Review of computer simulations of isotope effects on biochemical reactions: From the Bigeleisen equation to Feynman's path integral

2015 ◽  
Vol 1854 (11) ◽  
pp. 1782-1794 ◽  
Author(s):  
Kin-Yiu Wong ◽  
Yuqing Xu ◽  
Liang Xu
Keyword(s):  
Computer Simulations ◽  
Path Integral ◽  
Isotope Effects ◽  
Biochemical Reactions

Vapour Pressure Isotope Effect on Evaporation from Pure Organic Phases - a PIMD Approach

2020 ◽  
Author(s):  
Luis Vasquez ◽  
Agnieszka Dybala-Defratyka
Keyword(s):  
Path Integral ◽  
Vapour Pressure ◽  
Density Functional ◽  
Isotope Effects ◽  
Tight Binding ◽  
Decomposition Analysis ◽  
Energy Decomposition Analysis ◽  
Special Importance ◽  
Non Covalent Interactions ◽  
Covalent Interactions

<p></p><p>Very often in order to understand physical and chemical processes taking place among several phases fractionation of naturally abundant isotopes is monitored. Its measurement can be accompanied by theoretical determination to provide a more insightful interpretation of observed phenomena. Predictions are challenging due to the complexity of the effects involved in fractionation such as solvent effects and non-covalent interactions governing the behavior of the system which results in the necessity of using large models of those systems. This is sometimes a bottleneck and limits the theoretical description to only a few methods.<br> In this work vapour pressure isotope effects on evaporation from various organic solvents (ethanol, bromobenzene, dibromomethane, and trichloromethane) in the pure phase are estimated by combining force field or self-consistent charge density-functional tight-binding (SCC-DFTB) atomistic simulations with path integral principle. Furthermore, the recently developed Suzuki-Chin path integral is tested. In general, isotope effects are predicted qualitatively for most of the cases, however, the distinction between position-specific isotope effects observed for ethanol was only reproduced by SCC-DFTB, which indicates the importance of using non-harmonic bond approximations.<br> Energy decomposition analysis performed using the symmetry-adapted perturbation theory (SAPT) revealed sometimes quite substantial differences in interaction energy depending on whether the studied system was treated classically or quantum mechanically. Those observed differences might be the source of different magnitudes of isotope effects predicted using these two different levels of theory which is of special importance for the systems governed by non-covalent interactions.</p><br><p></p>

Chapter 5. Kinetic Isotope Effects from Hybrid Classical and Quantum Path Integral Computations

2009 ◽  
pp. 105-131 ◽  
Author(s):  
Jiali Gao ◽  
Kin-Yiu Wong ◽  
Dan T. Major ◽  
Alessandro Cembran ◽  
Lingchun Song ◽  
...  
Keyword(s):  
Path Integral ◽  
Isotope Effects ◽  
Kinetic Isotope Effects ◽  
Kinetic Isotope

scholarly journals Path integral evaluation of equilibrium isotope effects

2009 ◽  
Vol 131 (2) ◽  
pp. 024111 ◽  
Author(s):  
Tomáš Zimmermann ◽  
Jiří Vaníček
Keyword(s):  
Path Integral ◽  
Isotope Effects ◽  
Integral Evaluation

scholarly journals Vapour Pressure Isotope Effect on Evaporation from Pure Organic Phases - a PIMD Approach

2020 ◽  
Author(s):  
Luis Vasquez ◽  
Agnieszka Dybala-Defratyka
Keyword(s):  
Path Integral ◽  
Vapour Pressure ◽  
Density Functional ◽  
Isotope Effects ◽  
Tight Binding ◽  
Decomposition Analysis ◽  
Energy Decomposition Analysis ◽  
Special Importance ◽  
Non Covalent Interactions ◽  
Covalent Interactions

<p></p><p>Very often in order to understand physical and chemical processes taking place among several phases fractionation of naturally abundant isotopes is monitored. Its measurement can be accompanied by theoretical determination to provide a more insightful interpretation of observed phenomena. Predictions are challenging due to the complexity of the effects involved in fractionation such as solvent effects and non-covalent interactions governing the behavior of the system which results in the necessity of using large models of those systems. This is sometimes a bottleneck and limits the theoretical description to only a few methods.<br> In this work vapour pressure isotope effects on evaporation from various organic solvents (ethanol, bromobenzene, dibromomethane, and trichloromethane) in the pure phase are estimated by combining force field or self-consistent charge density-functional tight-binding (SCC-DFTB) atomistic simulations with path integral principle. Furthermore, the recently developed Suzuki-Chin path integral is tested. In general, isotope effects are predicted qualitatively for most of the cases, however, the distinction between position-specific isotope effects observed for ethanol was only reproduced by SCC-DFTB, which indicates the importance of using non-harmonic bond approximations.<br> Energy decomposition analysis performed using the symmetry-adapted perturbation theory (SAPT) revealed sometimes quite substantial differences in interaction energy depending on whether the studied system was treated classically or quantum mechanically. Those observed differences might be the source of different magnitudes of isotope effects predicted using these two different levels of theory which is of special importance for the systems governed by non-covalent interactions.</p><br><p></p>

scholarly journals The origin of similarity fields in steady elastoplastic crack propagation under K–T loading

2010 ◽  
Vol 467 (2130) ◽  
pp. 1739-1748
Author(s):  
Jae Beom Park ◽  
Tapan Sabuwala ◽  
Gustavo Gioia
Keyword(s):  
Plastic Zone ◽  
Crack Propagation ◽  
Fracture Energy ◽  
Computer Simulations ◽  
Path Integral ◽  
Path Integrals ◽  
Mathematical Physics ◽  
Length Scale ◽  
Intrinsic Length ◽  
Specific Fracture

It has been inferred from computer simulations that the plastic-zone fields of a crack that propagates steadily under K–T loading are similarity fields. Here, we show theoretically that these similarity fields are but a manifestation of the existence of an invariant path integral. We also show that the attendant similarity variable involves an intrinsic length scale set by the specific fracture energy that flows into the crack tip. Finally, we show that where the crack is stationary there can be no similarity fields, even though there exists a (different) invariant path integral. Our results afford some new insights into the relation between similarity fields and invariant path integrals in mathematical physics.

scholarly journals FIXED SCALE TRANSFORMATION APPROACH FOR BORN MODEL OF FRACTURES

Fractals ◽  
1995 ◽  
Vol 03 (04) ◽  
pp. 829-837
Author(s):  
GUIDO CALDARELLI ◽  
ALESSANDRO VESPIGNANI
Keyword(s):  
Computer Simulations ◽  
Path Integral ◽  
Theoretical Approach ◽  
Lattice Path ◽  
Scale Transformation ◽  
Careful Choice ◽  
Born Model ◽  
Fracture Evolution ◽  
Fractal Patterns ◽  
Good Agreement

We use the Fixed Scale Transformation theoretical approach to study the problem of fractal growth in fractures generated by using the Born Model. In this case the application of the method is more complex because of the vectorial nature of the model considered. In particular, one needs a careful choice of the lattice path integral for the fracture evolution and the identification of the appropriate way to take effectively into account screening effects. The good agreement of our results with computer simulations shows the validity and flexibility of the FST method in the study of fractal patterns evolution.

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