1
|
Xue Y, Sexton TM, Yang J, Tschumper GS. Systematic analysis of electronic barrier heights and widths for concerted proton transfer in cyclic hydrogen bonded clusters: (HF) n, (HCl) n and (H 2O) n where n = 3, 4, 5. Phys Chem Chem Phys 2024; 26:12483-12494. [PMID: 38619858 DOI: 10.1039/d4cp00422a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/16/2024]
Abstract
The MP2 and CCSD(T) methods are paired with correlation consistent basis sets as large as aug-cc-pVQZ to optimize the structures of the cyclic minima for (HF)n, (HCl)n and (H2O)n where n = 3-5, as well as the corresponding transition states (TSs) for concerted proton transfer (CPT). MP2 and CCSD(T) harmonic vibrational frequencies confirm the nature of each minimum and TS. Both conventional and explicitly correlated CCSD(T) computations are employed to assess the electronic dissociation energies and barrier heights for CPT near the complete basis (CBS) limit for all 9 clusters. Results for (HF)n are consistent with prior studies identifying Cnh and Dnh point group symmetry for the minima and TSs, respectively. Our computations also confirm that CPT proceeds through Cs TS structures for the C1 minima of (H2O)3 and (H2O)5, whereas the process goes through a TS with D2d symmetry for the S4 global minimum of (H2O)4. This work corroborates earlier findings that the minima for (HCl)3, (HCl)4 and (HCl)5 have C3h, S4 and C1 point group symmetry, respectively, and that the Cnh structures are not minima for n = 4 and 5. Moreover, our computations show the TSs for CPT in (HCl)3, (HCl)4 and (HCl)5 have D3h, D2d, and C2 point group symmetry, respectively. At the CCSD(T) CBS limit, (HF)4 and (HF)5 have the smallest electronic barrier heights for CPT (≈15 kcal mol-1 for both), followed by the HF trimer (≈21 kcal mol-1). The barriers are appreciably higher for the other clusters (around 27 kcal mol-1 for (H2O)4 and (HCl)3; roughly 30 kcal mol-1 for (H2O)3, (H2O)5 and (HCl)4; up to 38 kcal mol-1 for (HCl)5). At the CBS limit, MP2 significantly underestimates the CCSD(T) barrier heights (e.g., by ca. 2, 4 and 7 kcal mol-1 for the pentamers of HF, H2O and HCl, respectively), whereas CCSD overestimates these barriers by roughly the same magnitude. Scaling the barrier heights and dissociation energies by the number of fragments in the cluster reveals strong linear relationships between the two quantities and with the magnitudes of the imaginary vibrational frequency for the TSs.
Collapse
Affiliation(s)
- Yuan Xue
- Department of Chemistry and Biochemistry, University of Mississippi, University, MS 38677-1848, USA.
| | - Thomas More Sexton
- School of Arts and Sciences, Chemistry University of Mary, Bismark, ND 58504, USA.
| | - Johnny Yang
- Department of Chemistry and Biochemistry, University of Mississippi, University, MS 38677-1848, USA.
| | - Gregory S Tschumper
- Department of Chemistry and Biochemistry, University of Mississippi, University, MS 38677-1848, USA.
| |
Collapse
|
2
|
Li F, Yang X, Liu X, Cao J, Bian W. An Ab Initio Neural Network Potential Energy Surface for the Dimer of Formic Acid and Further Quantum Tunneling Dynamics. ACS OMEGA 2023; 8:17296-17303. [PMID: 37214673 PMCID: PMC10193396 DOI: 10.1021/acsomega.3c02169] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Accepted: 04/19/2023] [Indexed: 05/24/2023]
Abstract
We construct a full-dimensional ab initio neural network potential energy surface (PES) for the isomerization system of the formic acid dimer (FAD). This is based upon ab initio calculations using the DLPNO-CCSD(T) approach with the aug-cc-pVTZ basis set, performed at over 14000 symmetry-unique geometries. An accurate fit to the obtained energies is generated using a general neural network fitting procedure combined with the fundamental invariant method, and the overall energy-weighted root-mean-square fitting error is about 6.4 cm-1. Using this PES, we present a multidimensional quantum dynamics study on tunneling splittings with an efficient theoretical scheme developed by our group. The ground-state tunneling splitting of FAD calculated with a four-mode coupled method is in good agreement with the most recent experimental measurements. The PES can be applied for further dynamics studies. The effectiveness of the present scheme for constructing a high-dimensional PES is demonstrated, and this scheme is expected to be feasible for larger molecular systems.
Collapse
Affiliation(s)
- Fengyi Li
- Beijing
National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
- School
of Chemical Sciences, University of Chinese
Academy of Sciences, Beijing 100049, People’s
Republic of China
| | - Xingyu Yang
- Beijing
National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
- School
of Chemical Sciences, University of Chinese
Academy of Sciences, Beijing 100049, People’s
Republic of China
| | - Xiaoxi Liu
- Beijing
National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
- School
of Chemical Sciences, University of Chinese
Academy of Sciences, Beijing 100049, People’s
Republic of China
| | - Jianwei Cao
- Beijing
National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
| | - Wensheng Bian
- Beijing
National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
- School
of Chemical Sciences, University of Chinese
Academy of Sciences, Beijing 100049, People’s
Republic of China
| |
Collapse
|
3
|
Kurzydłowski D. Potential energy barrier for proton transfer in compressed benzoic acid. RSC Adv 2022; 12:11436-11441. [PMID: 35425083 PMCID: PMC9004587 DOI: 10.1039/d2ra01736a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 04/06/2022] [Indexed: 11/21/2022] Open
Abstract
Benzoic acid (BA) is a model system for studying proton transfer (PT) reactions. The properties of solid BA subject to high pressure (exceeding 1 kbar = 0.1 GPa) are of particular interest due to the possibility of compression-tuning of the PT barrier. Here we present simulations aimed at evaluating the value of this barrier in solid BA in the 1 atm – 15 GPa pressure range. We find that pressure-induced shortening of O⋯O contacts within the BA dimers leads to a decrease in the PT barrier, and subsequent symmetrization of the hydrogen bond. However, this effect is obtained only after taking into account zero-point energy (ZPE) differences between BA tautomers and the transition state. The obtained results shed light on previous experiments on compressed benzoic acid, and indicate that a common scaling behavior with respect to the O⋯O distance might be applicable for hydrogen-bond symmetrization in both organic and inorganic systems. Pressure-induced shortening of O⋯O contacts within the dimers of solid benzoic acid leads to a decrease in the PT barrier and subsequent symmetrization of the hydrogen bond (an effect obtained only after taking into account the ZPE correction).![]()
Collapse
Affiliation(s)
- Dominik Kurzydłowski
- Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszyński University in Warsaw 01-038 Warsaw Poland
| |
Collapse
|
4
|
Liu H, Cao J, Bian W. Efficient Quantum Mechanical Calculations of Mode-Specific Tunneling Splittings upon Fundamental Excitation in the Dimer of Formic Acid. J Phys Chem A 2020; 124:6536-6543. [PMID: 32662997 DOI: 10.1021/acs.jpca.0c05471] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The formic acid dimer (FAD) is an important benchmark system for understanding the double hydrogen transfer process. Most recently, Zhang et al. measured a few tunneling splittings upon fundamental excitation of FAD precisely (Zhang, Y. et al. J. Chem. Phys. 2017, 146, 244306); however, relevant theoretical studies are very limited. Here, we present a multidimensional quantum dynamics study on mode-specific tunneling splittings upon fundamental excitation in FAD with an efficient theoretical scheme developed by our group in which the process-oriented basis function customization strategy is combined with the preconditioned inexact spectral transform method. Various mode-specific tunneling splittings upon fundamental excitation are systematically calculated, and interesting mode-specific excitation effects on tunneling rate are identified. In particular, the calculated tunneling splittings for the ν22 and ν21 states are in good agreement with experiment, and the remarkable mode-specific suppression effects upon excitation should result from that the antisymmetric vibrational modes hinder the concerted double H-transfer. The present work is helpful to acquire a better understanding of the mode-specific excitation effects on tunneling processes.
Collapse
Affiliation(s)
- Hao Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, 100190 Beijing, China.,School of Chemical Sciences, University of Chinese Academy of Sciences, 100049 Beijing, China
| | - Jianwei Cao
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, 100190 Beijing, China
| | - Wensheng Bian
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, 100190 Beijing, China.,School of Chemical Sciences, University of Chinese Academy of Sciences, 100049 Beijing, China
| |
Collapse
|
5
|
Abstract
AbstractFormic acid dimer as the prototypical doubly hydrogen-bonded gas-phase species is discussed from the perspective of the three translational and the three rotational degrees of freedom which are lost when two formic acid molecules form a stable complex. The experimental characterisation of these strongly hindered translations and rotations is reviewed, as are attempts to describe the associated fundamental vibrations, their combinations, and their thermal shifts by different electronic structure calculations and vibrational models. A remarkable match is confirmed for the combination of a CCSD(T)-level harmonic treatment and an MP2-level anharmonic VPT2 correction. Qualitatively correct thermal shifts of the vibrational spectra can be obtained from classical molecular dynamics in CCSD(T)-quality force fields. A detailed analysis suggests that this agreement between experiment and composite theoretical treatment is not strongly affected by fortuitous error cancellation but fully converged variational treatments of the six pair or intermolecular modes and their overtones and combinations in this model system would be welcome.
Collapse
|
6
|
Liu H, Cao J, Bian W. Double Proton Transfer in the Dimer of Formic Acid: An Efficient Quantum Mechanical Scheme. Front Chem 2019; 7:676. [PMID: 31750286 PMCID: PMC6842929 DOI: 10.3389/fchem.2019.00676] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2019] [Accepted: 09/30/2019] [Indexed: 11/13/2022] Open
Abstract
Double proton transfer plays an important role in biology and chemistry, such as with DNA base pairs, proteins and molecular clusters, and direct information about these processes can be obtained from tunneling splittings. Carboxylic acid dimers are prototypes for multiple proton transfer, of which the formic acid dimer is the simplest one. Here, we present efficient quantum dynamics calculations of ground-state and fundamental excitation tunneling splittings in the formic acid dimer and its deuterium isotopologues. These are achieved with a multidimensional scheme developed by us, in which the saddle-point normal coordinates are chosen, the basis functions are customized for the proton transfer process, and the preconditioned inexact spectral transform method is used to solve the resultant eigenvalue problem. Our computational results are in excellent agreement with the most recent experiments (Zhang et al., 2017; Li et al., 2019).
Collapse
Affiliation(s)
- Hao Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing, China.,School of Chemical Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Jianwei Cao
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing, China
| | - Wensheng Bian
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing, China.,School of Chemical Sciences, University of Chinese Academy of Sciences, Beijing, China
| |
Collapse
|
7
|
Qu C, Bowman JM. High-dimensional fitting of sparse datasets of CCSD(T) electronic energies and MP2 dipole moments, illustrated for the formic acid dimer and its complex IR spectrum. J Chem Phys 2018; 148:241713. [DOI: 10.1063/1.5017495] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Chen Qu
- Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, Atlanta, Georgia 30322, USA
| | - Joel M. Bowman
- Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, Atlanta, Georgia 30322, USA
| |
Collapse
|
8
|
Cvitaš MT. Quadratic String Method for Locating Instantons in Tunneling Splitting Calculations. J Chem Theory Comput 2018; 14:1487-1500. [DOI: 10.1021/acs.jctc.7b00881] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Marko T. Cvitaš
- Department of Physical Chemistry, Ruđer Bošković Institute, Bijenička Cesta 54, 10000 Zagreb, Croatia
| |
Collapse
|
9
|
Ivanov SD, Grant IM, Marx D. Quantum free energy landscapes from ab initio path integral metadynamics: Double proton transfer in the formic acid dimer is concerted but not correlated. J Chem Phys 2016; 143:124304. [PMID: 26429008 DOI: 10.1063/1.4931052] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
With the goal of computing quantum free energy landscapes of reactive (bio)chemical systems in multi-dimensional space, we combine the metadynamics technique for sampling potential energy surfaces with the ab initio path integral approach to treating nuclear quantum motion. This unified method is applied to the double proton transfer process in the formic acid dimer (FAD), in order to study the nuclear quantum effects at finite temperatures without imposing a one-dimensional reaction coordinate or reducing the dimensionality. Importantly, the ab initio path integral metadynamics technique allows one to treat the hydrogen bonds and concomitant proton transfers in FAD strictly independently and thus provides direct access to the much discussed issue of whether the double proton transfer proceeds via a stepwise or concerted mechanism. The quantum free energy landscape we compute for this H-bonded molecular complex reveals that the two protons move in a concerted fashion from initial to product state, yet world-line analysis of the quantum correlations demonstrates that the protons are as quantum-uncorrelated at the transition state as they are when close to the equilibrium structure.
Collapse
Affiliation(s)
- Sergei D Ivanov
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany
| | - Ian M Grant
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany
| | - Dominik Marx
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany
| |
Collapse
|
10
|
Alves TV, Simón-Carballido L, Ornellas FR, Fernández-Ramos A. Hindered rotor tunneling splittings: an application of the two-dimensional non-separable method to benzyl alcohol and two of its fluorine derivatives. Phys Chem Chem Phys 2016; 18:8945-53. [PMID: 26960818 DOI: 10.1039/c5cp05307b] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this work we present a novel application of the two-dimensional non-separable (2D-NS) method to the calculation of torsional tunneling splittings in systems with two hindered internal rotors. This method could be considered an extension of one-dimensional methods for the case of compounds with two tops. The 2D-NS method includes coupling between torsions in the kinetic and potential energy. Specifically, it has been applied to benzyl alcohol (BA) and two of its fluorine derivatives: 3-fluorobenzyl alcohol (3FBA) and 4-fluorobenzyl alcohol (4FBA). These molecules present two torsions, i.e., about the -CH2OH (ϕ1) and -OH (ϕ2) groups. The electronic structure calculations to build the two-dimensional torsional potential energy surface were performed at the DF-LMP2-F12//DF-LMP2/cc-pVQZ level of theory. For BA and 4FBA the calculated ground-state vibrational level splittings are 429 and 453 MHz, respectively, in good agreement with the experimental values of 337.10 and 492.82 MHz, respectively. In these two cases there are four equivalent wells and the tunneling splitting is the result of transitions between the two closer minima along ϕ1. The analysis of the wavefunctions, as well as the previous experimental work on the system, supports this conclusion. For 3FBA the observed ground-state splitting is 0.82 MHz, whereas in this case the calculated value amounts only to 0.02 MHz. The 2D-NS method, through the analysis of the wavefunctions, shows that this tiny tunneling splitting occurs between the two most stable minima of the potential energy surface. Additionally, we predict that the first vibrationally excited tunneling splitting will also be small and exclusively due to the interconversion between the second lowest minima.
Collapse
Affiliation(s)
- Tiago Vinicius Alves
- Departamento de Química Fundamental, Instituto de Química, Universidade de São Paulo, Av. Prof. Lineu Prestes 748, São Paulo, SP 05508-000, Brazil
| | | | | | | |
Collapse
|
11
|
Jain A, Sibert EL. Tunneling splittings in formic acid dimer: An adiabatic approximation to the Herring formula. J Chem Phys 2015; 142:084115. [DOI: 10.1063/1.4908565] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Amber Jain
- Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Edwin L. Sibert
- Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| |
Collapse
|
12
|
Smedarchina Z, Siebrand W, Fernández-Ramos A. Tunneling splitting in double-proton transfer: Direct diagonalization results for porphycene. J Chem Phys 2014; 141:174312. [DOI: 10.1063/1.4900717] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
13
|
Fernández-Ramos A, Smedarchina Z, Siebrand W. Multidimensional Hamiltonian for tunneling with position-dependent mass. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:033306. [PMID: 25314563 DOI: 10.1103/physreve.90.033306] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2014] [Indexed: 06/04/2023]
Abstract
A multidimensional Hamiltonian for tunneling is formulated, based on the mode with imaginary frequency of the transition state as a reaction coordinate. To prepare it for diagonalization, it is transformed into a lower-dimension Hamiltonian by incorporating modes that move faster than the tunneling into a coordinate-dependent kinetic energy operator, for which a Hermitian form is chosen and tested for stability of the eigenvalues. After transformation to a three-dimensional form, which includes two normal modes strongly coupled to the tunneling mode, this Hamiltonian is diagonalized in terms of a basis set of harmonic oscillator functions centered at the transition state. This involves a sparse matrix which is easily partially diagonalized to yield tunneling splittings for the zero-point level and the two fundamental levels of the coupled modes. The method is tested on the well-known benchmark molecule malonaldehyde and a deuterium isotopomer, for which these splittings have been measured. Satisfactory agreement with experiment results is obtained.
Collapse
Affiliation(s)
- Antonio Fernández-Ramos
- Department of Physical Chemistry and Center for Research in Biological Chemistry and Molecular Materials, University of Santiago de Compostela, 15706 Santiago de Compostela, Spain
| | - Zorka Smedarchina
- Department of Physical Chemistry and Center for Research in Biological Chemistry and Molecular Materials, University of Santiago de Compostela, 15706 Santiago de Compostela, Spain
| | - Willem Siebrand
- Department of Physical Chemistry and Center for Research in Biological Chemistry and Molecular Materials, University of Santiago de Compostela, 15706 Santiago de Compostela, Spain
| |
Collapse
|