On a variational approach to the Soret coefficient

In this paper, a variational approach to the Soret coefficient initiated by Kempers [J. Chem. Phys. 90, 6541 (1989)] is critically revisited. We show that the physical coherence of the whole procedure leads to a very peculiar choice of the type of constraint one can select to mimic the nonequilibrium stationary state. However, we demonstrate that its precise definition would require a statistical evaluation of the heat of transfer, or a variational approach based on more microscopic ingredients.     

Metal phosphonates applied to biotechnologies: a novel approach to oligonucleotide microarrays

A new process for preparing oligonucleotide arrays is described that uses surface grafting chemistry which is fundamentally different from the electrostatic adsorption and organic covalent binding methods normally employed. Solid supports are modified with a mixed organic/inorganic zirconium phosphonate monolayer film providing a stable, well-defined interface. Oligonucleotide probes terminated with phosphate are spotted directly on to the zirconated surface forming a covalent linkage. Specific binding of terminal phosphate groups with minimal binding of the internal phosphate diesters has been demonstrated. The mixed organic/inorganic thin films have also been extended for use arraying DNA duplex probes, and therefore represent a viable general approach to DNA-based bioarrays. Ideas for interfacing mixed organic/inorganic interfaces to other bioapplications are also discussed.     

Maximum entropy principle applied to semiflexible ring polymers

Based on the success of the maximum entropy principle (MEP) in the study of semiflexible treelike polymers [M. Dolgushev and A. Blumen, J. Chem. Phys. 131, 044905 (2009)], it is of much interest to establish MEP's potential for general semiflexible polymers which contain loops. Here, we embark on this endeavor by considering discrete semiflexible polymer rings in a Rouse-type scheme. Now, for treelike polymers a beads-and-bonds (i.e., a discrete) picture is essential for an easy inclusion of branching points. Moreover, one may envisage (similar to our former work [M. Dolgushev and A. Blumen, J. Chem. Phys. 131, 044905 (2009)]) to impose for each angle between two bonds a distinct stiffness condition. Working in this way leads already for a polymer ring to a complicated problem. Hence, we follow a reduced variational approach as applied earlier to polymer chains, in which a single Lagrange multiplier is used for each set of identical conditions imposed on topologically equivalent bonds and bonds' orientations. In this way, we obtain for the discrete ring an analytically closed form which involves Chebyshev polynomials. This expression turns out to lead to a series of solutions: Apart from the regular solution, several other solutions appear. One may be tempted to discard the other solutions, since for them the potential energy matrix is not positive definite. A more careful analysis based on topological features suggests, however, that such solutions can be assigned to rings displaying knots. Monte Carlo simulations which take excluded volume interactions into account agree with our interpretation.     

A parametric variant of resonant activation: two-state model approach

Mean first passage time of a periodically driven particle for its escape over a fluctuating barrier with wells remaining unbiased exhibits a resonance when the frequency of the driving field is varied. This parametric variant of resonant activation and associated features of noise induced transition are realized in terms of a two-state model to estimate analytically several quantifiers of the escape event. Numerical simulation on a continuous double-well model collaborates our theoretical analysis.     

Response functions from Fourier component variational perturbation theory applied to a time-averaged quasienergy

It is demonstrated that frequency-dependent response functions can conveniently be derived from the time-averaged quasienergy. The variational criteria for the quasienergy determines the time-evolution of the wave-function parameters and the time-averaged time-dependent Hellmann–Feynman theorem allows an identification of response functions as derivatives of the quasienergy. The quasienergy therefore plays the same role as the usual energy in time-independent theory, and the same techniques can be used to obtain computationally tractable expressions for response properties, as for energy derivatives in time-independent theory. This includes the use of the variational Lagrangian technique for obtaining expressions for molecular properties in accord with the 2n+1 and 2n+2 rules. The derivation of frequency-dependent response properties becomes a simple extension of variational perturbation theory to a Fourier component variational perturbation theory. The generality and simplicity of this approach are illustrated by derivation of linear and higher-order response functions for both exact and approximate wave functions and for both variational and nonvariational wave functions. Examples of approximate models discussed in this article are coupled-cluster, self-consistent field, and second-order Møller–Plesset perturbation theory. A discussion of symmetry properties of the response functions and their relation to molecular properties is also given, with special attention to the calculation of transition- and excited-state properties. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 1–52, 1998     

Dynamical variational approach to non-adiabatic electronic structure

Studying non-adiabatic effects in molecular dynamics simulations and modeling their optical signatures in linear and non-linear spectroscopies calls for electronic structure calculations in a situation when the ground state is degenerate or almost degenerate. Such degeneracy causes serious problems in invoking single Slater determinant Hartree–Fock (HF) and density functional theory (DFT) methods. To resolve this problem, we develop a generalization of time-dependent (dynamical) variational approach which accounts for the degenerate or almost degenerate ground state structure. Specifically, we propose a ground state ansatz for the subspace of generalized electronic configurations spanned on the degenerate grounds state multi-electron wavefunctions. Further employing the invariant form of Hamilton dynamics we arrive with the classical equations of motion describing the time-evolution of this subspace in the vicinity of the stationary point. The developed approach can be used for accurate calculations of molecular excited states and electronic spectra in the degenerate case.     

Separable approximation for diatomic transition operators: a variational approach

A general finite-rank separable approximation for the two-body transition operator has been obtained from the Lippmann--Schwinger variational principle. The method involves expansion of the off-shell wavefunction in a finite set of square integrable functions, and is applied to ¹Σ and ³Σ potentials of H₂ for thermal energies and momenta.     

Rate processes with dynamical disorder: a direct variational approach

Using path integral approach, we develop variational approximations to the calculation of survival probability for rate processes with dynamical disorder. We derive both upper and lower bounds to the survival probability using Jensen's inequality. The inequalities involve the use of a trial action for which the path integrals can be evaluated exactly. Any parameter in the trial action can be varied to optimize the bounds. We have also derived a lower bound to the rate of the process. As a simple illustration, we apply the method to the problem of a particle undergoing Brownian motion in a harmonic potential well, in the presence of a delta function sink, for which one can calculate the exact survival probability numerically. The calculation confirms the two inequalities. The method should be very useful in similar but more complex problems where even numerical solution is not possible.     

Quantum two-state dynamics driven by stationary non-Markovian discrete noise: Exact results

We consider the problem of stochastic averaging of a quantum two-state dynamics driven by non-Markovian, discrete noises of the continuous time random walk type (multistate renewal processes). The emphasis is put on the proper averaging over the stationary noise realizations corresponding, e.g., to a stationary environment. A two-state non-Markovian process with an arbitrary non-exponential distribution of residence times (RTDs) in its states with a finite mean residence time provides a paradigm. For the case of a two-state quantum relaxation caused by such a classical stochastic field we obtain the explicit exact, analytical expression for the averaged Laplace-transformed relaxation dynamics. In the limit of Markovian noise (implying an exponential RTD), all previously known results are recovered. We exemplify new more general results for the case of non-Markovian noise with a biexponential RTD. The averaged, real-time relaxation dynamics is obtained in this case by numerically exact solving of a resulting algebraic polynomial problem. Moreover, the case of manifest non-Markovian noise with an infinite range of temporal autocorrelation (which in principle is not accessible to any kind of perturbative treatment) is studied, both analytically (asymptotic long-time dynamics) and numerically (by a precise numerical inversion of the Laplace-transformed averaged quantum relaxation).     

Self-consistent-field variational approach to the interaction between a polymer and a small molecule

A variational SCF treatment based on a perturbational concept is developed and applied to the interaction between trans-polyacetylene and a small molecule. The validity of the present method is examined by comparing the results with those from the conventional tight-binding SCF crystal orbital method. The interaction energies and charge distributions obtained are in good agreement between the two methods. This result suggests that the present variational approach is promising for application to complicated interactions between a polymer and impurities.     

A variational approach to relativistic effects in LCAO calculations

We suggest a simple procedure which makes it possible to include relativistic effects approximately in variational LCAO calculations. The scheme uses a free-particle projection, and is readily applicable to polyatomic systems. Pilot calculations on one-electron atoms are presented, and compared with exact Dirac solutions.     

Reorientation dynamics of nanoconfined water: power-law decay, hydrogen-bond jumps, and test of a two-state model

The reorientation dynamics of water confined within nanoscale, hydrophilic silica pores are investigated using molecular dynamics simulations. The effect of surface hydrogen-bonding and electrostatic interactions are examined by comparing with both a silica pore with no charges (representing hydrophobic confinement) and bulk water. The OH reorientation in water is found to slow significantly in hydrophilic confinement compared to bulk water, and is well-described by a power-law decay extending beyond one nanosecond. In contrast, the dynamics of water in the hydrophobic pore are more modestly affected. A two-state model, commonly used to interpret confined liquid properties, is tested by analysis of the position-dependence of the water dynamics. While the two-state model provides a good fit of the orientational decay, our molecular-level analysis evidences that it relies on an over-simplified picture of water dynamics. In contrast with the two-state model assumptions, the interface dynamics is markedly heterogeneous, especially in the hydrophilic pore and there is no single interfacial state with a common dynamics.     

On the characterization of three-state conical intersections using a group homomorphism approach: the two-state degeneracy spaces

Second-order degenerate perturbation theory, in conjunction with the group homomorphism method for describing a similarity transformation, are used to characterize the subspace of two-state conical intersections contained in the branching space of a three-state conical intersection. It is shown by explicit calculation, using the lowest three-state conical intersection of (CH)3N2, that a second-order treatment yields highly accurate absolute energies, even at significant distances from the reference point of three-state intersection. The excellent agreement between the second order and ab initio results depends on the average energy component, which is computed using 5 first-order terms and 15 second-order terms. The second-order absolute energy change over the range rho = 0.0-0.3 au, where rho is the distance from the three-state conical intersection in the branching space coordinates, is approximately 6500 and 9500 cm(-1) for the E(1=2) and E(2=3) seams, respectively, with the maximum ab initio energy deviation from degeneracy of 200 cm(-1) occurring at rho = 0.3 au. The characteristic parameters gIJ and hIJ are also predicted to great accuracy, even at large rho, with the error growing to only 10-15% at rho = 0.3 au.     

MILCH SHAKE: An efficient method for constraint dynamics applied to alkanes

We describe a method to impose constraints in a molecular dynamics simulation. A technique developed to solve the special case of a linear topology (MILC SHAKE) is hybridized with the SHAKE algorithm. The methodology, which we term MILC‐hybridized SHAKE (or MILCH SHAKE), applies to more complex topologies. Here we consider the important case of all atom models of alkanes. Exploiting the mass difference between carbon and hydrogen we show that for higher alkanes MILCH SHAKE can be an order of magnitude faster than SHAKE. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009