Review of Feynman’s Path Integral in Quantum Statistics: from the Molecular Schrödinger Equation to Kleinert’s Variational Perturbation Theory

Wong, Kin Yiu

doi:10.4208/cicp.140313.070513s

Cited by 11 publications

(24 citation statements)

References 152 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are a number of semi-classical, mixed quantum-classical, and fully quantum approaches developed or being developed. [55][56][57][58][59][60][61][62][63][64][65] From the point of view of MM theory, an excellent beginning is the work of Beck and colleagues 20, 66 who have derived a quantum version of the Widom potential distribution theorem; 23 using Fourier path integral methods, they derive a quantum expression for the excess chemical potential of a monatomic solute (see also Ref. 67 for a discretized path integral version).…”

Section: A Extensions: Molecular Liquids Nonadditive Vacuum Potentimentioning

confidence: 99%

See 1 more Smart Citation

McMillan-Mayer theory of solutions revisited: Simplifications and extensions

Vafaei

Tomberli

Gray

2014

The Journal of Chemical Physics

View full text Add to dashboard Cite

McMillan and Mayer (MM) proved two remarkable theorems in their paper on the equilibrium statistical mechanics of liquid solutions. They first showed that the grand canonical partition function for a solution can be reduced to one with an effectively solute-only form, by integrating out the solvent degrees of freedom. The total effective solute potential in the effective solute grand partition function can be decomposed into components which are potentials of mean force for isolated groups of one, two, three, etc., solute molecules. Second, from the first result, now assuming low solute concentration, MM derived an expansion for the osmotic pressure in powers of the solute concentration, in complete analogy with the virial expansion of gas pressure in powers of the density at low density. The molecular expressions found for the osmotic virial coefficients have exactly the same form as the corresponding gas virial coefficients, with potentials of mean force replacing vacuum potentials. In this paper, we restrict ourselves to binary liquid solutions with solute species A and solvent species B and do three things: (a) By working with a semi-grand canonical ensemble (grand with respect to solvent only) instead of the grand canonical ensemble used by MM, and avoiding graphical methods, we have greatly simplified the derivation of the first MM result, (b) by using a simple nongraphical method developed by van Kampen for gases, we have greatly simplified the derivation of the second MM result, i.e., the osmotic pressure virial expansion; as a by-product, we show the precise relation between MM theory and Widom potential distribution theory, and (c) we have extended MM theory by deriving virial expansions for other solution properties such as the enthalpy of mixing. The latter expansion is proving useful in analyzing ongoing isothermal titration calorimetry experiments with which we are involved. For the enthalpy virial expansion, we have also changed independent variables from semi-grand canonical, i.e., fixed {N(A), μ(B), V, T}, to those relevant to the experiment, i.e., fixed {N(A), N(B), p, T}, where μ denotes chemical potential, N the number of molecules, V the volume, p the pressure, and T the temperature.

show abstract

Section: A Extensions: Molecular Liquids Nonadditive Vacuum Potentimentioning

confidence: 99%

“…We use (59) in the first 1/c B term in (58) and expand (1 +bc A ) −1 as (1 −bc A ) to first order. We can use 1/c B .…”

Section: Virial Expansion At Constant Pressure For the Solvent Chemicmentioning

confidence: 99%

McMillan-Mayer theory of solutions revisited: Simplifications and extensions

Vafaei

Tomberli

Gray

2014

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…In this work, with the treatment of solvent effects by a dielectric continuum, we used our AIF‐PI method to determine the values of W , and then in turn used Eqs. and to compute EIE and KIE values along the reaction path of intrinsic reaction coordinate (IRC) on the ab initio potential energy surface .…”

Section: Computational Detailsmentioning

confidence: 99%

“…In the AIF‐PI method, we interpolated the original gas‐phase and solution‐phase PES along each normal mode by a 20 th ‐order polynomial at a step size of 0.1 Å . The centroid potential is computed up to the second order of KP expansion.…”

Section: Computational Detailsmentioning

confidence: 99%

See 1 more Smart Citation

Ab initio path‐integral calculations of kinetic and equilibrium isotope effects on base‐catalyzed RNA transphosphorylation models

Wong

York

2014

J Comput Chem

Self Cite

View full text Add to dashboard Cite

Detailed understandings of the reaction mechanisms of RNA catalysis in various environments can have profound importance for many applications, ranging from the design of new biotechnologies to the unraveling of the evolutionary origin of life. An integral step in the nucleolytic RNA catalysis is self-cleavage of RNA strands by 2′-O-transphosphorylation. Key to elucidating a reaction mechanism is determining the molecular structure and bonding characteristics of transition state. A direct and powerful probe of transition state is measuring isotope effects on biochemical reactions, particularly if we can reproduce isotope effect values from quantum calculations. This paper significantly extends the scope of our previous joint experimental and theoretical work in examining isotope effects on enzymatic and non-enzymatic 2′-O-transphosphorylation reaction models that mimic reactions catalyzed by RNA enzymes (ribozymes), and protein enzymes such as ribonuclease A (RNase A). Native reactions are studied, as well as reactions with thio substitutions representing chemical modifications often used in experiments to probe mechanism. Here, we report and compare results from eight levels of electronic-structure calculations for constructing the potential energy surfaces in kinetic and equilibrium isotope effects (KIE and EIE) computations, including a “gold-standard” coupled-cluster level of theory [CCSD(T)]. In addition to the widely-used Bigeleisen equation for estimating KIE and EIE values, internuclear anharmonicity and quantum tunneling effects were also computed using our recently-developed ab initio path-integral method, i.e., automated integration-free path-integral (AIF-PI) method. The results of this work establish an important set of benchmarks that serve to guide calculations of KIE and EIE for RNA catalysis.

show abstract

The 4D Dirac Equation in Five Dimensions

Breban

2018

Annalen der Physik

View full text Add to dashboard Cite

The Dirac equation may be thought as originating from a theory of five-dimensional (5D) spacetime. We define a special 5D Clifford algebra and introduce a spin-1/2 constraint equation to describe null propagation in a 5D space-time manifold. We explain how the 5D null formalism breaks down to four dimensions to recover two single-particle theories. Namely, we obtain Dirac's relativistic quantum mechanics and a formulation of statistical mechanics. Exploring the non-relativistic limit in five and four dimensions, we identify a new spin-electric interaction with possible applications to magnetic resonance spectroscopy (within quantum mechanics) and superconductivity (within statistical mechanics).

show abstract

Review of Feynman’s Path Integral in Quantum Statistics: from the Molecular Schrödinger Equation to Kleinert’s Variational Perturbation Theory

Cited by 11 publications

References 152 publications

McMillan-Mayer theory of solutions revisited: Simplifications and extensions

McMillan-Mayer theory of solutions revisited: Simplifications and extensions

Ab initio path‐integral calculations of kinetic and equilibrium isotope effects on base‐catalyzed RNA transphosphorylation models

The 4D Dirac Equation in Five Dimensions

Contact Info

Product

Resources

About