Variationally stable calculations for molecular systems: polarizabilities and two-photon ionization cross section for the hydrogen molecule

The variationally stable method of Gao and Starace [B. Gao and A. F. Starace, Phys. Rev. Lett. 61, 404 (1988); Phys. Rev. A 39, 4550 (1989)] has been applied for the first time to the study of multiphoton processes in molecular systems. The generalization in theory is presented, as well as the calculation of properties such as the static and dynamic polarizabilities of the hydrogen molecule and the generalized two-photon ionization cross section. The Schwinger variational iterative method [R. R. Lucchese and V. McKoy, Phys. Rev. A 21, 112 (1980)] has been applied in the achievement of the photoelectron wave function, while a Hartree-Fock representation has been used for the target. This research has been motivated by the scarceness of ab initio calculations of molecular multiphoton ionization cross sections in the literature.     

Electronic conductivity in polyaromatic hydrocarbon glasses: A theoretical perspective

Based upon Monte Carlo simulations of amorphous molecular glasses, we have computed the electronic structure of five prototypical polyaromatic hydrocarbons using an extended Su-Schrieffer-Heeger model [J. R. Schrieffer, W. P. Su, and A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979)]. In the presence of excess charges, the resulting potential energy surfaces have been analyzed using Marcus' [Annu. Rev. Phys. Chem. 15, 155 (1964)] theory of charge transfer to yield reaction coefficients and--via the application of linear response theory--local conductivities. Applying Kirchhoff's rules, the emerging random resistor network problem leads to global conductivities of the order of 10(-1)-1 Scm, which correlate with the structural characteristics of the underlying geometry.     

The vibrational Stokes shift of water (HOD in D2O)

The vibrational Stokes shift of the OH stretching transition nu(OH) of water is the shift between the ground-state absorption and the excited-state (v=1) emission. A recent measurement on HOD in D(2)O solvent [S. Woutersen and H. J. Bakker, Phys. Rev. Lett. 83, 2077 (1999)] of a 70 cm(-1) redshift, and a subsequent calculation of a 57 cm(-1) redshift using equilibrium molecular dynamics simulations [C. P. Lawrence and J. L. Skinner, J. Chem. Phys. 117, 8847 (2002)] were in good agreement. We now report extensive measurements of the vibrational Stokes shift in HOD/D(2)O using an ultrafast IR pump, Raman probe method. The vibrational Stokes shift is seen to depend on the pump pulse frequency and on time delay; by varying these parameters it can be made to range from 112 to -32 cm(-1) (negative values indicate a blueshift in the excited state). The equilibrium vibrational Stokes shift is actually a negative rather than a positive quantity. Possible reasons for the disagreement between experiment and theory are briefly discussed.     

Connection between the observable and centroid structural properties of a quantum fluid: application to liquid para-hydrogen

It is shown that the discrepancy between path integral Monte Carlo [M. Zoppi et al., Phys. Rev. B 65, 092204 (2002)] and path integral centroid molecular dynamics [F. J. Bermejo et al., Phys. Rev. Lett. 84, 5359 (2000)] calculations of the static structure factor of liquid para-hydrogen can be explained based on a deconvolution equation connecting centroid and physical radial distribution functions. An explicit expression for the kernel of the deconvolution equation has been obtained using functional derivative techniques. In the superposition approximation, this kernel is given by the functional derivative of the effective potential with respect to the pairwise classical potential. Results of path integral Monte Carlo calculations for the radial distribution function and the static structure factor of liquid para-hydrogen are presented.     

Differential virial theorem in relation to a sum rule for the exchange-correlation force in density-functional theory

Holas and March [Phys. Rev. A. 51, 2040 (1995)] gave a formally exact theory for the exchange-correlation (xc) force F(xc)(r)= -inverted Deltaupsilon(xc)(r) associated with the xc potential upsilon(xc)(r) of the density-functional theory in terms of low-order density matrices. This is shown in the present study to lead, rather directly, to the determination of a sum rule nF(xc)=0 relating the xc force with the ground-state density n(r). Some connection is also made with an earlier result relating to the external potential by Levy and Perdew [Phys. Rev. A. 32, 2010 (1985)] and with the quite recent study of Joubert [J. Chem. Phys. 119, 1916 (2003)] relating to the separation of the exchange and correlation contributions.     

Eckart axis conditions and the minimization of the root-mean-square deviation: two closely related problems

We highlight the fact that the rotation matrix minimizing the root-mean-square deviation between two molecular conformations [W. Kabsch, Acta Cryst. A32, 922 (1976)] also satisfies the Eckart axis conditions [C. Eckart, Phys. Rev. 47, 552 (1935)].     

Density functional theory of fluids in nanopores: analysis of the fundamental measures theory in extreme dimensional-crossover situations

Two density functional theories, the fundamental measures theory of Rosenfeld [Phys. Rev. Lett. 63, 980 (1989)] and a subsequent approximation by Tarazona [Phys. Rev. Lett. 84, 694 (2000)] are applied to the study of the hard-sphere fluid in two situations: the cylindrical pore and the spherical cavity. The results are compared with those obtained with grand canonical ensemble Monte Carlo simulations. The differences between both theories are evaluated and interpreted in the terms of the dimensional crossover from three to one and zero dimensions.     

Spin Seebeck coefficient of a molecular spin pump

Within a generalized version of previously considered model of a molecular spin pump controlled by an external electric field [J. Fransson and M. Galperin, Phys. Rev. B, 2010, 81, 075311] we discuss thermal properties of such spintronic devices. The spin Seebeck coefficient of a molecular spin pump is introduced, and several possible definitions of a nonequilibrium Seebeck coefficient are discussed. The influence of inelastic effects in spin transport on its thermospintronic characteristics are demonstrated within numerical examples.     

Constant pressure ab initio molecular dynamics with discrete variable representation basis sets

The use of discrete variable representation (DVR) basis sets within ab initio molecular dynamics calculations allows the latter to be performed with converged energies and, more importantly, converged forces. In this paper, we show how to carry out ab initio molecular dynamics calculations in the isothermal-isobaric ensemble with fully flexible simulation boxes within the DVR basis set framework. In particular, we derive the appropriate DVR based expression for the pressure tensor when the electronic structure is represented using Kohn-Sham density functional theory, and we examine the convergence of this expression as a function of the basis set size. An illustrative example using 64 silicon atoms in a fully flexible box using a combination of the Martyna-Tobias-Klein [Martyna et al., J. Chem. Phys. 101, 4177 (1994)] and Car-Parrinello [Car and Parinello, Phys. Rev. Lett. 55, 2471 (1985)] algorithms is presented to demonstrate the efficacy of the approach.     

Hard spheres revisited: accurate calculation of the solid-liquid interfacial free energy

We revise the earlier [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 85, 4751 (2000)] direct calculation of the hard sphere solid-liquid interfacial free energy by the cleaving walls method. The revisions of the method include modified interactions with the cleaving walls and the use of a nonequilibrium work measurements approach, which allows for a more robust control of the accuracy of the obtained results. We find that the new values are lower compared to the original ones, which is consistent with the more recent indirect estimates based on extrapolation from the soft-sphere results [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 94, 086102 (2005)], as well as those obtained using the capillary fluctuations method [R. L. Davidchack, J. R. Morris, and B. B. Laird, J. Chem. Phys. 125, 094710 (2006)].     

A dielectric fallacy in inferring Tg of water

In a recent analysis, Angell [Annu. Rev. Phys. Chem. 55, 559 (2004)] concluded that if water's Tg is assumed to be 160 K, the plot of dielectric loss tangent tan delta against T/Tg for unsintered amorphous solid water overlaps the corresponding plots for glycerol and propylene carbonate. We point out that such an analysis falsifies both dielectrics and molecular kinetics, and is not useful for ascertaining Tg.     

B80 and B101-103 clusters: remarkable stability of the core-shell structures established by validated density functionals

Prompted by the very recent claim that the volleyball-shaped B(80) fullerene [X. Wang, Phys. Rev. B 82, 153409 (2010)] is lower in energy than the B(80) buckyball [N. G. Szwacki, A. Sadrzadeh, and B. I. Yakobson, Phys. Rev. Lett. 98, 166804 (2007)] and core-shell structure [J. Zhao, L. Wang, F. Li, and Z. Chen, J. Phys. Chem. A 114, 9969 (2010)], and inspired by the most recent finding of another core-shell isomer as the lowest energy B(80) isomer [S. De, A. Willand, M. Amsler, P. Pochet, L. Genovese, and S. Goedecher, Phys. Rev. Lett. 106, 225502 (2011)], we carefully evaluated the performance of the density functional methods in the energetics of boron clusters and confirmed that the core-shell construction (stuffed fullerene) is thermodynamically the most favorable structural pattern for B(80). Our global minimum search showed that both B(101) and B(103) also prefer a core-shell structure and that B(103) can reach the complete core-shell configuration. We called for great attention to the theoretical community when using density functionals to investigate boron-related nanomaterials.     

Theoretical interpretation of Grimme's spin-component-scaled second order Møller-Plesset theory

It is shown that spin-component-scaled second order M?ller-Plesset theory proposed by Grimme [J. Chem. Phys. 118, 9095 (2003)] can be interpreted as a two-parameter scaling of the zero order Hamiltonian, a generalization of the approach reported by Feenberg [Phys. Rev. 103, 1116 (1956)].     

A proof of Jarzynski's nonequilibrium work theorem for dynamical systems that conserve the canonical distribution

We present a derivation of the Jarzynski [Phys. Rev. Lett. 78, 2690 (1997)] identity and the Crooks [J. Stat. Phys. 90, 1481 (1998)] fluctuation theorem for systems governed by deterministic dynamics that conserves the canonical distribution such as Hamiltonian dynamics, Nose-Hoover dynamics, Nose-Hoover chains, and Gaussian isokinetic dynamics. The proof is based on a relation between the heat absorbed by the system during the nonequilibrium process and the Jacobian of the phase flow generated by the dynamics.     

The self-referential method combined with thermodynamic integration

The self-referential method [M. B. Sweatman, Phys. Rev. E 72, 016711 (2005)] for calculating the free energy of crystalline solids via molecular simulation is combined with thermodynamic integration to produce a technique that is convenient and efficient. Results are presented for the chemical potential of hard sphere and Lennard-Jones face centered cubic crystals that agree well with this previous work. For the small system sizes studied, this technique is about 100 times more efficient than the parameter hopping technique used previously.     

A theoretical study of molecular conduction. II. A Hartree-Fock approach to transmission probability

In this paper, we discuss molecular conductivity based on Green's function methods. In our calculations, we adopted the self-energy formalism to accommodate semi-infinite electrodes connected to a molecule, and the self-energy was obtained from the surface Green's function of the electrodes. We adopted the formalism of the surface Green's function derived by Sanvito et al. [Phys. Rev. B 59, 11936 (1999)] and Krstic et al. [Phys. Rev. B 66, 205319 (2002)], and although their formalisms for the surface Green's function were different, we were able to demonstrate that these formalisms are mathematically identical. We analyzed the electron transmission probability by using the spectrum expression of Green's function, instead of using the inverse matrix of the effective Hamiltonian that includes an isolated molecule and the electrodes. Finally, we calculated the transmission probability of benzenedithiol based on the Hartree-Fock method and analyzed the disappearance of the transmission probability due to the orbital interference.     

Percus-Yevick theory for the structural properties of the seven-dimensional hard-sphere fluid

The direct correlation function and the (static) structure factor for a seven-dimensional hard-sphere fluid are considered. Analytical results for these quantities are derived within the Percus-Yevick [Phys. Rev.110, 1 (1958)] theory.     

Statistical mechanical theory for steady state systems. VI. Variational principles

Several variational principles that have been proposed for nonequilibrium systems are analyzed. These include the principle of minimum rate of entropy production due to Prigogine [Introduction to Thermodynamics of Irreversible Processes (Interscience, New York, 1967)], the principle of maximum rate of entropy production, which is common on the internet and in the natural sciences, two principles of minimum dissipation due to Onsager [Phys. Rev. 37, 405 (1931)] and to Onsager and Machlup [Phys. Rev. 91, 1505 (1953)], and the principle of maximum second entropy due to Attard [J. Chem.. Phys. 122, 154101 (2005); Phys. Chem. Chem. Phys. 8, 3585 (2006)]. The approaches of Onsager and Attard are argued to be the only viable theories. These two are related, although their physical interpretation and mathematical approximations differ. A numerical comparison with computer simulation results indicates that Attard's expression is the only accurate theory. The implications for the Langevin and other stochastic differential equations are discussed.     

Structural and dynamical properties of surfaces from ab-initio molecular dynamics

The recent application to the semiconductor surfaces of the powerful ab-initio molecular dynamics (Car-Parrinello) method [R. Car, M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985)] will be reviewed. The essential features of the method will be addressed first, then we will review a number of recent studies on the properties of the clean and adsorbate covered surfaces of Si, Ge and GaAs, obtained through Car-Parrinello simulations. Finally an original application of the ab-initio molecular dynamics for the clean and hydrogenated GaAs(110) surfaces is presented.