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Zhu X, Gu B. Making Peace with Random Phases: Ab Initio Conical Intersection Quantum Dynamics in Random Gauges. J Phys Chem Lett 2024; 15:8487-8493. [PMID: 39133253 DOI: 10.1021/acs.jpclett.4c01688] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/13/2024]
Abstract
Ab initio modeling of conical intersection wave packet dynamics is crucial for various photochemical, photophysical, and biological processes. However, adiabatic electronic states obtained from electronic structure computations involve random phases, or more generally, random gauge fixings, which cannot be directly used in the modeling of nonadiabatic wave packet simulations. Here we develop a random-gauge local diabatic representation that allows an exact modeling of conical intersection dynamics directly using the adiabatic electronic states with phases randomly assigned during the electronic structure computations. Its utility is demonstrated by an exact ab initio modeling of the two-dimensional Shin-Metiu model with and without an external magnetic field. Our results provide a simple approach to integrating the electronic structure computations into nonadiabatic quantum dynamics, thus paving the way for ab initio modeling of conical intersection dynamics.
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Affiliation(s)
- Xiaotong Zhu
- Department of Chemistry and Department of Physics, Westlake University, Hangzhou, Zhejiang 310030, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
| | - Bing Gu
- Department of Chemistry and Department of Physics, Westlake University, Hangzhou, Zhejiang 310030, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
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2
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Chen X, Franco I. Bexcitonics: Quasiparticle approach to open quantum dynamics. J Chem Phys 2024; 160:204116. [PMID: 38814013 DOI: 10.1063/5.0198567] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2024] [Accepted: 05/09/2024] [Indexed: 05/31/2024] Open
Abstract
We develop a quasiparticle approach to capture the dynamics of open quantum systems coupled to bosonic thermal baths of arbitrary complexity based on the Hierarchical Equations of Motion (HEOM). This is done by generalizing the HEOM dynamics and mapping it into that of the system in interaction with a few bosonic fictitious quasiparticles that we call bexcitons. Bexcitons arise from a decomposition of the bath correlation function into discrete features. Specifically, bexciton creation and annihilation couple the auxiliary density matrices in the HEOM. The approach provides a systematic strategy to construct exact quantum master equations that include the system-bath coupling to all orders even for non-Markovian environments. Specifically, by introducing different metrics and representations for the bexcitons it is possible to straightforwardly generate different variants of the HEOM, demonstrating that all these variants share a common underlying quasiparticle picture. Bexcitonic properties, while unphysical, offer a coarse-grained view of the correlated system-bath dynamics and its numerical convergence. For instance, we use it to analyze the instability of the HEOM when the bath is composed of underdamped oscillators and show that it leads to the creation of highly excited bexcitons. The bexcitonic picture can also be used to develop more efficient approaches to propagate the HEOM. As an example, we use the particle-like nature of the bexcitons to introduce mode-combination of bexcitons in both number and coordinate representation that uses the multi-configuration time-dependent Hartree to efficiently propagate the HEOM dynamics.
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Affiliation(s)
- Xinxian Chen
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - Ignacio Franco
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
- Department of Physics, University of Rochester, Rochester, New York 14627, USA
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3
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Gu B. Nonadiabatic Conical Intersection Dynamics in the Local Diabatic Representation with Strang Splitting and Fourier Basis. J Chem Theory Comput 2024; 20:2711-2718. [PMID: 38536965 DOI: 10.1021/acs.jctc.3c01317] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/10/2024]
Abstract
We develop and implement an exact conical intersection nonadiabatic wave packet dynamics method that combines the local diabatic representation, Strang splitting for the total molecular propagator, and discrete variable representation with uniform grids. By employing the local diabatic representation, this method captures all nonadiabatic effects, including nonadiabatic transitions, electronic coherences, and geometric phase. Moreover, it is free of singularities in the first and second derivative couplings and does not require the electronic wave function to be continuous with respect to the nuclear coordinates. We further show that in contrast to the adiabatic representation, the split-operator method can be directly applied to the full molecular propagator with the locally diabatic ansatz. The Fourier series, employed as the primitive nuclear basis functions, is universal and can be applied to all types of reactive coordinates. The combination of local diabatic representation, Strang splitting, and Fourier basis allows numerically exact modeling of conical intersection quantum dynamics directly with adiabatic electronic states that can be obtained from standard electronic structure computations.
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Affiliation(s)
- Bing Gu
- Department of Chemistry and Department of Physics, Westlake University, Hangzhou, Zhejiang 310030, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
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4
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Gu B. A Discrete-Variable Local Diabatic Representation of Conical Intersection Dynamics. J Chem Theory Comput 2023; 19:6557-6563. [PMID: 37737832 DOI: 10.1021/acs.jctc.3c00560] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/23/2023]
Abstract
Conical intersections (CIs) are ubiquitous in polyatomic molecules and are responsible for a wide range of phenomena in photochemistry and photophysics. Modeling the conical intersection dynamics with adiabatic electronic states is hindered by the divergence of the first- and second-order derivative couplings at CIs due to electronic degeneracy. We introduce and implement a novel diabatic representation for exact correlated electron-nuclear wave packet dynamics through conical intersections. It directly employs the adiabatic electronic states but avoids the singular first- and second-order derivative couplings and is robust to different gauge choices of the electronic wave function phases. The reference nuclear geometries defining the adiabatic electronic states are determined by a discrete-variable representation of the nuclear coordinates. The nonadiabatic effects are accounted for by the electronic overlap matrix instead of derivative couplings as in the adiabatic representation. Illustrated by a two-mode conical intersection model, this representation captures all nonadiabatic effects, including electronic transitions, electronic coherence, and geometric phases. Thus, this representation provides a singularity-free framework for modeling ab initio conical intersection wave packet dynamics.
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Affiliation(s)
- Bing Gu
- Department of Chemistry & Department of Physics, Westlake University, Hangzhou, Zhejiang 310030, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
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5
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Aarabi M, Sarka J, Pandey A, Nieman R, Aquino AJA, Eckert J, Poirier B. Quantum Dynamical Investigation of Dihydrogen-Hydride Exchange in a Transition-Metal Polyhydride Complex. J Phys Chem A 2023; 127:6385-6399. [PMID: 37494557 DOI: 10.1021/acs.jpca.3c01863] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/28/2023]
Abstract
The ongoing shift toward clean, sustainable energy is a primary driving force behind hydrogen fuel research. Safe and effective storage of hydrogen is a major challenge (particularly for mobile applications) and requires a detailed understanding of the atomic level interactions of hydrogen with its host materials. The light mass of hydrogen, however, implies that quantum effects are important, so a quantum dynamical treatment is required to properly account for these effects in computational simulations. As one such example, we describe herein the hydrogen exchange dynamics between a hydride and a dihydrogen ligand in the [FeH(H2)(PH3)4]+ model complex. A global three-dimensional (3D) potential energy surface (PES) was constructed by fitting to and interpolating from a discrete set of grid points computed using density functional theory; exact quantum dynamical calculations were then carried out on the 3D PES using discrete variable representation basis sets. Energy levels and their quantum tunneling splittings were computed up to 3000 cm-1 above the ground state. Within that energy range, all three fundamentals have been identified using wave function plots, as well as the first three overtones of the exchange (reaction coordinate) motion and several of its combination bands. From the tunneling splittings, the Boltzmann-averaged tunneling rates were computed. The Arrhenius plot of the total exchange rate shows a clear transition around 150 K, below which the activation energy is essentially zero and above which it is less than half of the electronic structure barrier. This indicates that exchange rates are governed by quantum tunneling throughout the relevant temperature range with the low-temperature regime dominated by a single quantum (ground) state. This work is the first-ever fully quantum dynamical study to investigate the hydrogen exchange dynamics between hydride and dihydrogen ligands coordinated to a transition-metal complex.
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Affiliation(s)
- Mahdi Aarabi
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, United States
| | - János Sarka
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, United States
- Institute of Chemistry, Eötvös Loránd University, H-1117 Budapest, Hungary
| | - Ankit Pandey
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, United States
| | - Reed Nieman
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, United States
| | - Adelia J A Aquino
- Department of Mechanical Engineering, Texas Tech University, Lubbock, Texas 79409-1061, United States
| | - Juergen Eckert
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, United States
- Theoretical Division (T-1, MS B221), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Bill Poirier
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, United States
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6
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Tan JA, Barbarona RF, Kuo JL. Approaching the "Zundel" Limit: Tuning the Vibrational Coupling in N 2H +Ng, Ng = {He, Ne, Ar, Kr, Xe, and Rn}. J Phys Chem A 2023. [PMID: 37418837 DOI: 10.1021/acs.jpca.3c01956] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/09/2023]
Abstract
The diazenylium ion (N2H+) is a ubiquitous ion in dense molecular clouds. This ion is often used as a dense gas tracer in outer space. Most of the previous works on diazenylium ion have focused on the shared-proton stretch band, νH+. In this work, we have performed reduced-dimensional calculations to investigate the vibrational structure of N2H+Ng, Ng = {He, Ne, Ar, Kr, Xe, and Rn}. We demonstrate a few interesting things about this system. First, the vibrational coupling in N2H+ can be tuned to switch on interesting anharmonic effects such as Fermi resonance or combination bands by tagging it with different noble gases. Second, a comparison of the vibrational spectrum from N2H+He to N2H+Rn shows that the νH+ can be swept from an "Eigen-like" to a "Zundel-like" limiting case. Anharmonic calculations were performed using a multilevel approach, which utilized the MP2 and CCSD(T) levels of theories. Binding energies for the elimination of Ng in N2H+Ng are also reported.
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Affiliation(s)
- Jake A Tan
- Institute of Atomic and Molecular Science, Academia Sinica, Taipei 10617, Taiwan
| | - Rona F Barbarona
- Institute of Atomic and Molecular Science, Academia Sinica, Taipei 10617, Taiwan
- Molecular Science and Technology Program, Taiwan International Graduate Program, Academia Sinica, Taipei 11529, Taiwan
- Department of Physics, National Central University, Taoyuan 32001, Taiwan
| | - Jer-Lai Kuo
- Institute of Atomic and Molecular Science, Academia Sinica, Taipei 10617, Taiwan
- Molecular Science and Technology Program, Taiwan International Graduate Program, Academia Sinica, Taipei 11529, Taiwan
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7
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Algebraic DVR Approaches Applied to Piecewise Potentials: Symmetry and Degeneracy. Symmetry (Basel) 2022. [DOI: 10.3390/sym14030445] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Algebraic discrete variable representation (DVR) methods that have been recently proposed are applied to describe 1D and 2D piecewise potentials. First, it is shown that it is possible to use a DVR approach to describe 1D square well potentials testing the wave functions with exact results. Thereafter, Morse and Pöschl-Teller (PT) potentials are described with multistep piecewise potentials in order to explore the sensibility of the potential to reproduce the transition from a pure square well energy pattern to an anharmonic energy spectrum. Once the properties of the different algebraic DVR approaches are identified, the 2D square potential as a function of the potential depth is studied. We show that this system displays natural degeneracy, accidental degeneracy and systematic accidental degeneracy. The latter appears only for a confined potential, where the symmetry group is identified and irreducible representations are constructed. One particle confined in a rectangular well potential with commensurate sides is also analyzed. It is proved that the systematic accidental degeneracy appearing in this system is removed for finite potential depth.
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8
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Poirier B, Jerke J. Full-dimensional Schrödinger wavefunction calculations using tensors and quantum computers: the Cartesian component-separated approach. Phys Chem Chem Phys 2022; 24:4437-4454. [PMID: 35113096 DOI: 10.1039/d1cp02036f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Traditional methods in quantum chemistry rely on Hartree-Fock-based Slater-determinant (SD) representations, whose underlying zeroth-order picture assumes separability by particle. Here, we explore a radically different approach, based on separability by Cartesian component, rather than by particle [J. Jerke and B. Poirier, J. Chem. Phys., 2018, 148, 104101]. The approach appears to be very well suited for 3D grid-based methods in quantum chemistry, and thereby also for so-called "first-quantized" quantum computing. We first present an overview of the approach as implemented on classical computers, including numerical results that justify performance claims. In particular, we perform numerical calculations with four explicit electrons that are equivalent to full-CI matrix diagonalization with nearly 1015 SDs. We then present an implementation for quantum computers for which the number of quantum gates (and to a lesser extent, the number of qubits) can be dramatically reduced, in comparison with other quantum circuitry that has been envisioned for implementing first-quantized "quantum computational chemistry" (QCC).
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Affiliation(s)
- Bill Poirier
- Department of Chemistry and Biochemistry and Department of Physics, Texas Tech University, P.O. Box 41061, Lubbock, Texas 79409-1061, USA.
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9
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Abstract
Recent studies have demonstrated that higher than two-body bath-impurity correlations are not important for quantitatively describing the ground state of the Bose polaron. Motivated by the above, we employ the so-called Gross Ansatz (GA) approach to unravel the stationary and dynamical properties of the homogeneous one-dimensional Bose-polaron for different impurity momenta and bath-impurity couplings. We explicate that the character of the equilibrium state crossovers from the quasi-particle Bose polaron regime to the collective-excitation stationary dark-bright soliton for varying impurity momentum and interactions. Following an interspecies interaction quench the temporal orthogonality catastrophe is identified, provided that bath-impurity interactions are sufficiently stronger than the intraspecies bath ones, thus generalizing the results of the confined case. This catastrophe originates from the formation of dispersive shock wave structures associated with the zero-range character of the bath-impurity potential. For initially moving impurities, a momentum transfer process from the impurity to the dispersive shock waves via the exerted drag force is demonstrated, resulting in a final polaronic state with reduced velocity. Our results clearly demonstrate the crucial role of non-linear excitations for determining the behavior of the one-dimensional Bose polaron.
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10
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Sarka J, Poirier B. Hitting the Trifecta: How to Simultaneously Push the Limits of Schrödinger Solution with Respect to System Size, Convergence Accuracy, and Number of Computed States. J Chem Theory Comput 2021; 17:7732-7744. [PMID: 34761945 DOI: 10.1021/acs.jctc.1c00824] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Methods for solving the Schrödinger equation without approximation are in high demand but are notoriously computationally expensive. In practical terms, there are just three primary factors that currently limit what can be achieved: 1) system size/dimensionality; 2) energy level excitation; and 3) numerical convergence accuracy. Broadly speaking, current methods can deliver on any two of these three goals, but achieving all three at once remains an enormous challenge. In this paper, we shall demonstrate how to "hit the trifecta" in the context of molecular vibrational spectroscopy calculations. In particular, we compute the lowest 1000 vibrational states for the six-atom acetonitrile molecule (CH3CN), to a numerical convergence of accuracy 10-2 cm-1 or better. These calculations encompass all vibrational states throughout most of the dynamically relevant range (i.e., up to ∼4250 cm-1 above the ground state), computed in full quantum dimensionality (12 dimensions), to near spectroscopic accuracy. To our knowledge, no such vibrational spectroscopy calculation has ever previously been performed.
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Affiliation(s)
- János Sarka
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States
| | - Bill Poirier
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States
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11
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Rodríguez-Arcos M, Bermúdez-Montana M, Lemus R. Algebraic discrete variable representation approach applied to Lennard-Jones and H 2 potentials. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1957169] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
| | | | - R. Lemus
- Instituto de Ciencias Nucleares, UNAM, Mexico, CDMX, Mexico
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12
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Han J, Grofe A, Gao J. Variational Energy Decomposition Analysis of Charge-Transfer Interactions between Metals and Ligands in Carbonyl Complexes. Inorg Chem 2021; 60:14060-14071. [PMID: 34460236 DOI: 10.1021/acs.inorgchem.1c01367] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Variational energy decomposition analyses have been presented to quantify the σ-dative, ligand-to-metal forward charge transfer (CT) and the π-conjugative, metal-to-ligand backward charge delocalization on a series of isolelectronic transition-metal carbonyl complexes M(CO)6, including M = Ti2-, V-, Cr, Mn+, and Fe2+. Although the qualitative features of these energy terms are understood, well-defined quantitative studies have been scarce. Consistent with early findings, electrostatic and Pauli exchange effects play a key role in σ-donation, resulting in blue shifts in ligand vibrational frequency in the complex geometries. Excluding chemical bonding interactions between the CO ligand and the metal fragments in the energy decomposition analysis, we found that loosely bound electrostatic complexes can be formed at a longer metal-to-ligand distance due to the exponential decay of Pauli exchange. In all complexes, the overall binding stabilization can be attributed to CT effects, with opposing trends between σ-donation and π-back bonding that follows an order of Ti2- (4.4) > V1- (2.6) > Cr (1.5) > Mn1+ (1.1) > Fe2+ (0.5) in π-to-σ CT ratio. These electronic and energetic features are mirrored in the vibrational frequency shifts induced by different factors. The present investigation may help stimulate the use of energy decomposition techniques to understand the structure and activity of metallocatalysts using density functional theory.
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Affiliation(s)
- Jingting Han
- Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun, Jilin Province 130023, China
| | - Adam Grofe
- Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun, Jilin Province 130023, China.,Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, China
| | - Jiali Gao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, China.,Beijing University Shenzhen Graduate School, Shenzhen 518055, China.,Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, United States
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13
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Cunha LA, Lee J, Hait D, McCurdy CW, Head-Gordon M. Exploring spin symmetry-breaking effects for static field ionization of atoms: Is there an analog to the Coulson-Fischer point in bond dissociation? J Chem Phys 2021; 155:014309. [PMID: 34241406 DOI: 10.1063/5.0054387] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Löwdin's symmetry dilemma is an ubiquitous issue in approximate quantum chemistry. In the context of Hartree-Fock (HF) theory, the use of Slater determinants with some imposed constraints to preserve symmetries of the exact problem may lead to physically unreasonable potential energy surfaces. On the other hand, lifting these constraints leads to the so-called broken symmetry solutions that usually provide better energetics, at the cost of losing information about good quantum numbers that describe the state of the system. This behavior has previously been extensively studied in the context of bond dissociation. This paper studies the behavior of different classes of HF spin polarized solutions (restricted, unrestricted, and generalized) in the context of ionization by strong static electric fields. We find that, for simple two electron systems, unrestricted Hartree-Fock (UHF) is able to provide a qualitatively good description of states involved during the ionization process (neutral, singly ionized, and doubly ionized states), whereas RHF fails to describe the singly ionized state. For more complex systems, even though UHF is able to capture some of the expected characteristics of the ionized states, it is constrained to a single Ms (diabatic) manifold in the energy surface as a function of field intensity. In this case, a better qualitative picture can be painted by using generalized Hartree-Fock as it is able to explore different spin manifolds and follow the lowest solution due to lack of collinearity constraints on the spin quantization axis.
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Affiliation(s)
- Leonardo A Cunha
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Joonho Lee
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Diptarka Hait
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - C William McCurdy
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Martin Head-Gordon
- Department of Chemistry, University of California, Berkeley, California 94720, USA
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14
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Morales-Hernández GE, Castellanos JC, Romero JL, Klimov AB. Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems. ENTROPY 2021; 23:e23060684. [PMID: 34071644 PMCID: PMC8229760 DOI: 10.3390/e23060684] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Revised: 05/23/2021] [Accepted: 05/25/2021] [Indexed: 11/20/2022]
Abstract
We apply the semi-classical limit of the generalized SO(3) map for representation of variable-spin systems in a four-dimensional symplectic manifold and approximate their evolution terms of effective classical dynamics on T*S2. Using the asymptotic form of the star-product, we manage to “quantize” one of the classical dynamic variables and introduce a discretized version of the Truncated Wigner Approximation (TWA). Two emblematic examples of quantum dynamics (rotor in an external field and two coupled spins) are analyzed, and the results of exact, continuous, and discretized versions of TWA are compared.
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15
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Novario S, Gysbers P, Engel J, Hagen G, Jansen GR, Morris TD, Navrátil P, Papenbrock T, Quaglioni S. Coupled-Cluster Calculations of Neutrinoless Double-β Decay in ^{48}Ca. PHYSICAL REVIEW LETTERS 2021; 126:182502. [PMID: 34018796 DOI: 10.1103/physrevlett.126.182502] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2020] [Revised: 01/15/2021] [Accepted: 04/06/2021] [Indexed: 06/12/2023]
Abstract
We use coupled-cluster theory and nuclear interactions from chiral effective field theory to compute the nuclear matrix element for the neutrinoless double-β decay of ^{48}Ca. Benchmarks with the no-core shell model in several light nuclei inform us about the accuracy of our approach. For ^{48}Ca we find a relatively small matrix element. We also compute the nuclear matrix element for the two-neutrino double-β decay of ^{48}Ca with a quenching factor deduced from two-body currents in recent ab initio calculation of the Ikeda sum rule in ^{48}Ca [Gysbers et al., Nat. Phys. 15, 428 (2019)NPAHAX1745-247310.1038/s41567-019-0450-7].
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Affiliation(s)
- S Novario
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
- Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - P Gysbers
- TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T 2A3, Canada
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - J Engel
- Department of Physics, University of North Carolina, Chapel Hill, North Carolina 27514, USA
| | - G Hagen
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
- Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T 2A3, Canada
| | - G R Jansen
- Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - T D Morris
- Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - P Navrátil
- TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T 2A3, Canada
| | - T Papenbrock
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
- Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - S Quaglioni
- Lawrence Livermore National Laboratory, P.O. Box 808, L-414, Livermore, California 94551, USA
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16
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Rodríguez-Arcos M, Bermúdez-Montaña M, Arias JM, Gómez-Camacho J, Orgaz E, Lemus R. Algebraic discrete variable representation approaches: application to interatomic effective potentials. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1876264] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- M. Rodríguez-Arcos
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Coyoacan, México, DF, México
| | - M. Bermúdez-Montaña
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Coyoacan, México, DF, México
- Facultad de Química, Universidad Nacional Autónoma de México, Coyoacan, México, DF, México
| | - J. M. Arias
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Sevilla, Spain
- Instituto Carlos I (iCI) de Física Teórica y Computacional, Universidad de Sevilla, Sevilla, Spain
| | - J. Gómez-Camacho
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Sevilla, Spain
- CN de Aceleradores (U. Sevilla, J. Andalucía, CSIC), Sevilla, Spain
| | - E. Orgaz
- Facultad de Química, Universidad Nacional Autónoma de México, Coyoacan, México, DF, México
| | - R. Lemus
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Coyoacan, México, DF, México
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17
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Revuelta F, Vergini E, Benito RM, Borondo F. Short-periodic-orbit method for excited chaotic eigenfunctions. Phys Rev E 2020; 102:042210. [PMID: 33212620 DOI: 10.1103/physreve.102.042210] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2019] [Accepted: 09/18/2020] [Indexed: 11/07/2022]
Abstract
An alternative method for the calculation of excited chaotic eigenfunctions in arbitrary energy windows is presented. We demonstrate the feasibility of using wave functions localized on unstable periodic orbits as efficient basis sets for this task in classically chaotic systems. The number of required localized wave functions is only of the order of the ratio t_{H}/t_{E}, with t_{H} the Heisenberg time and t_{E} the Ehrenfest time. As an illustration, we present convincing results for a coupled two-dimensional quartic oscillator with chaotic dynamics.
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Affiliation(s)
- F Revuelta
- Grupo de Sistemas Complejos, Escuela Técnica Superior de Ingeniería Agronómica, Alimentaria y de Biosistemas, Universidad Politécnica de Madrid, Avenida Puerta de Hierro 2-4, 28040 Madrid, Spain
| | - E Vergini
- Departamento de Física, Comisión Nacional de Energía Atómica, Avenida del Libertador 8250, 1429 Buenos Aires, Argentina
| | - R M Benito
- Grupo de Sistemas Complejos, Escuela Técnica Superior de Ingeniería Agronómica, Alimentaria y de Biosistemas, Universidad Politécnica de Madrid, Avenida Puerta de Hierro 2-4, 28040 Madrid, Spain
| | - F Borondo
- Instituto de Ciencias Matemáticas (ICMAT), Cantoblanco, 28049 Madrid, Spain.,Departamento de Química, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain
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18
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Abstract
Two algebraic approaches based on a discrete variable representation are introduced and applied to describe the Stark effect in the non-relativistic Hydrogen atom. One approach consists of considering an algebraic representation of a cutoff 3D harmonic oscillator where the matrix representation of the operators r2 and p2 are diagonalized to define useful bases to obtain the matrix representation of the Hamiltonian in a simple form in terms of diagonal matrices. The second approach is based on the U(4) dynamical algebra which consists of the addition of a scalar boson to the 3D harmonic oscillator space keeping constant the total number of bosons. This allows the kets associated with the different subgroup chains to be linked to energy, coordinate and momentum representations, whose involved branching rules define the discrete variable representation. Both methods, although originating from the harmonic oscillator basis, provide different convergence tests due to the fact that the associated discrete bases turn out to be different. These approaches provide powerful tools to obtain the matrix representation of 3D general Hamiltonians in a simple form. In particular, the Hydrogen atom interacting with a static electric field is described. To accomplish this task, the diagonalization of the exact matrix representation of the Hamiltonian is carried out. Particular attention is paid to the subspaces associated with the quantum numbers n=2,3 with m=0.
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19
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Farfan CA, Turner DB. A systematic model study quantifying how conical intersection topography modulates photochemical reactions. Phys Chem Chem Phys 2020; 22:20265-20283. [PMID: 32966428 DOI: 10.1039/d0cp03464a] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Despite their important role in photochemistry and expected presence in most polyatomic molecules, conical intersections have been thoroughly characterized in a comparatively small number of systems. Conical intersections can confer molecular photoreactivity or photostability, often with remarkable efficacy, due to their unique structure: at a conical intersection, the adiabatic potential energy surfaces of two or more electronic states are degenerate, enabling ultrafast decay from an excited state without radiative emission, known as nonadiabatic transfer. Furthermore, the precise conical intersection topography determines fundamental properties of photochemical processes, including excited-state decay rate, efficacy, and molecular products that are formed. However, these relationships have yet to be defined comprehensively. In this article, we use an adaptable computational model to investigate a variety of conical intersection topographies, simulate resulting nonadiabatic dynamics, and calculate key photochemical observables. We varied the vibrational mode frequencies to modify conical intersection topography systematically in four primary classes of conical intersections and quantified the resulting rate, total yield, and product yield of nonadiabatic decay. The results reveal that higher vibrational mode frequencies reduce nonadiabatic transfer, but increase the transfer rate and resulting photoproduct formation. These trends can inform progress toward experimental control of photochemical reactions or tuning of molecules' photochemical properties based on conical intersections and their topography.
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Affiliation(s)
- Camille A Farfan
- Department of Chemistry, New York University, New York, NY 10003, USA
| | - Daniel B Turner
- Department of Chemistry, New York University, New York, NY 10003, USA
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20
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Pandey A, Poirier B. An algorithm to find (and plug) “holes” in multi-dimensional surfaces. J Chem Phys 2020; 152:214102. [DOI: 10.1063/5.0005681] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Affiliation(s)
- Ankit Pandey
- Department of Chemistry and Biochemistry, Texas Tech University, P.O. Box 41061, Lubbock, Texas 79409-1061, USA
| | - Bill Poirier
- Department of Chemistry and Biochemistry, Texas Tech University, P.O. Box 41061, Lubbock, Texas 79409-1061, USA
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21
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Rodríguez-Arcos M, Lemus R, Arias JM, Gómez-Camacho J. Unitary group approach to describe interatomic potentials in 3D systems. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1662959] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- M. Rodríguez-Arcos
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, México, DF, México
| | - R. Lemus
- Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, México, DF, México
| | - J. M. Arias
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Sevilla, Spain
- Instituto Carlos I (iCI) de Física Teórica y Computacional, Universidad de Sevilla, Sevilla, Spain
| | - J. Gómez-Camacho
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Sevilla, Spain
- CN de Aceleradores (U. Sevilla, J. Andalucía,CSIC), Sevilla, Spain
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22
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Farfan CA, Turner DB. Nonadiabatic Photochemistry Induced by Inaccessible Conical Intersections. J Phys Chem A 2019; 123:7768-7776. [DOI: 10.1021/acs.jpca.9b07739] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Camille A. Farfan
- Department of Chemistry, New York University, 100 Washington Square East, New York New York 10003, United States
| | - Daniel B. Turner
- Department of Chemistry, New York University, 100 Washington Square East, New York New York 10003, United States
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23
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Jerke J, Karwowski J, Poirier B. Exact matrix elements for general two-body central-force interactions, expressed as sums of products. Mol Phys 2019. [DOI: 10.1080/00268976.2018.1538541] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Jonathan Jerke
- Department of Chemistry and Biochemistry, and Department of Physics, Texas Tech University, Lubbock, TX, USA
| | - Jacek Karwowski
- Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University, Toruń, Poland
| | - Bill Poirier
- Department of Chemistry and Biochemistry, and Department of Physics, Texas Tech University, Lubbock, TX, USA
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24
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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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25
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Affiliation(s)
- He Yin
- Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, P. R. China
| | - Hui Li
- Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, P. R. China
| | - Adam Grofe
- Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, P. R. China
| | - Jiali Gao
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, United States
- Lab of Computational Chemistry and Drug Design, State Key Laboratory of Chemical Oncogenomics, Peking University Shenzhen Graduate School, Shenzhen 518055, China
- Shenzhen Bay Laboratory, Shenzhen 518055, China
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26
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Kuenzer U, Hofer TS. A four-dimensional Numerov approach and its application to the vibrational eigenstates of linear triatomic molecules – The interplay between anharmonicity and inter-mode coupling. Chem Phys 2019. [DOI: 10.1016/j.chemphys.2019.01.007] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
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27
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Macridin A, Spentzouris P, Amundson J, Harnik R. Electron-Phonon Systems on a Universal Quantum Computer. PHYSICAL REVIEW LETTERS 2018; 121:110504. [PMID: 30265100 DOI: 10.1103/physrevlett.121.110504] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2018] [Indexed: 06/08/2023]
Abstract
We present an algorithm that extends existing quantum algorithms for simulating fermion systems in quantum chemistry and condensed matter physics to include bosons in general and phonons in particular. We introduce a qubit representation for the low-energy subspace of phonons which allows an efficient simulation of the evolution operator of the electron-phonon systems. As a consequence of the Nyquist-Shannon sampling theorem, the phonons are represented with exponential accuracy on a discretized Hilbert space with a size that increases linearly with the cutoff of the maximum phonon number. The additional number of qubits required by the presence of phonons scales linearly with the size of the system. The additional circuit depth is constant for systems with finite-range electron-phonon and phonon-phonon interactions and linear for long-range electron-phonon interactions. Our algorithm for a Holstein polaron problem was implemented on an Atos quantum learning machine quantum simulator employing the quantum phase estimation method. The energy and the phonon number distribution of the polaron state agree with exact diagonalization results for weak, intermediate, and strong electron-phonon coupling regimes.
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Affiliation(s)
| | | | | | - Roni Harnik
- Fermilab, P.O. Box 500, Batavia, Illinois 60510, USA
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28
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Large Scale Exact Quantum Dynamics Calculations: Using Phase Space to Truncate the Basis Effectively. ADVANCES IN CHEMICAL PHYSICS 2018. [DOI: 10.1002/9781119374978.ch9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register]
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29
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Jerke J, Poirier B. Two-body Schrödinger wave functions in a plane-wave basis via separation of dimensions. J Chem Phys 2018; 148:104101. [DOI: 10.1063/1.5017621] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jonathan Jerke
- Department of Chemistry and Biochemistry, and Department of Physics, Texas Tech University, P.O. Box 41061, Lubbock, Texas 79409-1061, USA
- Department of Physics, Texas Southern University, Houston, Texas 77004, USA
| | - Bill Poirier
- Department of Chemistry and Biochemistry, and Department of Physics, Texas Tech University, P.O. Box 41061, Lubbock, Texas 79409-1061, USA
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30
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Yu HG. A coherent discrete variable representation method on a sphere. J Chem Phys 2017; 147:094101. [DOI: 10.1063/1.4996891] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Hua-Gen Yu
- Division of Chemistry, Department of Energy and Photon Sciences, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
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31
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Hofmeister C, Coto PB, Thoss M. Controlling the conductance of molecular junctions using proton transfer reactions: A theoretical model study. J Chem Phys 2017. [DOI: 10.1063/1.4974512] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Chriszandro Hofmeister
- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstrasse 7/B2, D-91058 Erlangen, Germany
| | - Pedro B. Coto
- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstrasse 7/B2, D-91058 Erlangen, Germany
| | - Michael Thoss
- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstrasse 7/B2, D-91058 Erlangen, Germany
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32
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Paul S, Tiesinga E. Wannier functions using a discrete variable representation for optical lattices. PHYSICAL REVIEW. A 2016; 94:033606. [PMID: 29876532 PMCID: PMC5986193 DOI: 10.1103/physreva.94.033606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We propose a numerical method using the discrete variable representation (DVR) for constructing real-valued Wannier functions localized in a unit cell for both symmetric and asymmetric periodic potentials. We apply these results to finding Wannier functions for ultracold atoms trapped in laser-generated optical lattices. Following S. Kivelson [Phys. Rev. B 26, 4269 (1982)], for a symmetric lattice with inversion symmetry, we construct Wannier functions as eigenstates of the position operators x̂, ŷ, and ẑ restricted to single-particle Bloch functions belonging to one or more bands. To ensure that the Wannier functions are real-valued, we numerically obtain the band structure and real-valued eigenstates using a uniform Fourier grid DVR. We then show, by a comparison of tunneling energies, that the Wannier functions are accurate for both inversion-symmetric and asymmetric potentials to better than 10 significant digits when using double-precision arithmetic. The calculations are performed for an optical lattice with double-wells per unit cell with tunable asymmetry along the x axis and a single sinusoidal potential along the perpendicular directions. Localized functions at the two potential minima within each unit cell are similarly constructed, but using a superposition of single-particle solutions from the two lowest bands. We finally use these localized basis functions to determine the two-body interaction energies in the Bose-Hubbard model and show the dependence of these energies on lattice asymmetry.
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Affiliation(s)
- Saurabh Paul
- Joint Center for Quantum Information and Computer Science, Joint Quantum Institute and University of Maryland, Maryland 20742, USA
| | - Eite Tiesinga
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, National Institute of Standards and Technology and University of Maryland, Gaithersburg, Maryland 20899, USA
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33
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Halverson T, Poirier B. Calculation of exact vibrational spectra for P2O and CH2NH using a phase space wavelet basis. J Chem Phys 2014; 140:204112. [DOI: 10.1063/1.4879216] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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34
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Pesonen J. Eckart frame vibration-rotation Hamiltonians: Contravariant metric tensor. J Chem Phys 2014; 140:074101. [DOI: 10.1063/1.4865750] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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35
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Lauvergnat D, Nauts A. Quantum dynamics with sparse grids: a combination of Smolyak scheme and cubature. Application to methanol in full dimensionality. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2014; 119:18-25. [PMID: 23859892 DOI: 10.1016/j.saa.2013.05.068] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2013] [Revised: 05/12/2013] [Accepted: 05/19/2013] [Indexed: 06/02/2023]
Abstract
Quantum dynamical approaches based on product-grids are limited to the studies of molecular systems with few degrees of freedom, typically less than ten. Recently, Avila et al. [G. Avila, T. Carrington, J. Chem. Phys., 131 (2009) 174103] have introduced the Smolyak scheme [S.A. Smolyak, Sov. Math. Dokl., 4 (1963) 240], which considerably reduces the size of the grids. This approach has pushed back the present calculation limits on the vibrational spectra of polyatomic molecules. In the present study, we have developed an extension of the standard Smolyak scheme in which this scheme is combined with multidimensional grids, such as cubatures, to obtain new sparse grids. This scheme has been applied to the study of the torsional energy levels of methanol in full dimensionality (12D).
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Affiliation(s)
- David Lauvergnat
- Laboratoire de Chimie Physique, Bâtiment 349, CNRS, UMR8000, Univ Paris-Sud, Orsay F-91405, France.
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36
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Avila G, Carrington T. Solving the Schroedinger equation using Smolyak interpolants. J Chem Phys 2013; 139:134114. [DOI: 10.1063/1.4821348] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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37
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Tyuterev VG, Kochanov RV, Tashkun SA, Holka F, Szalay PG. New analytical model for the ozone electronic ground state potential surface and accurate ab initio vibrational predictions at high energy range. J Chem Phys 2013; 139:134307. [DOI: 10.1063/1.4821638] [Citation(s) in RCA: 91] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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38
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Szalay V. About the variational property of generalized discrete variable representation. J Phys Chem A 2013; 117:7075-80. [PMID: 23527631 DOI: 10.1021/jp400112p] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
It is explained why the generalized discrete variable representation is variational neither with respect to the size (truncation) of the basis set nor with respect to the selection of grid points.
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Affiliation(s)
- Viktor Szalay
- Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary.
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39
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Wang XG, Carrington T. Computing rovibrational levels of polyatomic molecules with polyspherical coordinates and a contracted basis built with a K-independent vibrational primitive basis. Mol Phys 2013. [DOI: 10.1080/00268976.2013.808387] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Xiao-Gang Wang
- Chemistry Department, Queen’s University , Kingston, Ontario, Canada
| | - Tucker Carrington
- Chemistry Department, Queen’s University , Kingston, Ontario, Canada
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40
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Dawes R, Wang XG, Carrington T. CO Dimer: New Potential Energy Surface and Rovibrational Calculations. J Phys Chem A 2013; 117:7612-30. [DOI: 10.1021/jp404888d] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Richard Dawes
- Department
of Chemistry, Missouri University of Science and Technology, Rolla,
Missouri 65409, United States
| | - Xiao-Gang Wang
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6,
Canada
| | - Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6,
Canada
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41
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42
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Power J, Rawitscher G. Accuracy of a hybrid finite-element method for solving a scattering Schrödinger equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:066707. [PMID: 23368078 DOI: 10.1103/physreve.86.066707] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2012] [Revised: 09/25/2012] [Indexed: 06/01/2023]
Abstract
This hybrid method [finite-element discrete variable representation (FE-DVR)], introduced by Resigno and McCurdy [Phys. Rev. A 62, 032706 (2000)], uses Lagrange polynomials in each partition, rather than "hat" functions or Gaussian functions. These polynomials are discrete variable representation functions, and they are orthogonal under the Gauss-Lobatto quadrature discretization approximation. Accuracy analyses of this method are performed for the case of a one-dimensional Schrödinger equation with various types of local and nonlocal potentials for scattering boundary conditions. The accuracy is ascertained by a comparison with a spectral Chebyshev integral equation method, accurate to 1:10⁻¹¹. For an accuracy of the phase shift of 1:10⁻⁸, the FE-DVR method is found to be 100 times faster than a sixth-order finite-difference method (Numerov), it is easy to program, and it can routinely achieve an accuracy of better than 1:10⁻⁸ for the numerical examples studied.
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Affiliation(s)
- Joseph Power
- Physics Department, University of Connecticut, Storrs, Connecticut 06269, USA
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43
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Ning QC, Peng LY, Hou XF, Xu Z, Gong Q. Application of discrete variable representation to planar H2+ in strong xuv laser fields. J Chem Phys 2012; 137:094101. [PMID: 22957549 DOI: 10.1063/1.4748137] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present an efficient and accurate grid method to study the strong field dynamics of planar H(2)(+) under Born-Oppenheimer approximation. After introducing the elliptical coordinates to the planar H(2)(+), we show that the Coulomb singularities at the nuclei can be successfully overcome so that both bound and continuum states can be accurately calculated by the method of separation of variables. The time-dependent Schrödinger equation (TDSE) can be accurately solved by a two-dimensional discrete variable representation (DVR) method, where the radial coordinate is discretized with the finite-element discrete variable representation for easy parallel computation and the angular coordinate with the trigonometric DVR which can describe the periodicity in this direction. The bound states energies can be accurately calculated by the imaginary time propagation of TDSE, which agree very well with those computed by the separation of variables. We apply the TDSE to study the ionization dynamics of the planar H(2)(+) by short extreme ultra-violet (xuv) pulses, in which case the differential momentum distributions from both the length and the velocity gauge agree very well with those calculated by the lowest order perturbation theory.
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Affiliation(s)
- Qi-Cheng Ning
- State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking University, Beijing 100871, China
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Szalay V, Ádám P. Variational properties of the discrete variable representation: discrete variable representation via effective operators. J Chem Phys 2012; 137:064118. [PMID: 22897266 DOI: 10.1063/1.4740486] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A variational finite basis representation/discrete variable representation (FBR/DVR) Hamiltonian operator has been introduced. By calculating its matrix elements exactly one obtains, depending on the choice of the basis set, either a variational FBR or a variational DVR. The domain of grid points on which the FBR/DVR is variational has been shown to consist of the subsets of the set of grid points one obtains by diagonalizing commuting variational basis representations of the coordinate operators. The variational property implies that the optimal of the subsets of a fixed number of points, i.e., the subset which gives the possible highest accuracy eigenpairs, gives the DVR of the smallest trace. The symmetry properties of the variational FBR/DVR Hamiltonian operator are analyzed and methods to incorporate symmetry into FBR/DVR calculations are discussed. It is shown how the Fourier-basis FBR/DVR suitable to solving periodic systems arise within the theory presented. Numerical examples are given to illustrate the theoretical results. The use of variational effective Hamiltonian and coordinate operators has been instrumental in this study. They have been introduced in a novel way by exploiting quasi-Hermiticity.
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Affiliation(s)
- Viktor Szalay
- Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, P. O. Box 49, H-1525 Budapest, Hungary.
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46
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Van-Oanh NT, Falvo C, Calvo F, Lauvergnat D, Basire M, Gaigeot MP, Parneix P. Improving anharmonic infrared spectra using semiclassically prepared molecular dynamics simulations. Phys Chem Chem Phys 2012; 14:2381-90. [DOI: 10.1039/c2cp23101h] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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47
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XIAO YINGSHENG, POIRIER BILL. USING DISCRETE VARIABLE REPRESENTATION PATH INTEGRAL MONTE CARLO WITH METROPOLIS SAMPLING TO COMPUTE GROUND STATE WAVEFUNCTIONS. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2011. [DOI: 10.1142/s021963360700299x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The discrete variable representation (DVR) matrix dynamics formulation of the path integral Monte Carlo (PIMC) method, implemented numerically in a way that enables Metropolis sampling to be employed, is proposed as a means of computing ground state quantum wavefunctions. A key advantage of the DVR-PIMC approach is that customized marginal potentials may be employed, leading to significantly larger PIMC time step sizes, and substantial reductions in computational (CPU) effort. An additional key advantage of the present implementation is that the DVR provides a natural set of interpolant functions that can be used for accurate interpolation and extrapolation of function and tensor quantities away from predefined grid points. The new method is applied here to compute the ground state wavefunction of a model one degree-of-freedom (1 DOF) Morse oscillator system. A one-to-two order-of-magnitude reduction in CPU effort is observed, in comparison with a conventional PIMC simulation. The generalization for many DOFs is straightforward, and expected to result in even greater performance enhancement.
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Affiliation(s)
- YINGSHENG XIAO
- Department of Chemistry and Biochemistry and Department of Physics, Texas Tech University, Box 41061, Lubbock, Texas 79409-1061, USA
| | - BILL POIRIER
- Department of Chemistry and Biochemistry and Department of Physics, Texas Tech University, Box 41061, Lubbock, Texas 79409-1061, USA
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BIAN WENSHENG, POIRIER BILL. ACCURATE AND HIGHLY EFFICIENT CALCULATION OF THE O(1D)HCl VIBRATIONAL BOUND STATES, USING A COMBINATION OF METHODS. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2011. [DOI: 10.1142/s0219633603000768] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Hypochlorous acid, HOCl, is an important intermediate in the O (1D) HCl reactive system. Due in part to a large number of vibrational bound states (over 800), extremely large direct product basis sets (around 300,000) are required to compute the energy levels just below the dissociation threshold. This situation, combined with a very high density of states, results in difficult convergence for iterative methods — e.g. Lanczos requires 50,000 iterations, and filter diagonalization uses 60,000 iterations. In contrast, using new methodologies, we are able to compute the highest-lying bound states with only 271 iterations, although the CPU cost per iteration is substantially greater. Lower lying states are also computed, for a fraction of the CPU cost of the highest energy calculation.
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Affiliation(s)
- WENSHENG BIAN
- Department of Chemistry and Biochemistry, and Department of Physics, Texas Tech University, Box 41061, Lubbock, Texas 79409-1061, USA
| | - BILL POIRIER
- Department of Chemistry and Biochemistry, and Department of Physics, Texas Tech University, Box 41061, Lubbock, Texas 79409-1061, USA
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Szalay V, Lengyel K, Kovács L, Timón V, Hernández-Laguna A. Vibrations of H+(D+) in stoichiometric LiNbO3 single crystal. J Chem Phys 2011; 135:124501. [PMID: 21974529 DOI: 10.1063/1.3626839] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A first principles quantum mechanical calculation of the vibrational energy levels and transition frequencies associated with protons in stoichiometric LiNbO(3) single crystal has been carried out. The hydrogen contaminated crystal has been approximated by a model one obtains by translating a supercell, i.e., a cluster of LiNbO(3) unit cells containing a single H(+) and a Li(+) vacancy. Based on the supercell model an approximate Hamiltonian operator describing vibrations of the proton sublattice embedded in the host crystal has been derived. It is further simplified to a sum of uncoupled Hamiltonian operators corresponding to different wave vectors (ks) and each describing vibrations of a quasi-particle (quasi-proton). The three dimensional (3D) Hamiltonian operator of k=0 has been employed to calculate vibrational levels and transition frequencies. The potential energy surface (PES) entering this Hamiltonian operator has been calculated point wise on a large set of grid points by using density functional theory, and an analytical approximation to the PES has been constructed by non-parametric approximation. Then, the nuclear motion Schrödinger equation has been solved by employing the method of discrete variable representation. It has been found that the (quasi-)H(+) vibrates in a strongly anharmonic PES. Its vibrations can be described approximately as a stretching, and two orthogonal bending vibrations. The theoretically calculated transition frequencies agree within 1% with those experimentally determined, and they have allowed the assignment of one of the hitherto unassigned bands as a combination of the stretching and the bending of lower fundamental frequency.
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Affiliation(s)
- Viktor Szalay
- Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, P. O. Box 49, H-1525 Budapest, Hungary.
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McAfee JL, Poirier B. Quantum dynamics of hydrogen interacting with single-walled carbon nanotubes: multiple H-atom adsorbates. J Chem Phys 2011; 134:074308. [PMID: 21341845 DOI: 10.1063/1.3537793] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In a previous paper [J. L. McAfee and B. Poirier, J. Chem. Phys. 130, 064701 (2009)], using spin-polarized density functional theory (DFT), the authors reported a binding energy of 0.755 eV, for a single hydrogen atom adsorbed on a pristine (unrelaxed) (5,5) single-walled carbon nanotube (SWNT) substrate. A full three-dimensional (3D) potential energy surface (PES) for the SWNT-H system was also developed, and used in a quantum dynamics calculation to compute all rovibrational bound states, and associated equatorial and longitudinal adsorbate migration rates. A highly pronounced preference for the latter migration pathway at ambient temperatures was observed. In this work, we extend the aforementioned study to include multiple H-atom adsorbates. Extensive DFT calculations are performed, in order to ascertain the most relevant dynamical pathways. For two adsorbates, the SWNT-H-H system is found to exhibit highly site-specific binding, as well as long-range correlation and pronounced binding energy enhancement. The latter effect is even more pronounced in the full-hydrogenation limit, increasing the per-adsorbate binding energy to 2.6 eV. To study migration dynamics, a single-hole model is developed, for which the binding energy drops to 2.11 eV. A global 3D PES is developed for the hole migration model, using 40 radial × 18 cylindrical ab initio geometries, fit to a Fourier basis with radially dependent expansion coefficients (rms error 4.9 meV). As compared with the single-adsorbate case, the hole migration PES does not exhibit separate chemisorption and physisorption wells. The barrier to longitudinal migration is also found to be much lower. Quantum dynamics calculations for all rovibrational states are then performed (using a mixed spectral basis/phase-space optimized discrete variable representation), and used to compute longitudinal migration rates. Ramifications for the use of SWNTs as potential hydrogen storage materials are discussed.
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Affiliation(s)
- Jason L McAfee
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, USA
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