Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action

It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them theta-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding field theory. In the present article, we discuss the problem of constructing theta-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract theta-modified actions of the relativistic particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as theta-modified actions of the relativistic particles. To confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The theta-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case.

Electronic properties of liquid hydrogen fluoride: A sequential quantum mechanical/Born-Oppenheimer molecular dynamics approach

The electronic properties of liquid hydrogen fluoride (HF) were investigated by carrying out sequential quantum mechanics/Born-Oppenheimer molecular dynamics. The structure of the liquid is in good agreement with recent experimental information. Emphasis was placed on the analysis of polarisation effects, dynamic polarisability and electronic excitations in liquid HF. Our results indicate an increase in liquid phase of the dipole moment (similar to 0.5 D) and isotropic polarisability (5%) relative to their gas-phase values. Our best estimate for the first vertical excitation energy in liquid HF indicates a blue-shift of 0.4 +/- 0.2 eV relative to that of the gas-phase monomer (10.4 eV). (C) 2010 Elsevier B.V. All rights reserved.

Canonical quantum potential scattering theory

A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find nonlinear first-order differential equations for the low-energy scattering parameters such as scattering length and effective range. They significantly simplify typical calculations, as we illustrate for atom-atom and neutron-nucleus scattering systems. A generalization to charged particle scattering is also possible.

Genesis of quantum nonlocality

We revisit the problem of an otherwise classical particle immersed in the zero-point radiation field, with the purpose of tracing the origin of the nonlocality characteristic of Schrodinger`s equation. The Fokker-Planck-type equation in the particles phase-space leads to an infinite hierarchy of equations in configuration space. In the radiationless limit the first two equations decouple from the rest. The first is the continuity equation: the second one, for the particle flux, contains a nonlocal term due to the momentum fluctuations impressed by the field. These equations are shown to lead to Schrodinger`s equation. Nonlocality (obtained here for the one-particle system) appears thus as a property of the description, not of Nature. (C) 2011 Elsevier B.V. All rights reserved.

Dynamical noncommutativity

The model of dynamical noncommutativity is proposed. The system consists of two interrelated parts. The first of them describes the physical degrees of freedom with the coordinates q(1) and q(2), and the second corresponds to the noncommutativity eta which has a proper dynamics. After quantization, the commutator of two physical coordinates is proportional to the function of eta. The interesting feature of our model is the dependence of nonlocality on the energy of the system. The more the energy, the more the nonlocality. The leading contribution is due to the mode of noncommutativity; however, the physical degrees of freedom also contribute in nonlocality in higher orders in theta .

Coherent state quantization of paragrassmann algebras

By using a coherent state quantization of paragrassmann variables, operators are constructed in finite Hilbert spaces. We thus obtain in a straightforward way a matrix representation of the paragrassmann algebra. This algebra of finite matrices realizes a deformed Weyl-Heisenberg algebra. The study of mean values in coherent states of some of these operators leads to interesting conclusions.

Star products made (somewhat) easier

We develop an approach to the deformation quantization on the real plane with an arbitrary Poisson structure which is based on Weyl symmetrically ordered operator products. By using a polydifferential representation for the deformed coordinates, xj we are able to formulate a simple and effective iterative procedure which allowed us to calculate the fourth-order star product (and may be extended to the fifth order at the expense of tedious but otherwise straightforward calculations). Modulo some cohomology issues which we do not consider here, the method gives an explicit and physics-friendly description of the star products.

Continuum, Discrete, and Explicit Solvation Models for Describing the Low-Lying Absorption Spectrum of the Pterin Acid in Aqueous Environment

The absorption spectrum of the acid form of pterin in water was investigated theoretically. Different procedures using continuum, discrete, and explicit models were used to include the solvation effect on the absorption spectrum, characterized by two bands. The discrete and explicit models used Monte Carlo simulation to generate the liquid structure and time-dependent density functional theory (B3LYP/6-31G+(d)) to obtain the excitation energies. The discrete model failed to give the correct qualitative effect on the second absorption band. The continuum model, in turn, has given a correct qualitative picture and a semiquantitative description. The explicit use of 29 solvent molecules, forming a hydration shell of 6 angstrom, embedded in the electrostatic field of the remaining solvent molecules, gives absorption transitions at 3.67 and 4.59 eV in excellent agreement with the S(0)-S(1) and S(0)-S(2) absorption bands at of 3.66 and 4.59 eV, respectively, that characterize the experimental spectrum of pterin in water environment. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110: 2371-2377, 2010

Excited state electronic polarization and reappraisal of the n <- pi* emission of acetone in water

Electronic polarization of the acetone molecule in the excited n -> pi* state is considered and its influence on the solvent shift in the emission spectrum is analyzed. Using an iterative procedure the electronic polarizations of both the ground and the excited states are included and compared with previous results obtained with Car-Parrinello dynamics. Analysis of the emission transition obtained using CIS(D)/aug-cc-pVDZ on statistically uncorrelated solute-solvent structures, composed of acetone and twelve explicit water molecules embedded in the electrostatic field of remaining 263 water molecules, corroborates that the solvent effect is mild, calculated here between 80 and 380 cm (1). (c) 2010 Published by Elsevier B.V.

Electronic spectroscopy of biomolecules in solution: fluorescein dianion in water

A combined and sequential Monte Carlo-quantum mechanics methodology is used to describe the electronic absorption spectrum of the fluorescein dianion in water. Different sets of 100 statistically relevant configurations composed of the solute and several solvent molecules are sampled from the Monte Carlo simulation for a posteriori quantum mechanical calculations of the spectra. In the largest case the configurations are composed of fluorescein and 90 explicit water molecules embedded in the electrostatic field of all remaining water molecules within a distance of 11.3 angstrom. These configurations include 305 atoms and 842 valence electrons, justifying the use of a semi-empirical approach. The electronic spectrum is then calculated using the INDO/CIS method. The solvatochromic shift of fluorescein in water, compared with in isolation, is calculated using the discrete and explicit solvent models. The use of electrostatically embedded explicit water molecules, in INDO/CIS calculations, gives a good description of the spectral shift of the fluorescein dianion in aqueous environment. The results are verified to converge both statistically and with respect to the number of explicit solvent molecules used.

NMR Chemical Shielding and Spin-Spin Coupling Constants of Liquid NH(3): A Systematic Investigation using the Sequential QM/MM Method

The NMR spin coupling parameters, (1)J(N,H) and (2)J(H,H), and the chemical shielding, sigma((15)N), of liquid ammonia are studied from a combined and sequential QM/MM methodology. Monte Carlo simulations are performed to generate statistically uncorrelated configurations that are submitted to density functional theory calculations. Two different Lennard-Jones potentials are used in the liquid simulations. Electronic polarization is included in these two potentials via an iterative procedure with and without geometry relaxation, and the influence on the calculated properties are analyzed. B3LYP/aug-cc-pVTZ-J calculations were used to compute the V(N,H) constants in the interval of -67.8 to -63.9 Hz, depending on the theoretical model used. These can be compared with the experimental results of -61.6 Hz. For the (2)J(H,H) coupling the theoretical results vary between -10.6 to -13.01 Hz. The indirect experimental result derived from partially deuterated liquid is -11.1 Hz. Inclusion of explicit hydrogen bonded molecules gives a small but important contribution. The vapor-to-liquid shifts are also considered. This shift is calculated to be negligible for (1)J(N,H) in agreement with experiment. This is rationalized as a cancellation of the geometry relaxation and pure solvent effects. For the chemical shielding, U(15 N) Calculations at the B3LYP/aug-pcS-3 show that the vapor-to-liquid chemical shift requires the explicit use of solvent molecules. Considering only one ammonia molecule in an electrostatic embedding gives a wrong sign for the chemical shift that is corrected only with the use of explicit additional molecules. The best result calculated for the vapor to liquid chemical shift Delta sigma((15)N) is -25.2 ppm, in good agreement with the experimental value of -22.6 ppm.

Solvent Effects in Chemical Processes. Water-Assisted Proton Transfer Reaction of Pterin in Aqueous Environment

Pterins are members of a family of heterocyclic compounds present in a wide variety of biological systems and may exist in two forms, corresponding to an acid and a basic tautomer. In this work, the proton transfer reaction between these tautomeric forms was investigated in the gas phase and in aqueous solution. In gas phase, the intramolecular mechanism was carried out for die isolated pterin by quantum mechanical second-order Moller-Plesset Perturbation theory (MP2/aug-cc-pVDZ) calculations and it indicates that the acid form is more stable than the basic form by -1.4 kcal/mol with a barrier of 34.2 kcal/mol with respect to the basic form. In aqueous solution, the role of the water molecules in the proton transfer reaction was analyzed in two separated parts, the direct participation of one water molecule in the reaction path, called water-assisted mechanism, and the complementary participation of the aqueous solvation. The water-assisted mechanism was carried out for one pterin-water cluster by quantum mechanical calculations and it indicates that the acid form is still more stable by -3.3 kcal/mol with a drastic reduction of 70% of the barrier, The bulk solution effect on the intramolecular and water-assisted mechanisms was included by free energy perturbation implemented on Monte Carlo simulations. The bulk water effect is found to be substantial and decisive when the reaction path involves the water-assisted mechanism. In this case, the free energy barrier is only 6.7 kcal/mol and the calculated relative Gibbs free energy for the two tautomers is -11.2 kcal/mol. This value is used to calculate the pK(a) value of 8.2 +/- 0.6 that is in excellent agreement with the experimental result of 7.9.

Dipole polarizability and Rayleigh light scattering by the hydrated electron

Assuming the existence of a confined state of the electron in bulk water the polarizability of the hydrated electron is analyzed. Statistically uncorrelated supermolecular structures composed of seven water molecules (first solvation shell) with an extra electron were extracted from classical Monte Carlo simulation and used in quantum mechanical second-order Moller-Plesset calculations. It is found that the bound excess electron contributes with 274 a.u. to the total dipole polarizability of 345 a.u. for (H(2)O)(7)(-). From the calculated polarizabilities the Rayleigh elastic light scattering properties are inferred and found to considerably enhance activity and light depolarization. (C) 2009 Elsevier B.V. All rights reserved.

Polarization and Spectral Shift of Benzophenone in Supercritical Water

Monte Carlo simulation and quantum mechanics calculations based on the INDO/CIS and TD-DFT methods were utilized to study the solvatochromic shift of benzophenone when changing the environment from normal water to supercritical (P = 340.2 atm and T = 673 K) condition. Solute polarization increases the dipole moment of benzophenone, compared to gas phase, by 88 and 35% in normal and supercritical conditions, giving the in-solvent dipole value of 5.8 and 4.2 D, respectively. The average number of solute-solvent hydrogen bonds was analyzed, and a large decrease of 2.3 in normal water to only 0.8 in the supercritical environment was found. By using these polarized models of benzophenone in the two different conditions of water, we performed MC simulations to generate statistically uncorrelated configurations of the solute surrounded by the solvent molecules and subsequent quantum mechanics calculations on these configurations. When changing from normal to supercritical water environment, INDO/CIS calculations explicitly considering all valence electrons of the 235 solvent water molecules resulted in a solvatochromic shift of 1425 cm(-1) for the most intense transition of benzophenone, that is, slightly underestimated in comparison with the experimentally inferred result of 1700 cm(-1). TD-B3LYP/6-311+G(2d,p) calculations on the same configurations but with benzophenone electrostatically embedded in the 320 water molecules resulted in a solvatochromic shift of 1715 cm(-1) for this transition, in very good agreement with the experimental result. When using the unpolarized model of the benzophenone, this calculated solvatochromic shift was only 640 cm(-1). Additional calculations were also made by using BHandHLYP/6-311+G(2d,p) to analyze the effect of the asymptotic decay of the exchange functional. This study indicates that, contrary to the general expectation, there is a sizable solute polarization even in the low-density regime of supercritical condition and that the inclusion of this polarization is important for a reliable description of the spectral shifts considered here.

Polarization and solvatochromic shift of ortho-betaine in water

Betaine dyes are known to show very large transition energy shifts in different solvents. The ortho-betaine molecule - a simple two-ring prototype of the E-T(30) Reichardt dye - has been investigated theoretically from a combined statistical and quantum mechanics approach. Using sequential Monte Carlo (MC) simulations and MP2/cc-pVDZ calculations the in-water dipole moment of ortho-betaine is obtained as 12.30 +/- 0.05 D. This result shows a considerable increase of 75% compared to the in-vacuum dipole moment. For comparison, the use of a polarizable continuum model using the same MP2/cc-pVDZ leads to an in-water dipole moment of 11.6 D, in good agreement. This large polarization is incorporated in the classical potential for another MC simulation to generate solute-solvent configurations and to obtain the contribution of the polarization effect in the solvatochromic shift. Using statistically uncorrelated configurations and supermolecular INDO/CIS calculations, including the solute and, explicitly, 230 solvent water molecules, the statistically converged calculated shift is obtained here as 6360 cm(-1), in good agreement with the experimental result of 7550 cm(-1). (c) 2007 Elsevier B.V. All rights reserved.