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Eraković M, Cvitaš MT. Tunneling splittings in the vibrationally excited states of water trimer. Phys Chem Chem Phys 2024; 26:12965-12981. [PMID: 38634688 DOI: 10.1039/d4cp00013g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/19/2024]
Abstract
Tunneling splitting (TS) patterns in vibrationally excited states of the water trimer are calculated, taking into account six tunneling pathways that describe the flips of free OH bonds and five bifurcation mechanisms that break and reform hydrogen bonds in the trimer ring. A tunneling matrix (TM) model is used to derive the energy shifts due to tunneling in terms of the six distinct TM elements in symbolic form. TM elements are calculated using the recently-developed modified WKB (Wentzel-Kramers-Brillouin) method in full dimensionality. Convergence was achieved for the lowest six excited vibrational modes. Bifurcation widths of the pseudorotational quartets are shown to be of comparable size to the ground-state widths, obtained using instanton theory, or increased for some particular modes of vibration. The largest increase is obtained for the excited out-of-phase flip of two adjacent water monomers with free OH bonds pointing in opposite directions relative to the ring plane. Bifurcation widths in (D2O)3 are found to be two orders of magnitude smaller than in (H2O)3. Geometrical arguments were used to explain the order of states in some TS multiplets in vibrationally excited water trimers.
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Affiliation(s)
- Mihael Eraković
- Department of Physical Chemistry, Ruđer Bošković Institute, Zagreb, Croatia.
| | - Marko T Cvitaš
- Department of Physics, University of Zagreb Faculty of Science, Zagreb, Croatia.
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Eraković M, Cvitaš MT. Vibrational Tunneling Spectra of Molecules with Asymmetric Wells: A Combined Vibrational Configuration Interaction and Instanton Approach. J Chem Theory Comput 2022; 18:2785-2802. [PMID: 35439012 PMCID: PMC9097297 DOI: 10.1021/acs.jctc.2c00124] [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] [Indexed: 11/29/2022]
Abstract
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A combined approach
that uses the vibrational configuration interaction
(VCI) and semiclassical instanton theory was developed to study vibrational
tunneling spectra of molecules with multiple wells in full dimensionality.
The method can be applied to calculate low-lying vibrational states in the systems with an
arbitrary number of minima, which are not necessarily equal in energy
or shape. It was tested on a two-dimensional double-well model system
and on malonaldehyde, and the calculations reproduced the exact quantum
mechanical (QM) results with high accuracy. The method was subsequently
applied to calculate the vibrational spectrum of the asymmetrically
deuterated malonaldehyde with nondegenerate vibrational frequencies
in the two wells. The spectrum is obtained at a cost of single-well
VCI calculations used to calculate the local energies. The interactions
between states of different wells are computed semiclassically using
the instanton theory at a comparatively negligible computational cost.
The method is particularly suited to systems in which the wells are
separated by large potential barriers and tunneling splittings are
small, for example, in some water clusters, when the exact QM methods
come at a prohibitive computational cost.
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Affiliation(s)
- Mihael Eraković
- Department of Physical Chemistry, Rud̵er Bošković Institute, Bijenička Cesta 54, 10000 Zagreb, Croatia
| | - Marko T Cvitaš
- Department of Physics, Faculty of Science, University of Zagreb, Bijenička Cesta 32, 10000 Zagreb, Croatia
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Eraković M, Cvitaš MT. Tunnelling splitting patterns in some partially deuterated water trimers. Phys Chem Chem Phys 2021; 23:4240-4254. [PMID: 33586727 DOI: 10.1039/d0cp06135b] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We apply our recently developed semiclassical method for calculating tunnelling splittings (TS) in asymmetric systems to make the first characterization of the ground-state TS pattern of some partially deuterated water trimers. Similarly to homoisotopic water trimers, the ground-state TS patterns are explained in terms of six distinct rearrangement mechanisms. TS patterns in (D2O)(H2O)2 and (H2O)(D2O)2 are composed of sextets induced by the dynamics of flips, and each of its levels is further finely split into a quartet of doublets and a doublet of quartets, respectively, due to various bifurcation dynamics. The TS pattern is obtained using 18 distinct tunnelling matrix elements. TS patterns of (HOD)(H2O)2 and (HOD)(D2O)2 each consists of two sextets, belonging to in-bond and out-of-bond substituted isomers. These sextet levels are further split into quartets by bifurcations. The TS pattern is computed in terms of 13 matrix elements. We also derive analytic expressions for bifurcation tunnelling splittings in terms of tunnelling matrix elements using symmetry. The present approach can be applied to other water clusters and also to the low-lying vibrationally excited states and should help in the interpretation and assignment of experimental spectra in the future.
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Affiliation(s)
- Mihael Eraković
- Department of Physical Chemistry, Ruđer Bošković Institute, 10000 Zagreb, Croatia.
| | - Marko T Cvitaš
- Department of Physical Chemistry, Ruđer Bošković Institute, 10000 Zagreb, Croatia.
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Eraković M, Cvitaš MT. Tunneling splittings of vibrationally excited states using general instanton paths. J Chem Phys 2020; 153:134106. [PMID: 33032414 DOI: 10.1063/5.0024210] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
A multidimensional semiclassical method for calculating tunneling splittings in vibrationally excited states of molecules using Cartesian coordinates is developed. It is an extension of the theory by Mil'nikov and Nakamura [J. Chem. Phys. 122, 124311 (2005)] to asymmetric paths that are necessary for calculating tunneling splitting patterns in multi-well systems, such as water clusters. Additionally, new terms are introduced in the description of the semiclassical wavefunction that drastically improves the splitting estimates for certain systems. The method is based on the instanton theory and builds the semiclassical wavefunction of the vibrationally excited states from the ground-state instanton wavefunction along the minimum action path and its harmonic neighborhood. The splittings of excited states are thus obtained at a negligible added numerical effort. The cost is concentrated, as for the ground-state splittings, in the instanton path optimization and the hessian evaluation along the path. The method can thus be applied without modification to many mid-sized molecules in full dimensionality and in combination with on-the-fly evaluation of electronic potentials. The tests were performed on several model potentials and on the water dimer.
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Affiliation(s)
- Mihael Eraković
- Department of Physical Chemistry, Ruder Bošković Institute, Bijenička Cesta 54, 10000 Zagreb, Croatia
| | - Marko T Cvitaš
- Department of Physical Chemistry, Ruder Bošković Institute, Bijenička Cesta 54, 10000 Zagreb, Croatia
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Jahr E, Laude G, Richardson JO. Instanton theory of tunneling in molecules with asymmetric isotopic substitutions. J Chem Phys 2020; 153:094101. [PMID: 32891112 DOI: 10.1063/5.0021831] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We consider quantum tunneling in asymmetric double-well systems for which the local minima in the two wells have the same energy, but the frequencies differ slightly. In a molecular context, this situation can arise if the symmetry is broken by isotopic substitutions. We derive a generalization of instanton theory for these asymmetric systems, leading to a semiclassical expression for the tunneling matrix element and hence the energy-level splitting. We benchmark the method using a set of one- and two-dimensional models, for which the results compare favorably with numerically exact quantum calculations. Using the ring-polymer instanton approach, we apply the method to compute the level splittings in various isotopomers of malonaldehyde in full dimensionality and analyze the relative contributions from the zero-point energy difference and tunneling effects.
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Affiliation(s)
- Elena Jahr
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - Gabriel Laude
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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Schwan R, Qu C, Mani D, Pal N, Schwaab G, Bowman JM, Tschumper GS, Havenith M. Observation of the Low‐Frequency Spectrum of the Water Trimer as a Sensitive Test of the Water‐Trimer Potential and the Dipole‐Moment Surface. Angew Chem Int Ed Engl 2020. [DOI: 10.1002/ange.202003851] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Raffael Schwan
- Physical Chemistry II Department of Chemistry and Biochemistry Ruhr-Universität Bochum Bochum Germany
| | - Chen Qu
- Department of Chemistry Biochemistry University of Maryland College Park MD 20742 USA
| | - Devendra Mani
- Physical Chemistry II Department of Chemistry and Biochemistry Ruhr-Universität Bochum Bochum Germany
| | - Nitish Pal
- Physical Chemistry II Department of Chemistry and Biochemistry Ruhr-Universität Bochum Bochum Germany
| | - Gerhard Schwaab
- Physical Chemistry II Department of Chemistry and Biochemistry Ruhr-Universität Bochum Bochum Germany
| | - Joel M. Bowman
- Cherry L. Emerson Center for Scientific Computations and Department of Chemistry Emory University Atlanta GA 30322 USA
| | - Gregory S. Tschumper
- Department of Chemistry and Biochemistry University of Mississippi University MS 38677 USA
| | - Martina Havenith
- Physical Chemistry II Department of Chemistry and Biochemistry Ruhr-Universität Bochum Bochum Germany
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Schwan R, Qu C, Mani D, Pal N, Schwaab G, Bowman JM, Tschumper GS, Havenith M. Observation of the Low-Frequency Spectrum of the Water Trimer as a Sensitive Test of the Water-Trimer Potential and the Dipole-Moment Surface. Angew Chem Int Ed Engl 2020; 59:11399-11407. [PMID: 32307809 PMCID: PMC7383990 DOI: 10.1002/anie.202003851] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2020] [Indexed: 12/03/2022]
Abstract
Intermolecular interactions in bulk water are dominated by pairwise and non‐pairwise cooperative interactions. While accurate descriptions of the pairwise interactions are available and can be tested by precise low‐frequency spectra of the water dimer up to 550 cm−1, the same does not hold for the three‐body interactions. Here, we report the first comprehensive spectrum of the water trimer in the frequency region from 70 to 620 cm−1 using helium‐nanodroplet isolation and free‐electron lasers. By comparison to accompanying high‐level quantum calculations, the experimentally observed intermolecular bands can be assigned. The transition frequencies of the degenerate translation, the degenerate in‐plane and the non‐degenerate out‐of‐plane libration, as well as additional bands of the out‐of‐plane librational mode are reported for the first time. These provide a benchmark for state‐of‐the‐art water potentials and dipole‐moment surfaces, especially with respect to three‐body interactions.
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Affiliation(s)
- Raffael Schwan
- Physical Chemistry II, Department of Chemistry and Biochemistry, Ruhr-Universität Bochum, Bochum, Germany
| | - Chen Qu
- Department of Chemistry Biochemistry, University of Maryland, College Park, MD, 20742, USA
| | - Devendra Mani
- Physical Chemistry II, Department of Chemistry and Biochemistry, Ruhr-Universität Bochum, Bochum, Germany
| | - Nitish Pal
- Physical Chemistry II, Department of Chemistry and Biochemistry, Ruhr-Universität Bochum, Bochum, Germany
| | - Gerhard Schwaab
- Physical Chemistry II, Department of Chemistry and Biochemistry, Ruhr-Universität Bochum, Bochum, Germany
| | - Joel M Bowman
- Cherry L. Emerson Center for Scientific Computations and Department of Chemistry, Emory University, Atlanta, GA, 30322, USA
| | - Gregory S Tschumper
- Department of Chemistry and Biochemistry, University of Mississippi, University, MS, 38677, USA
| | - Martina Havenith
- Physical Chemistry II, Department of Chemistry and Biochemistry, Ruhr-Universität Bochum, Bochum, Germany
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