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Haggag O, Levinsky N, Ruhman S. Coherent intramolecular excimer formation in solid [2,2]‐Paracyclophane: Time resolved springing of a molecular “trap”. CHEMPHOTOCHEM 2022. [DOI: 10.1002/cptc.202200181] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Omer Haggag
- The Hebrew University of Jerusalem - Givat Ram Campus: Hebrew University of Jerusalem - Edmond J Safra Campus Chemistry 9190401 ISRAEL
| | - Noam Levinsky
- The Hebrew University of Jerusalem - Givat Ram Campus: Hebrew University of Jerusalem - Edmond J Safra Campus Chemistry 9190401 ISRAEL
| | - Sanford Ruhman
- Hebrew University of Jerusalem Chemistry Givat-Ram 9190401 Jerusalem ISRAEL
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2
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Kallullathil SD, Carrington T. Computing vibrational energy levels by solving linear equations using a tensor method with an imposed rank. J Chem Phys 2021; 155:234105. [PMID: 34937358 DOI: 10.1063/5.0075412] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Present day computers do not have enough memory to store the high-dimensional tensors required when using a direct product basis to compute vibrational energy levels of a polyatomic molecule with more than about five atoms. One way to deal with this problem is to represent tensors using a tensor format. In this paper, we use the canonical polyadic (CP) format. Energy levels are computed by building a basis from vectors obtained by solving linear equations. The method can be thought of as a CP realization of a block inverse iteration method with multiple shifts. The CP rank of the tensors is fixed, and the linear equations are solved with an method. There is no need for rank reduction and no need for orthogonalization, and tensors with a rank larger than the fixed rank used to solve the linear equations are never generated. The ideas are tested by computing vibrational energy levels of a 64-D bilinearly coupled model Hamiltonian and of acetonitrile (12-D).
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Affiliation(s)
| | - Tucker Carrington
- Chemistry Department, Queen's University, Kingston, Ontario K7L 3N6, Canada
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3
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Gabas F, Conte R, Ceotto M. On-the-Fly ab Initio Semiclassical Calculation of Glycine Vibrational Spectrum. J Chem Theory Comput 2017; 13:2378-2388. [PMID: 28489368 PMCID: PMC5472367 DOI: 10.1021/acs.jctc.6b01018] [Citation(s) in RCA: 49] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
We
present an on-the-fly ab initio semiclassical study of vibrational
energy levels of glycine, calculated by Fourier transform of the wavepacket
correlation function. It is based on a multiple coherent states approach
integrated with monodromy matrix regularization for chaotic dynamics.
All four lowest-energy glycine conformers are investigated by means
of single-trajectory semiclassical spectra obtained upon classical
evolution of on-the-fly trajectories with harmonic zero-point energy.
For the most stable conformer I, direct dynamics trajectories are
also run for each vibrational mode with energy equal to the first
harmonic excitation. An analysis of trajectories evolved up to 50 000
atomic time units demonstrates that, in this time span, conformers
II and III can be considered as isolated species, while conformers
I and IV show a pretty facile interconversion. Therefore, previous
perturbative studies based on the assumption of isolated conformers
are often reliable but might be not completely appropriate in the
case of conformer IV and conformer I for which interconversion occurs
promptly.
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Affiliation(s)
- Fabio Gabas
- Dipartimento di Chimica, Università degli Studi di Milano , via Golgi 19, 20133 Milano, Italy
| | - Riccardo Conte
- Dipartimento di Chimica, Università degli Studi di Milano , via Golgi 19, 20133 Milano, Italy
| | - Michele Ceotto
- Dipartimento di Chimica, Università degli Studi di Milano , via Golgi 19, 20133 Milano, Italy
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Kraack JP, Wand A, Buckup T, Motzkus M, Ruhman S. Mapping multidimensional excited state dynamics using pump-impulsive-vibrational-spectroscopy and pump-degenerate-four-wave-mixing. Phys Chem Chem Phys 2013; 15:14487-501. [DOI: 10.1039/c3cp50871d] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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GUO HUA, CHEN RONGQING, XIE DAIQIAN. CALCULATION OF TRANSITION AMPLITUDES WITH A SINGLE LANCZOS PROPAGATION. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2012. [DOI: 10.1142/s0219633602000129] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We review in this article a recently proposed energy-global method that is capable of calculating the entire transition amplitude matrix with a single Lanczos propagation. This method requires neither explicit computation nor storage of the eigenfunctions, rendering it extremely memory efficient. Procedures are proposed to handle situations where "spurious" eigenvalues aggregate around true eigenvalues due to round-off errors. This method is amenable to both real-symmetric and complex-symmetric Hamiltonians. Applications to molecular spectra and reactive scattering are presented. Its relationships with other methods are also discussed.
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Affiliation(s)
- HUA GUO
- Department of Chemistry, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - RONGQING CHEN
- Department of Chemistry, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - DAIQIAN XIE
- Department of Chemistry and Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing, Jiangsu, 210093, P. R. China
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MANDELSHTAM VLADIMIRA, NEUMAIER ARNOLD. FURTHER GENERALIZATION AND NUMERICAL IMPLEMENTATION OF PSEUDO-TIME SCHRÖDINGER EQUATIONS FOR QUANTUM SCATTERING CALCULATIONS. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2012. [DOI: 10.1142/s0219633602000142] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We review and further develop the recently introduced numerical approach [Phys. Rev. Lett. 86, 5031, (2001)] for scattering calculations based on a so called pseudo-time Schrödinger equation, which is in turn a modification of the damped Chebyshev polynomial expansion scheme [J. Chem. Phys. 103, 2903, (1995)]. The method utilizes a special energy-dependent form for the absorbing potential in the time-independent Schrödinger equation, in which the complex energy spectrum is mapped inside the unit disk Ek → uk, where uk are the eigenvalues of some explicitly known sparse matrix U. Most importantly for the numerical implementation, all the physical eigenvalues uk are the extreme eigenvalues of U (i.e. |uk| ≈ 1 for resonances and |uk| = 1 for the bound states), which allows one to extract these eigenvalues very efficiently by harmonic inversion of a pseudo-time autocorrelation function y(t) = ϕ T Ut ϕ using the filter diagonalization method. The computation of y(t) up to time t = 2T requires only T sparse real matrix-vector multiplications. We describe and compare different schemes, effectively corresponding to different choices of the energy-dependent absorbing potential, and test them numerically by calculating resonances of the HCO molecule. Our numerical tests suggest an optimal scheme that provide accurate estimates for most resonance states using a single autocorrelation function.
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Affiliation(s)
| | - ARNOLD NEUMAIER
- Institut für Mathematik, Universität Wien Strudlhofgasse 4, A-1090 Wien, Austria
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MANDELSHTAM VLADIMIRA. ON HARMONIC INVERSION OF CROSS-CORRELATION FUNCTIONS BY THE FILTER DIAGONALIZATION METHOD. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2011. [DOI: 10.1142/s0219633603000641] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Harmonic inversion of Chebyshev correlation and cross-correlation functions by the filter diagonalization method (FDM) is one of the most efficient ways to accurately compute the complex spectra of low dimensional quantum molecular systems. This explains the growing popularity of the FDM in the past several years. Some of its most attractive features are the predictable convergence properties and the lack of adjusting parameters. These issues however are often misunderstood and mystified. We discuss the questions relevant to the optimal choices for the FDM parameters, such as the window size and the number of basis functions. We also demonstrate that the cross-correlation approach (using multiple initial states) is significantly more effective than the conventional autocorrelation approach (single initial state) for the common case of a non-uniform eigenvalue distribution.
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Bowman JM, Carrington T, Meyer HD. Variational quantum approaches for computing vibrational energies of polyatomic molecules. Mol Phys 2008. [DOI: 10.1080/00268970802258609] [Citation(s) in RCA: 303] [Impact Index Per Article: 18.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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9
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Khorasani RR, Dumont RS. Non-normal Lanczos methods for quantum scattering. J Chem Phys 2008; 129:034110. [PMID: 18647019 DOI: 10.1063/1.2940733] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
This article presents a new complex absorbing potential (CAP) block Lanczos method for computing scattering eigenfunctions and reaction probabilities. The method reduces the problem of computing energy eigenfunctions to solving two energy dependent systems of equations. An energy independent block Lanczos factorization casts the system into a block tridiagonal form, which can be solved very efficiently for all energies. We show that CAP-Lanczos methods exhibit instability due to the non-normality of CAP Hamiltonians and may break down for some systems. The instability is not due to loss of orthogonality but to non-normality of the Hamiltonian matrix. While use of a Woods-Saxon exponential CAP-as opposed to a polynomial CAP-reduced non-normality, it did not always ensure convergence. Our results indicate that the Arnoldi algorithm is more robust for non-normal systems and less prone to break down. An Arnoldi version of our method is applied to a nonadiabatic tunneling Hamiltonian with excellent results, while the Lanczos algorithm breaks down for this system.
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Affiliation(s)
- Reza Rajaie Khorasani
- Department of Chemistry, McMaster University, 1280 Main St. W. Hamilton, Ontario L8S 4M1, Canada
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Khorasani RR, Dumont RS. Long time wave packet dynamics from energy eigenfunctions: nonuniform energy resolution via adaptive bisection fast Fourier transformation. J Chem Phys 2007; 127:184107. [PMID: 18020630 DOI: 10.1063/1.2780155] [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
This article presents a new approach to long time wave packet propagation. The methodology relies on energy domain calculations and an on-the-surface straightforward energy to time transformation to provide wave packet time evolution. The adaptive bisection fast Fourier transform method employs selective bisection to create a multiresolution energy grid, dense near resonances. To implement fast Fourier transforms on the nonuniform grid, the uniform grid corresponding to the finest resolution is reconstructed using an iterative interpolation process. By proper choice of the energy grid points, we are able to produce results equivalent to grids of the finest resolution, with far fewer grid points. We have seen savings 20-fold in the number of eigenfunction calculations. Since the method requires computation of energy eigenfunctions, it is best suited for situations where many wave packet propagations are of interest at a fixed small set of points--as in time dependent flux computations. The fast Fourier transform (FFT) algorithm used is an adaptation of the Danielson-Lanczos FFT algorithm to sparse input data. A specific advantage of the adaptive bisection FFT is the possibility of long time wave packet propagations showing slow resonant decay. A method is discussed for obtaining resonance parameters by least squares fitting of energy domain data. The key innovation presented is the means of separating out the smooth background from the sharp resonance structure.
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Affiliation(s)
- Reza Rajaie Khorasani
- Department of Chemistry, McMaster University, 1280 Main Street W., Hamilton, Ontario L8S 4M1, Canada
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11
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Karlsson HO. Reduced-Order Modeling, Error Estimation, and the Role of the Start-Vector: The Recursive Residue Generation Method Revisited. J Phys Chem A 2007; 111:10263-8. [PMID: 17663534 DOI: 10.1021/jp072647c] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The recursive residue generation method (RRGM) [Wyatt, R. E. Adv. Chem. Phys. 1989, 73, 231] is re-derived using the formalism of reduced-order modeling [Bai, Z. Appl. Numerical Math. 2002, 43, 9]. A stopping criteria for the RRGM recursions is proposed, on the basis of an expression for an upper bound to the absolute error [Bai, Z.; Ye, Q. Electron. Trans. Numerical Anal. 1998, 7, 1]. It is further pointed out that, in general, the start-vector has a negligible effect on the convergence of the RRGM.
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Affiliation(s)
- Hans O Karlsson
- Quantum Chemistry, Department of Physical and Analytical Chemistry, Uppsala University Box 518, SE-751 20 Uppsala, Sweden
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12
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Recursive Solutions to Large Eigenproblems in Molecular Spectroscopy and Reaction Dynamics. REVIEWS IN COMPUTATIONAL CHEMISTRY 2007. [DOI: 10.1002/9780470189078.ch7] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/21/2023]
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Gelman D, Katz G, Kosloff R, Ratner MA. Dissipative dynamics of a system passing through a conical intersection: Ultrafast pump-probe observables. J Chem Phys 2005; 123:134112. [PMID: 16223280 DOI: 10.1063/1.2032968] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Abstract
The dynamics of a system incorporating a conical intersection, in the presence of a dissipative environment, is studied with the purpose of identifying observable ultrafast spectroscopic signatures. A model system consisting of two vibronically coupled electronic states with two nuclear degrees of freedom is constructed. Dissipation is treated by two different methods, Lindblad semigroup formalism and the surrogate Hamiltonian approach. Pump-probe experimental expectation values such as transient emission and transient absorption are calculated and compared to the adiabatic and diabatic population transfer. The ultrafast population transfer reflecting the conical intersection is not mirrored in transient absorption measurements such as the recovery of the bleach. Emission from the excited state can be suppressed on the ultrafast time scale, but the existence of a conical intersection is only one of the possible mechanisms that can provide ultrafast damping of emission.
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Affiliation(s)
- David Gelman
- Fritz Haber Research Center for Molecular Dynamics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel.
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15
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Zhang H, Smith SC. Symmetry contaminations in reactive scattering through long-lived collision complexes. Chem Phys 2005. [DOI: 10.1016/j.chemphys.2004.05.030] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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16
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Shalashilin DV, Child MS. The phase space CCS approach to quantum and semiclassical molecular dynamics for high-dimensional systems. Chem Phys 2004. [DOI: 10.1016/j.chemphys.2004.06.013] [Citation(s) in RCA: 116] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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17
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Vijay A, Kouri DJ, Hoffman DK. Scattering and Bound States: A Lorentzian Function-Based Spectral Filter Approach. J Phys Chem A 2004. [DOI: 10.1021/jp040356n] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Amrendra Vijay
- Department of Chemistry, University of Houston, Houston, Texas 77204-5003
| | - Donald J. Kouri
- Departments of Chemistry, Mathematics, and Physics, University of Houston, Houston, Texas 77204-5003
| | - David K. Hoffman
- Department of Chemistry and Ames Laboratory, Iowa State University, Ames, Iowa 50011
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Main J, Atilgan E, Taylor HS, Wunner G. Classical, semiclassical, and quantum investigations of the four-sphere scattering system. Phys Rev E 2004; 69:056227. [PMID: 15244924 DOI: 10.1103/physreve.69.056227] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2003] [Indexed: 11/07/2022]
Abstract
A genuinely three-dimensional system, viz. the hyperbolic four-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and scaling properties of the computations are discussed by comparisons to the two-dimensional three-disk system. While in systems with few degrees of freedom modern quantum calculations are, in general, numerically more efficient than semiclassical methods, this situation can be reversed with increasing dimension of the problem. For the four-sphere system with large separations between the spheres, we demonstrate the superiority of semiclassical versus quantum calculations, i.e., semiclassical resonances can easily be obtained even in energy regions which are unattainable with the currently available quantum techniques. The four-sphere system with touching spheres is a challenging problem for both quantum and semiclassical techniques. Here, semiclassical resonances are obtained via harmonic inversion of a cross-correlated periodic orbit signal.
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Affiliation(s)
- Jörg Main
- Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
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Giese K, Kuhn O. Semiclassical tunneling splittings from short time dynamics: Herman-Kluk-propagation and harmonic inversion. J Chem Phys 2004; 120:4107-18. [PMID: 15268577 DOI: 10.1063/1.1643734] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate a recently proposed method [J. Chem. Phys. 108, 9206 (1998)] to obtain tunneling splittings from short time cross-correlation matrices that were propagated according to the semiclassical propagator of Herman and Kluk. The energy levels were extracted by harmonic inversion of the cross-correlation matrix using the filter diagonalization technique. The aim of this study is twofold: First, the short time behavior of the Herman-Kluk-propagator and the meaning of using cross-correlation matrices rather than autocorrelation functions is addressed. Numerical examples are given for one- and two-dimensional model potentials. Second, the performance of the method is investigated for a system with considerable anharmonicity and coupling. Here the proton transfer in 3,7-dichlorotropolone is considered using an ab initio reaction surface Hamiltonian approach. For this example also the extension to more dimensions is critically discussed.
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Affiliation(s)
- Kai Giese
- Institut fur Chemie, Physikalische und Theoretische Chemie, Freie Universitat Berlin, Takustr. 3, D-14195 Berlin, Germany
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Shalashilin DV, Child MS. Nine-dimensional quantum molecular dynamics simulation of intramolecular vibrational energy redistribution in the CHD3 molecule with the help of coupled coherent states. J Chem Phys 2003. [DOI: 10.1063/1.1584663] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
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Lüchow A, Neuhauser D, Ka J, Baer R, Chen J, Mandelshtam VA. Computing Energy Levels by Inversion of Imaginary-Time Cross-Correlation Functions. J Phys Chem A 2003. [DOI: 10.1021/jp034381p] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Arne Lüchow
- Institut für Theoretische Chemie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany, Chemistry Department, University of California, Los Angeles, California 90095, Chemistry Department, Hebrew University of Jerusalem, Givat Ram, Jerusalem, Israel, and Chemistry Department, University of California, Irvine, California 92697
| | - Daniel Neuhauser
- Institut für Theoretische Chemie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany, Chemistry Department, University of California, Los Angeles, California 90095, Chemistry Department, Hebrew University of Jerusalem, Givat Ram, Jerusalem, Israel, and Chemistry Department, University of California, Irvine, California 92697
| | - Jaejin Ka
- Institut für Theoretische Chemie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany, Chemistry Department, University of California, Los Angeles, California 90095, Chemistry Department, Hebrew University of Jerusalem, Givat Ram, Jerusalem, Israel, and Chemistry Department, University of California, Irvine, California 92697
| | - Roi Baer
- Institut für Theoretische Chemie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany, Chemistry Department, University of California, Los Angeles, California 90095, Chemistry Department, Hebrew University of Jerusalem, Givat Ram, Jerusalem, Israel, and Chemistry Department, University of California, Irvine, California 92697
| | - Jianhan Chen
- Institut für Theoretische Chemie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany, Chemistry Department, University of California, Los Angeles, California 90095, Chemistry Department, Hebrew University of Jerusalem, Givat Ram, Jerusalem, Israel, and Chemistry Department, University of California, Irvine, California 92697
| | - Vladimir A. Mandelshtam
- Institut für Theoretische Chemie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany, Chemistry Department, University of California, Los Angeles, California 90095, Chemistry Department, Hebrew University of Jerusalem, Givat Ram, Jerusalem, Israel, and Chemistry Department, University of California, Irvine, California 92697
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22
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Karlsson HO, Holmgren S. Cross correlation functions Cnm(E) via Lanczos algorithms without diagonalization. J Chem Phys 2002. [DOI: 10.1063/1.1515767] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Florido R, Martín-González JM, Gomez Llorente JM. Locating Pollicott-Ruelle resonances in chaotic dynamical systems: a class of numerical schemes. PHYSICAL REVIEW E 2002; 66:046208. [PMID: 12443300 DOI: 10.1103/physreve.66.046208] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2002] [Indexed: 11/06/2022]
Abstract
A class of numerical methods to determine Pollicott-Ruelle resonances in chaotic dynamical systems is proposed. This is achieved by relating some existing procedures that make use of the Padé approximants, and interpolating exponentials to both the memory function techniques used in the theory of relaxation and the filter diagonalization method used in the harmonic inversion of time correlation functions. This relationship leads to a theoretical framework in which all these methods become equivalent and which allows for new and improved numerical schemes.
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Affiliation(s)
- R Florido
- Departamento de Física Fundamental II, Universidad de La Laguna, 38205 Tenerife, Spain
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Ying Lin S, Guo H. Full-dimensional quantum wave packet study of rotationally inelastic transitions in H2+H2 collision. J Chem Phys 2002. [DOI: 10.1063/1.1500731] [Citation(s) in RCA: 90] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Xu D, Xie D, Guo H. Theoretical study of predissociation dynamics of HCN/DCN in their first absorption bands. J Chem Phys 2002. [DOI: 10.1063/1.1480874] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Katz G, Zeiri Y, Kosloff R. Three-dimensional quantum time-dependent study of the photodissociation dynamics of Na⋯FH/D. Chem Phys Lett 2002. [DOI: 10.1016/s0009-2614(02)00741-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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27
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Koch CP, Klüner T, Kosloff R. A complete quantum description of an ultrafast pump-probe charge transfer event in condensed phase. J Chem Phys 2002. [DOI: 10.1063/1.1450124] [Citation(s) in RCA: 65] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
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28
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Katz G, Yamashita K, Zeiri Y, Kosloff R. The Fourier method for tri-atomic systems in the search for the optimal coordinate system. J Chem Phys 2002. [DOI: 10.1063/1.1448285] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
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29
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Burant JC, Batista VS. Real time path integrals using the Herman–Kluk propagator. J Chem Phys 2002. [DOI: 10.1063/1.1436306] [Citation(s) in RCA: 51] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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Zhang H, Smith SC. Efficient time-independent wave packet scattering calculations within a Lanczos subspace: H+O2 (J=0) state-to-state reaction probabilities. J Chem Phys 2002. [DOI: 10.1063/1.1429951] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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Li S, Li G, Guo H. A single Lanczos propagation method for calculating transition amplitudes. III. S-matrix elements with a complex-symmetric Hamiltonian. J Chem Phys 2001. [DOI: 10.1063/1.1413984] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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32
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Shalashilin DV, Child MS. Multidimensional quantum propagation with the help of coupled coherent states. J Chem Phys 2001. [DOI: 10.1063/1.1394939] [Citation(s) in RCA: 98] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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33
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Shalashilin DV, Child MS. Description of tunneling with the help of coupled frozen Gaussians. J Chem Phys 2001. [DOI: 10.1063/1.1367392] [Citation(s) in RCA: 48] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Neumaier A, Mandelshtam VA. Pseudotime Schrödinger equation with absorbing potential for quantum scattering calculations. PHYSICAL REVIEW LETTERS 2001; 86:5031-5034. [PMID: 11384413 DOI: 10.1103/physrevlett.86.5031] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2001] [Indexed: 05/23/2023]
Abstract
The Schrödinger equation (Hpsi) (r) = [E+u(E)W(r)]psi(r) with an energy-dependent complex absorbing potential -u(E)W(r), associated with a scattering system, can be reduced for a special choice of u(E) to a harmonic inversion problem of a discrete pseudotime correlation function y(t) = phi(T)U(t)phi. An efficient formula for Green's function matrix elements is also derived. Since the exact propagation up to time 2t can be done with only approximately t real matrix-vector products, this gives an unprecedently efficient scheme for accurate calculations of quantum spectra for possibly very large systems.
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Affiliation(s)
- A Neumaier
- Institut für Mathematik, Universität Wien Strudlhofgasse 4, A-1090 Wien, Austria.
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Gershgoren E, Vala J, Kosloff R, Ruhman S. Impulsive Control of Ground Surface Dynamics of I3- in Solution. J Phys Chem A 2001. [DOI: 10.1021/jp0039518] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Erez Gershgoren
- Institute of Chemistry, The Hebrew University, Jerusalem, 91904 Israel
| | - J. Vala
- Institute of Chemistry, The Hebrew University, Jerusalem, 91904 Israel
| | - R. Kosloff
- Institute of Chemistry, The Hebrew University, Jerusalem, 91904 Israel
| | - S. Ruhman
- Institute of Chemistry, The Hebrew University, Jerusalem, 91904 Israel
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36
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Mandelshtam VA. The Regularized Resolvent Transform for Quantum Dynamics Calculations,. J Phys Chem A 2001. [DOI: 10.1021/jp0036689] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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37
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Affiliation(s)
- Hans O. Karlsson
- Department of Quantum Chemistry, Uppsala University, Box 518, S-751 20 Uppsala, Sweden
| | - Osvaldo Goscinski
- Department of Quantum Chemistry, Uppsala University, Box 518, S-751 20 Uppsala, Sweden
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Sukiasyan S, Meyer HD. On the Effect of Initial Rotation on Reactivity. A Multi-Configuration Time-Dependent Hartree (MCTDH) Wave Packet Propagation Study on the H + D2 and D + H2 Reactive Scattering Systems. J Phys Chem A 2001. [DOI: 10.1021/jp003767m] [Citation(s) in RCA: 65] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- S. Sukiasyan
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
| | - H.-D. Meyer
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
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Beck MH, Meyer HD. Efficiently computing bound-state spectra: A hybrid approach of the multi-configuration time-dependent Hartree and filter-diagonalization methods. J Chem Phys 2001. [DOI: 10.1063/1.1334618] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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40
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Tannor DJ, Garashchuk S. Semiclassical calculation of chemical reaction dynamics via wavepacket correlation functions. Annu Rev Phys Chem 2000; 51:553-600. [PMID: 11031293 DOI: 10.1146/annurev.physchem.51.1.553] [Citation(s) in RCA: 142] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Calculation of chemical reaction dynamics is central to theoretical chemistry. The majority of calculations use either classical mechanics, which is computationally inexpensive but misses quantum effects, such as tunneling and interference, or quantum mechanics, which is computationally expensive and often conceptually opaque. An appealing middle ground is the use of semiclassical mechanics. Indeed, since the early 1970s there has been great interest in using semiclassical methods to calculate reaction probabilities. However, despite the elegance of classical S-matrix theory, numerical results on even the simplest reactive systems remained out of reach. Recently, with advances both in correlation function formulations of reactive scattering as well as in semiclassical methods, it has become possible for the first time to calculate reaction probabilities semiclassically. The correlation function methods are contrasted with recent flux-based methods, which, although providing somewhat more compact expressions for the cumulative reactive probability, are less compatible with semiclassical implementation.
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Affiliation(s)
- D J Tannor
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
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41
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Anderson SM, Ka J, Felker PM, Neuhuaser D. Semi-classical versus exact eigenvalues of He–benzene using cross-correlation filter-diagonalization. Chem Phys Lett 2000. [DOI: 10.1016/s0009-2614(00)00934-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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42
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Santra R, Breidbach J, Zobeley J, Cederbaum LS. Parallel filter diagonalization: A novel method to resolve quantum states in dense spectral regions. J Chem Phys 2000. [DOI: 10.1063/1.481545] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
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43
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Chen J, Mandelshtam VA. Multiscale filter diagonalization method for spectral analysis of noisy data with nonlocalized features. J Chem Phys 2000. [DOI: 10.1063/1.481005] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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44
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Špirko V, Piecuch P, Bludský O. Bound and quasibound states of the Na⋯FH van der Waals molecule. J Chem Phys 2000. [DOI: 10.1063/1.480632] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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45
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Chen R, Guo H. A single Lanczos propagation method for calculating transition amplitudes. J Chem Phys 1999. [DOI: 10.1063/1.480347] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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46
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Main J, Weibert K, Mandelshtam VA, Wunner G. Semiclassical spectra and diagonal matrix elements by harmonic inversion of cross-correlated periodic orbit sums. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:1639-42. [PMID: 11969926 DOI: 10.1103/physreve.60.1639] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/1998] [Indexed: 04/18/2023]
Abstract
Semiclassical spectra weighted with products of diagonal matrix elements of operators A(alpha), i.e., g(alphaalpha')(E)= summation operator(n)<nA(alpha)n><nA(alpha')n>/(E-E(n)), are obtained by harmonic inversion of a cross-correlation signal constructed of classical periodic orbits. The method provides highly resolved semiclassical spectra even in situations of nearly degenerate states, and opens the way to reducing the required signal lengths to shorter than the Heisenberg time. This implies a significant reduction of the number of orbits required for periodic orbit quantization by harmonic inversion.
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Affiliation(s)
- J Main
- Institut für Theoretische Physik I, Ruhr-Universität Bochum, D-44780 Bochum, Germany
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Chen R, Guo H. Efficient calculation of matrix elements in low storage filter diagonalization. J Chem Phys 1999. [DOI: 10.1063/1.479327] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
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48
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Chen R, Guo H. A low-storage filter-diagonalization method to calculate expectation values of operators non-commutative with the Hamiltonian: Vibrational assignment of HOCl. Chem Phys Lett 1999. [DOI: 10.1016/s0009-2614(99)00582-5] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Skokov S, Bowman JM. Variation of the resonance width of HOCl(6νOH) with total angular momentum: Comparison between ab initio theory and experiment. J Chem Phys 1999. [DOI: 10.1063/1.478953] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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