an excellent efficiency for parallel calculations.
129(2008); http://dx.doi.org/10.1063/1.2944272View Description Hide Description
Self-interaction is one of the most substantial problems in present-day density functional theory. A widely used approach to overcome this problem is the self-interaction correction proposed by Perdew and Zunger. However, the thus given functional not only depends on the orbitals explicitly but is also variant under unitary transformation of the orbitals. In this manuscript, we present a generalized version of the optimized effective potential equation which is able to deal with both problems in one go. Calculations for molecules exemplify the approach.
- Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry
Theoretical study of one-photon and two-photon absorption properties of perylene tetracarboxylic derivatives129(2008); http://dx.doi.org/10.1063/1.2938374View Description Hide Description
The geometrical structure,electronic structure, one-photon absorption (OPA) and two-photon absorption(TPA)properties of the perylene tetracarboxylic derivatives (PTCDs) were studied theoretically by using density functional theory(DFT) and Zerner’s intermediate neglect of differential overlap (ZINDO) methods. The results revealed that increasing the number of naphthalene nucleus, extending the conjugated length on long axis, increasing the strength of donor group on lateral side, decreasing the (energy gap between the highest occupied orbital and the lowest unoccupied orbital) and keeping the conjugation effect and inductive effect along the same molecular axis are the efficient ways to enlarge TPA cross section of PTCDs compounds. The results that PTCDs compounds exhibited extremely large TPA cross section of around (near infrared region) shed light into the significance of the PTCDs compounds for applications in TPA labeling materials in vivo.
Mixed quantum/classical investigation of the photodissociation of and a practical method for maintaining zero-point energy in classical trajectories129(2008); http://dx.doi.org/10.1063/1.2943213View Description Hide Description
The photodissociationdynamics of ammonia upon excitation of the out-of-plane bending mode (mode with quanta of vibration) in the electronic state is investigated by means of several mixed quantum/classical methods, and the calculated final-state properties are compared to experiments. Five mixed quantum/classical methods are tested: one mean-field approach (the coherent switching with decay of mixing method), two surface-hopping methods [the fewest switches with time uncertainty (FSTU) and FSTU with stochastic decay (FSTU/SD) methods], and two surface-hopping methods with zero-point energy (ZPE) maintenance [the projection onto ZPE orbit (TRAPZ) and TRAPZ (mTRAPZ) methods]. We found a qualitative difference between final internal energy distributions obtained for and , as observed in experiments. Distributions obtained for present an intermediate behavior between distributions obtained for smaller and larger values. The dynamics is found to be highly electronically nonadiabatic with all these methods. internal energy distributions may have a negative energy tail when the ZPE is not maintained throughout the dynamics. The original TRAPZ method was designed to maintain ZPE in classical trajectories, but we find that it leads to unphysically high internal vibrational energies. The mTRAPZ method, which is new in this work and provides a general method for maintaining ZPE in either single-surface or multisurface trajectories, does not lead to unphysical results and is much less time consuming. The effect of maintaining ZPE in mixed quantum/classical dynamics is discussed in terms of agreement with experimental findings. The dynamics for and are also analyzed to reveal details not available from experiment, in particular, the time required for quenching of electronic excitation and the adiabatic energy gap and geometry at the time of quenching.
129(2008); http://dx.doi.org/10.1063/1.2943668View Description Hide Description
We report the energy dependence of strong collisions of with highly vibrationally excited azulene for two initial energies, and . These studies show that both the distribution of transferred energy and the energy transfer rates are sensitive to the azulene energy. Highly excited azulene was prepared in separate studies by absorption of pulsed excitation at or , followed by rapid radiationless decay from or to vibrationally excited levels of the ground electronic state. The appearance of scattered molecules with was monitored by high-resolution transient IR absorption at . The average rotational and translational energies of the scattered molecules double when the azulene energy is increased by a factor of 2. The rate of energy transfer in strong collisions increases by nearly a factor of 4 when the azulene energy is doubled. The energy transfer probability distribution function for at each initial energy is an exponential decay with curvature that correlates with the energy dependence of the state density, in excellent agreement with predictions from GRETCHEN, a model based on Fermi’s golden rule to describe collisional quenching of highly excited molecules.
- Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation
Do ionic and hydrophobic probes sense similar microenvironment in Triton X-100 nonionic reverse micelles?129(2008); http://dx.doi.org/10.1063/1.2946705View Description Hide Description
Rotational diffusion of two structurally similar ionic probes, rhodamine 110 and fluorescein, has been examined in nonionic reverse micellar system of Triton X-100/benzene–-hexane/water as a function of mole ratio of the water to surfactant,. This study has been undertaken to find out whether ionic and hydrophobic probes experience similar microenvironment in these reverse micelles. Experimental results indicate that, from to 3, the average reorientation time, which is a measure of the microviscosity experienced by the probe molecule, increases by 90% and 40% for rhodamine 110 and fluorescein, respectively, and from to 8, it decreases by 20% for both the probes. The increase in the average reorientation time with has been rationalized on the basis of the flexible oxyethylene chains of the TX-100 surfactant being hydrogen bonded by the water molecules, which makes the core region less fluid. However, once the hydration of the oxyethylene chains is complete, further addition of water results in formation of water droplet; which renders the micelle-water interface in the core region less compact leading to a marginal decrease in the average reorientation time of the probe molecules. These explanations are consistent with the location of the probes and the structure of the Triton X-100/benzene–hexane/water reverse micelles. To compare how the microenvironment experienced by these ionic probes is different from the hydrophobic ones, results from our earlier work [J. Phys. Chem. B108, 7944 (2004)] have been considered. Such a comparison revealed that both ionic and hydrophobic probes experience similar microenvironment in these reverse micelles until the hydration of the oxyethylene chains is complete. In case of hydrophobic probes, however, the onset of water dropletformation does not alter their microenvironment, which is due to their location in the reverse micellar cores.
Shear thinning and shear dilatancy of liquid -hexadecane via equilibrium and nonequilibrium molecular dynamics simulations: Temperature, pressure, and density effects129(2008); http://dx.doi.org/10.1063/1.2943314View Description Hide Description
Equilibrium and nonequilibrium molecular dynamics (MD) simulations have been performed in both isochoric-isothermal and isobaric-isothermal ensemble systems. Under steady state shearing conditions, thermodynamic states and rheological properties of liquid -hexadecane molecules have been studied. Between equilibrium and nonequilibrium states, it is important to understand how shear rates affect the thermodynamic state variables of temperature, pressure, and density. At lower shear rates of , the relationships between the thermodynamic variables at nonequilibrium states closely approximate those at equilibrium states, namely, the liquid is very near its Newtonian fluid regime. Conversely, at extreme shear rates of , specific behavior of shear dilatancy is observed in the variations of nonequilibrium thermodynamic states. Significantly, by analyzing the effects of changes in temperature, pressure, and density on shear flow system, we report a variety of rheological properties including the shear thinning relationship between viscosity and shear rate, zero-shear-rate viscosity, rotational relaxation time, and critical shear rate. In addition, the flowactivation energy and the pressure-viscosity coefficient determined through Arrhenius and Barus equations acceptably agree with the related experimental and MD simulation results.
129(2008); http://dx.doi.org/10.1063/1.2939579View Description Hide Description
Heat capacities measured for isolated aluminum clusters show peaks due to melting. For some clusters with around 60 and 80 atoms there is a dip in the heat capacities at a slightly lower temperature than the peak. The dips have been attributed to structural transitions. Here we report studies where the clusters are annealed before the heat capacity is measured. The dips disappear for some clusters, but in many cases they persist, even when the clusters are annealed to well above their melting temperature. This indicates that the dips do not result from badly formed clusters generated during cluster growth, as originally suggested. We develop a simple kinetic model of melting and freezing in a system consisting of one liquidlike and two solidlike states with different melting temperatures and latent heats. Using this model we are able to reproduce the experimental results including the dependence on the annealing conditions. The dips result from freezing into a high energy geometry and then annealing into the thermodynamically preferred solid. The thermodynamically preferred solid has the higher freezing temperature. However, the liquid can bypass freezing into the thermodynamically preferred solid (at high cooling rates) if the higher energy geometry has a larger freezing rate.
129(2008); http://dx.doi.org/10.1063/1.2939572View Description Hide Description
NMR is a popular and mature technique used in fields as diverse as chemistry, biology, or material science. One reason for this versatility lies in its ability to correlate the nuclei that are present in one molecule to another. This provides the researcher with correlation maps allowing for studies of the molecules at an atomic level. Selective experiments allow isolation of one such correlation to focus on spins of interest. This leads to a savings in precious experimental time by reducing the dimension of the experiment, which in turn may enable one to record more elaborate experiments that would otherwise not be amenable within reasonable acquisition times. Here, we present an alternative method to selectively transfer magnetization using a single rf field. This technique, which we call single field polarization transfer, allows to obtain longitudinal two-spin order of two scalar-coupled spins when only one of them is irradiated. The method is easy to implement and does not depend on stringent conditions, such as Hartmann–Hahn matching for selective cross-polarization transfers or very long inversion pulses and identification of coupling satellites in selective population inversion experiments.
129(2008); http://dx.doi.org/10.1063/1.2952270View Description Hide Description
The all-trans pentaene, 3,12-di(tert-butyl)-2,2,13,13-tetramethyl-3,5,7,9,11-tetradecapentaene (ttbP5) fluoresces in two different regions of the visible spectrum. It produces an extremely weak emission in the gas phase that can also be detected in the condensed phase; such an emission exhibits a negligible Stokes shift with respect to the absorption transition and can in principle be assigned to the emission of the compound. ttbP5 also exhibits a second fluorescence emission at approximately in both the gas phase and the condensed phase. The emission in the condensed phase increases in strength and structure, with no change in spectral position, as the solvent viscosity increases by effect of the solution temperature being lowered. The spectral behavior of this pentaene (ttbP5) is different enough from that reported [J. Catalán et al., J. Chem. Phys.128, 104504 (2008)] for its tetraene counterpart (ttbP4) to warrant a separate analysis in order to facilitate a better understanding of the way the photophysics of these polyenes changes as their chain is lengthened.
129(2008); http://dx.doi.org/10.1063/1.2943315View Description Hide Description
We applied our recently developed protocol of the conductorlike continuum model of solvation to describe the title reaction in aqueous solution. The model has the unique feature of the molecular cavity being dependent on the atomic charges in the solute and can be extended naturally to transition states and reaction pathways. It was used to calculate the reaction energetics and reaction rate in solution for the title reaction. The rate of reaction calculated using canonical variational transition state theory in the context of the equilibrium solvation path approximation, and including correction for tunneling through the small curvature approximation, was found to be , significantly slower than in the gas phase in accord with experiment. These results suggest that the present protocol of the conductorlike continuum model of solvation with the charge-dependent cavity definition captures qualitatively and quantitatively the solvation effects at transition states and allows for quantitative estimates of reaction rates in solutions.
Frequency autocorrelation function of stochastically fluctuating fields caused by specific magnetic field inhomogeneities129(2008); http://dx.doi.org/10.1063/1.2949097View Description Hide Description
Signal formation in NMR is due to incoherent dephasing of nuclear spins. Of particular practical importance is the situation of nuclear spins undergoing independent stochastic motion in inhomogeneous local magnetic fields, e.g., created by magnetized objects. Since it was demonstrated recently that the frequency correlation function of nuclear spins can be measured directly, a theoretical analysis of such functions is of interest. Here, we provide a numerically exact analysis of that correlation function for the inhomogeneous fields around two particular geometries: cylinders and spheres. The functional form exhibits three regimes: after an initial transient, there is an algebraic regime with a time dependence ( being the space dimension), followed by an exponential cutoff due to microscopic system size effects. The main parameter controlling the range of the individual regimes is the volume fraction of the magnetized objects. In addition to our numerical analysis, which is based on eigenfunction expansions, we provide analytical results and approximations based on the generalized moment expansion.