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Conte R, Aieta C, Cazzaniga M, Ceotto M. A Perspective on the Investigation of Spectroscopy and Kinetics of Complex Molecular Systems with Semiclassical Approaches. J Phys Chem Lett 2024; 15:7566-7576. [PMID: 39024505 DOI: 10.1021/acs.jpclett.4c01338] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/20/2024]
Abstract
In this Perspective we show that semiclassical methods provide a rigorous hierarchical way to study the vibrational spectroscopy and kinetics of complex molecular systems. The time averaged approach to spectroscopy and the semiclassical transition state theory for kinetics, which have been first adopted and then further developed in our group, provide accurate quantum results on rigorous physical grounds and can be applied even when dealing with a large number of degrees of freedom. In spectroscopy, the multiple coherent, divide-and-conquer, and adiabatically switched semiclassical approaches have practically permitted overcoming issues related to the convergence of results. In this Perspective we demonstrate the possibility of studying the semiclassical vibrational spectroscopy of a molecule adsorbed on an anatase (101) surface, a system made of 51 atoms. In kinetics, the semiclassical transition state theory is able to account for anharmonicity and the coupling between the reactive and bound modes. Our group has developed this technique for practical applications involving the study of phenomena like kinetic isotope effect, heavy atom tunneling, and elusive conformer lifetimes. Here, we show that our multidimensional anharmonic quantum approach is able to tackle on-the-fly the thermal kinetic rate constant of a 135 degree-of-freedom system. Overall, semiclassical methods open up the possibility to describe at the quantum mechanical level systems characterized by hundreds of degrees of freedom leading to the accurate spectroscopic and kinetic description of biomolecules and complex molecular systems.
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Affiliation(s)
- Riccardo Conte
- Dipartimento di Chimica, Università degli Studi di Milano, via Golgi 19, 20133 Milano, Italy
| | - Chiara Aieta
- Dipartimento di Chimica, Università degli Studi di Milano, via Golgi 19, 20133 Milano, Italy
| | - Marco Cazzaniga
- Dipartimento di Chimica, Università degli Studi di Milano, via Golgi 19, 20133 Milano, Italy
| | - Michele Ceotto
- Dipartimento di Chimica, Università degli Studi di Milano, via Golgi 19, 20133 Milano, Italy
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Pollak E. A note on vibrational perturbation theory for tunneling splitting in a symmetric double well potential. J Chem Phys 2024; 161:036101. [PMID: 39007393 DOI: 10.1063/5.0220517] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2024] [Accepted: 06/28/2024] [Indexed: 07/16/2024] Open
Abstract
The modified version of second and fourth order vibrational perturbation theory, whereby the Euclidean action for tunneling is computed on the inverted potential at a shifted energy that is ℏ2 dependent, is applied to a symmetric double well quartic potential. The mean energies of the doublets in each well are also computed using vibrational perturbation theory. Results show that the modified vibrational perturbation theory significantly improves the estimates of tunneling splitting energies both for the ground state and for excited state doublets.
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Affiliation(s)
- Eli Pollak
- Chemical and Biological Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel
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Upadhyayula S, Pollak E. ℏ2 Corrections to Semiclassical Transmission Coefficients. J Phys Chem A 2024; 128:3434-3448. [PMID: 38630022 PMCID: PMC11077496 DOI: 10.1021/acs.jpca.4c00452] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2024] [Revised: 03/21/2024] [Accepted: 03/21/2024] [Indexed: 05/03/2024]
Abstract
The uniform semiclassical expression for the energy-dependent transmission probability through a barrier has been a staple of reaction rate theory for almost 90 years. Yet, when using the classical Euclidean action, the transmission probability is identical to 1/2 when the energy equals the barrier height since the Euclidean action vanishes at this energy. This result is generally incorrect. It also leads to an inaccurate estimate of the leading order term in an ℏ2n expansion of the thermal transmission coefficient. The central result of this paper is that adding an ℏ2 dependent correction to the uniform semiclassical expression, whether as a constant action or as a shift in the energy scale, not only corrects this inaccuracy but also leads to a theory that is more accurate than the previous one for almost any energy. Shifting the energy scale is a generalization of the vibrational perturbation theory 2 (VPT2) and is much more accurate than the "standard" VPT2 theory, especially when the potential is asymmetric. Shifting the action by a constant is a generalization of a result obtained by Yasumori and Fueki (YF) only for the Eckart barrier. The resulting modified VPT2 and YF semiclassical theories are applied to the symmetric and asymmetric Eckart barrier, a Gaussian barrier, and a tanh barrier. The one-dimensional theories are also generalized to many-dimensional systems. Their effect on the thermal instanton theory is discussed.
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Affiliation(s)
- Sameernandan Upadhyayula
- Chemical and Biological Physics
Department, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Eli Pollak
- Chemical and Biological Physics
Department, Weizmann Institute of Science, Rehovot 76100, Israel
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4
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Pollak E. A personal perspective of the present status and future challenges facing thermal reaction rate theory. J Chem Phys 2024; 160:150902. [PMID: 38639316 DOI: 10.1063/5.0199557] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2024] [Accepted: 03/06/2024] [Indexed: 04/20/2024] Open
Abstract
Reaction rate theory has been at the center of physical chemistry for well over one hundred years. The evolution of the theory is not only of historical interest. Reliable and accurate computation of reaction rates remains a challenge to this very day, especially in view of the development of quantum chemistry methods, which predict the relevant force fields. It is still not possible to compute the numerically exact rate on the fly when the system has more than at most a few dozen anharmonic degrees of freedom, so one must consider various approximate methods, not only from the practical point of view of constructing numerical algorithms but also on conceptual and formal levels. In this Perspective, I present some of the recent analytical results concerning leading order terms in an ℏ2m series expansion of the exact rate and their implications on various approximate theories. A second aspect has to do with the crossover temperature between tunneling and thermal activation. Using a uniform semiclassical transmission probability rather than the "primitive" semiclassical theory leads to the conclusion that there is no divergence problem associated with a "crossover temperature." If one defines a semiclassical crossover temperature as the point at which the tunneling energy of the instanton equals the barrier height, then it is a factor of two higher than its previous estimate based on the "primitive" semiclassical approximation. In the low temperature tunneling regime, the uniform semiclassical theory as well as the "primitive" semiclassical theory were based on the classical Euclidean action of a periodic orbit on the inverted potential. The uniform semiclassical theory wrongly predicts that the "half-point," which is the energy at which the transmission probability equals 1/2, for any barrier potential, is always the barrier energy. We describe here how augmenting the Euclidean action with constant terms of order ℏ2 can significantly improve the accuracy of the semiclassical theory and correct this deficiency. This also leads to a deep connection with and improvement of vibrational perturbation theory. The uniform semiclassical theory also enables an extension of the quantum version of Kramers' turnover theory to temperatures below the "crossover temperature." The implications of these recent advances on various approximate methods used to date are discussed at length, leading to the conclusion that reaction rate theory will continue to challenge us both on conceptual and practical levels for years to come.
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Affiliation(s)
- Eli Pollak
- Chemical and Biological Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel
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Fusè M, Mazzeo G, Longhi G, Abbate S, Yang Q, Bloino J. Scaling-up VPT2: A feasible route to include anharmonic correction on large molecules. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2024; 311:123969. [PMID: 38330757 DOI: 10.1016/j.saa.2024.123969] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2023] [Revised: 01/18/2024] [Accepted: 01/24/2024] [Indexed: 02/10/2024]
Abstract
Vibrational analysis plays a crucial role in the investigation of molecular systems. Though methodologies like second-order vibrational perturbation theory (VPT2) have paved the way to more accurate simulations, the computational cost remains a difficult barrier to overcome when the molecular size increases. Building upon recent advances in the identification of resonances, we propose an approach making anharmonic simulations possible for large-size systems, typically unreachable by standard means. This relies on the fact that, often, only portions of the whole spectra are of actual interest. Therefore, the anharmonic corrections can be included selectively on subsets of normal modes directly related to the regions of interest. Starting from the VPT2 equations, we evaluate rigorously and systematically the impact of the truncated anharmonic treatment onto simulations. The limit and feasibility of the reduced-dimensionality approach are detailed, starting on a smaller model system. The methodology is then challenged on the IR absorption and vibrational circular dichroism spectra of an organometallic complex in three different spectral ranges.
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Affiliation(s)
- Marco Fusè
- Dipartimento di Medicina Molecolare e Traslazionale, Università di Brescia, Viale Europa 11, 25123, Brescia, Italy.
| | - Giuseppe Mazzeo
- Dipartimento di Medicina Molecolare e Traslazionale, Università di Brescia, Viale Europa 11, 25123, Brescia, Italy
| | - Giovanna Longhi
- Dipartimento di Medicina Molecolare e Traslazionale, Università di Brescia, Viale Europa 11, 25123, Brescia, Italy; Istituto Nazionale di Ottica (INO), CNR, Research Unit of Brescia, c/o CSMT, VIA Branze 45, 25123, Brescia, Italy
| | - Sergio Abbate
- Dipartimento di Medicina Molecolare e Traslazionale, Università di Brescia, Viale Europa 11, 25123, Brescia, Italy; Istituto Nazionale di Ottica (INO), CNR, Research Unit of Brescia, c/o CSMT, VIA Branze 45, 25123, Brescia, Italy
| | - Qin Yang
- Institute of Organic Chemistry and Biochemistry, Czech Academy of Sciences, Flemingovo náměstí 542/2, 160 00, Prague, Czech Republic
| | - Julien Bloino
- Scuola Normale Superiore, Piazza dei Cavalieri, 56125, Pisa, Italy.
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Puzzarini C, Stanton JF. Connections between the accuracy of rotational constants and equilibrium molecular structures. Phys Chem Chem Phys 2023; 25:1421-1429. [PMID: 36562443 DOI: 10.1039/d2cp04706c] [Citation(s) in RCA: 27] [Impact Index Per Article: 27.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
Rotational spectroscopy is the technique of choice for investigating molecular structures in the gas phase. Indeed, rotational constants are strongly connected to the geometry of the molecular system under consideration. Therefore, they are powerful tools for assessing the accuracy that quantum chemical approaches can reach in structural determinations. In this review article, it is shown how it is possible to measure the accuracy of a computed equilibrium geometry based on the comparison of rotational constants. But, it is also addressed what accuracy is required by computations for providing molecular structures and thus rotational constants that are useful to experiment. Quantum chemical methodologies for obtaining the "0.1% accuracy" for rotational constants are reviewed for systems ranging in size from small molecules to small polycyclic aromatic hydrocarbons. This accuracy for systems containing two dozen or so atoms opens the way towards future applications such as the accurate characterization of non-covalent interactions, which play a key role in several biological and technological processes.
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Affiliation(s)
- Cristina Puzzarini
- Dipartimento di Chimica "Giacomo Ciamician", Università di Bologna, via F. Selmi 2, 40126, Bologna, Italy.
| | - John F Stanton
- Department of Chemistry, University of Florida, Gainesville, FL, 32611, USA.
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Yang Q, Bloino J. An Effective and Automated Processing of Resonances in Vibrational Perturbation Theory Applied to Spectroscopy. J Phys Chem A 2022; 126:9276-9302. [DOI: 10.1021/acs.jpca.2c06460] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/02/2022]
Affiliation(s)
- Qin Yang
- Faculty of Science, Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126Pisa, Italy
- Institute of Organic Chemistry and Biochemistry, Czech Academy of Sciences, 16610Prague, Czech Republic
| | - Julien Bloino
- Faculty of Science, Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126Pisa, Italy
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Pollak E, Cao J. $\hbar ^{2}$ Expansion of the transmission probability through a barrier. J Chem Phys 2022; 157:074109. [DOI: 10.1063/5.0106649] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Ninety years ago, Wigner derived the leading order expansionterm in $\hbar ^{2}$ for the tunneling rate through a symmetric barrier. Hisderivation included two contributions, one came from the parabolic barrier,but a second term involved the fourth order derivative of the potential atthe barrier top. He left us with a challenge which is answered in thispaper, to derive the same but for an asymmetric barrier. A crucial elementof the derivation is obtaining the $\hbar^{2}$ expansion term for theprojection operator which appears in the flux-side expression for the rate. It is also reassuring that an analytical calculation of semiclassical transition state theory (SCTST) reproduces the anharmonic corrections to the leading order of $\hbar^2$. The efficacy of the resulting expression is demonstrated for an Eckartbarrier, leading to the conclusion that especially when considering heavy atom tunneling, one should use the expansion derived in this paper, ratherthan the parabolic barrier approximation. The rate expression derived here reveals how the classical TST limit is approached as a function of $\hbar$ and thus provides critical insights to understand the validity of popular approximate theories, such as the classical Wigner, centroid molecular dynamics and ring polymer molecular dynamics methods.
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Affiliation(s)
- Eli Pollak
- Department of Chemical Physics, Weizmann Institute of Science Faculty of Chemistry, Israel
| | - Jianshu Cao
- Department of Chemistry, MIT, United States of America
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Pollak E, Upadhyayula S, Liu J. Coherent state representation of thermal correlation functions with applications to rate theory. J Chem Phys 2022; 156:244101. [DOI: 10.1063/5.0088163] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
A coherent state phase space representation of operators, based on the Husimi distribution, is used to derive an exact expression for the symmetrized version of thermal correlation functions. In addition to the time and temperature independent phase space representation of the two operators whose correlation function is of interest, the integrand includes a non-negative distribution function where only one imaginary time and one real time propagation are needed to compute it. The methodology is exemplified for the flux side correlation function used in rate theory. The coherent state representation necessitates the use of a smeared Gaussian flux operator whose coherent state phase space representation is identical to the classical flux expression. The resulting coherent state expression for the flux side correlation function has a number of advantages as compared to previous formulations. Since only one time propagation is needed, it is much easier to converge it with a semiclassical initial value representation. There is no need for forward–backward approximations, and in principle, the computation may be implemented on the fly. It also provides a route for analytic semiclassical approximations for the thermal rate, as exemplified by a computation of the transmission factor through symmetric and asymmetric Eckart barriers using a thawed Gaussian approximation for both imaginary and real time propagations. As a by-product, this example shows that one may obtain “good” tunneling rates using only above barrier classical trajectories even in the deep tunneling regime.
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Affiliation(s)
- Eli Pollak
- Chemical and Biological Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel
| | - Sameernandan Upadhyayula
- Chemical and Biological Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel
| | - Jian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
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Fang W, Winter P, Richardson JO. Microcanonical Tunneling Rates from Density-of-States Instanton Theory. J Chem Theory Comput 2020; 17:40-55. [PMID: 33351621 DOI: 10.1021/acs.jctc.0c01118] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Semiclassical instanton theory is a form of quantum transition-state theory which can be applied to the computation of thermal reaction rates in complex molecular systems including quantum tunneling effects. There have been a number of attempts to extend the theory to treat microcanonical rates. However, the previous formulations are either computationally unfeasible for large systems due to an explicit sum over states or they involve extra approximations, which make them less reliable. We propose a robust and practical microcanonical formulation called density-of-states instanton theory, which avoids the sum over states altogether. In line with the semiclassical approximations inherent to the instanton approach, we employ the stationary-phase approximation to the inverse Laplace transform to obtain the densities of states. This can be evaluated using only post-processing of the data available from a small set of instanton calculations, such that our approach remains computationally efficient. We show that the new formulation predicts results that agree well with quantum scattering theory for an atom-diatom reaction and with experiments for a photoexcited unimolecular hydrogen transfer in a Criegee intermediate. When the thermal rate is evaluated from a Boltzmann average over our new microcanonical formalism, it can overcome some problems of conventional instanton theory. In particular, it predicts a smooth transition at the crossover temperature and is able to describe bimolecular reactions with pre-reactive complexes such as CH3OH + OH.
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Affiliation(s)
- Wei Fang
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - Pierre Winter
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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A never-ending story in the sky: The secrets of chemical evolution. Phys Life Rev 2020; 32:59-94. [DOI: 10.1016/j.plrev.2019.07.001] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2019] [Revised: 06/26/2019] [Accepted: 07/02/2019] [Indexed: 01/13/2023]
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Puzzarini C, Bloino J, Tasinato N, Barone V. Accuracy and Interpretability: The Devil and the Holy Grail. New Routes across Old Boundaries in Computational Spectroscopy. Chem Rev 2019; 119:8131-8191. [DOI: 10.1021/acs.chemrev.9b00007] [Citation(s) in RCA: 114] [Impact Index Per Article: 22.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Affiliation(s)
- Cristina Puzzarini
- Dipartimento di Chimica “Giacomo Ciamician”, Università di Bologna, Via F. Selmi 2, I-40126 Bologna, Italy
| | - Julien Bloino
- Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
| | - Nicola Tasinato
- Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
| | - Vincenzo Barone
- Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
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Shan X, Burd TAH, Clary DC. New Developments in Semiclassical Transition-State Theory. J Phys Chem A 2019; 123:4639-4657. [DOI: 10.1021/acs.jpca.9b01987] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Xiao Shan
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Timothy A. H. Burd
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - David C. Clary
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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