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Stachowiak M, Grabowska E, Wang XG, Carrington T, Szalewicz K, Jankowski P. Theory cracks old data: Rovibrational energy levels of orthoH 2-CO derived from experiment. Sci Adv 2024; 10:eadj8632. [PMID: 38394212 PMCID: PMC10889352 DOI: 10.1126/sciadv.adj8632] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2023] [Accepted: 01/22/2024] [Indexed: 02/25/2024]
Abstract
Measurements of rovibrational spectra of clusters provide physical insight only if spectral lines can be assigned to pairs of quantum states, and further insight is obtained if one can deduce the quantitative energy-level pattern. Both steps can be so difficult that some measured spectra remain unassigned, one example is orthoH2-CO. To extend the scope of spectroscopic insights, we propose to use theoretical information in interpretation of spectra. We first performed high accuracy, full-dimensional calculations of the orthoH2-CO spectrum, at the highest practically achievable levels of electronic structure theory and quantum nuclear dynamics. Then, an iterative, theory-guided method developed here allowed us to fully interpret the spectrum of orthoH2-CO, extending the range of van der Waals clusters for which spectroscopy can provide physical insights.
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Affiliation(s)
- Marcin Stachowiak
- Faculty of Chemistry, Nicolaus Copernicus University in Toruń, Gagarina 7, 87-100 Toruń, Poland
| | - Ewelina Grabowska
- Faculty of Chemistry, Nicolaus Copernicus University in Toruń, Gagarina 7, 87-100 Toruń, Poland
| | - 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
| | - Krzysztof Szalewicz
- Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA
| | - Piotr Jankowski
- Faculty of Chemistry, Nicolaus Copernicus University in Toruń, Gagarina 7, 87-100 Toruń, Poland
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2
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Kallullathil SD, Carrington T. Computing vibrational energy levels using a canonical polyadic tensor method with a fixed rank and a contraction tree. J Chem Phys 2023; 158:2893704. [PMID: 37259992 DOI: 10.1063/5.0149832] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2023] [Accepted: 05/10/2023] [Indexed: 06/02/2023] Open
Abstract
In this paper, we use the previously introduced Canonical Polyadic (CP)-Multiple Shift Block Inverse Iteration (MSBII) eigensolver [S. D. Kallullathil and T. Carrington, J. Chem. Phys. 155, 234105 (2021)] in conjunction with a contraction tree to compute vibrational spectra. The CP-MSBII eigensolver uses the CP format. The memory cost scales linearly with the number of coordinates. A tensor in CP format represents a wavefunction constrained to be a sum of products (SOP). An SOP wavefunction can be made more accurate by increasing the number of terms, the rank. When the required rank is large, the runtime of a calculation in CP format is long, although the memory cost is small. To make the method more efficient, we break the full problem into pieces using a contraction tree. The required rank for each of the sub-problems is small. To demonstrate the effectiveness of the ideas, we computed vibrational energy levels of acetonitrile (12-D) and ethylene oxide (15-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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Simmons J, Carrington T. Computing vibrational spectra using a new collocation method with a pruned basis and more points than basis functions: Avoiding quadrature. J Chem Phys 2023; 158:144115. [PMID: 37061500 DOI: 10.1063/5.0146703] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/17/2023] Open
Abstract
We present a new collocation method for computing the vibrational spectrum of a polyatomic molecule. Some form of quadrature or collocation is necessary when the potential energy surface does not have a simple form that simplifies the calculation of the potential matrix elements required to do a variational calculation. With quadrature, better accuracy is obtained by using more points than basis functions. To achieve the same advantage with collocation, we introduce a collocation method with more points than basis functions. Critically important, the method can be used with a large basis because it is incorporated into an iterative eigensolver. Previous collocation methods with more points than functions were incompatible with iterative eigensolvers. We test the new ideas by computing energy levels of molecules with as many as six atoms. We use pruned bases but expect the new method to be advantageous whenever one uses a basis for which it is not possible to find an accurate quadrature with about as many points as there are basis functions. For our test molecules, accurate energy levels are obtained even using non-optimal, simple, equally spaced points.
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Affiliation(s)
- Jesse Simmons
- Department of Physics, Engineering Physics and Astronomy, Queen's University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Department of Chemistry, Queen's University, Kingston, Ontario K7L 3N6, Canada
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Manzhos S, Ihara M, Carrington T. Using Collocation to Solve the Schrödinger Equation. J Chem Theory Comput 2023; 19:1641-1656. [PMID: 36974479 DOI: 10.1021/acs.jctc.2c01232] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/10/2023]
Abstract
We review the collocation approach to the solution of the Schrödinger equation and its uses in applications. Interrelations between collocation and other methods are highlighted. We also stress advantages and disadvantages of the rectangular collocation formulation. Using collocation makes it possible to use any, e.g. optimized, coordinates and basis functions, including nonintegrable basis functions, and provides a straightforward way of dealing with singularities in the potential. In addition, we stress that using collocation facilitates tuning the shape of basis functions and the placement of points, both of which can be done with machine-learning methods. Applications to electronic and vibrational problems are reviewed focusing on calculations for molecules on surfaces for which there are few variational calculations. Collocation has advantages when potential energy surfaces are unavailable, in particular, for molecule-surface systems, and for systems for which standard direct product quadrature grids, often used with variational methods, are costly.
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Affiliation(s)
- Sergei Manzhos
- School of Materials and Chemical Technology, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro-ku, Tokyo 152-8552, Japan
| | - Manabu Ihara
- School of Materials and Chemical Technology, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro-ku, Tokyo 152-8552, Japan
| | - Tucker Carrington
- Department of Chemistry, Queen’s University, 90 Bader Lane, Kingston, Ontario K7L 3N6, Canada
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Wang XG, Carrington T. Computing excited OH stretch states of water dimer in 12D using contracted intermolecular and intramolecular basis functions. J Chem Phys 2023; 158:084107. [PMID: 36859104 DOI: 10.1063/5.0139586] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
Due to the ubiquity and importance of water, water dimer has been intensively studied. Computing the (ro-)vibrational spectrum of water dimer is challenging. The potential has eight wells separated by low barriers, which makes harmonic approximations of limited utility. A variational approach is imperative, but difficult because there are 12 coupled vibrational coordinates. In this paper, we use a product contracted basis whose functions are products of intramolecular and intermolecular functions computed using an iterative eigensolver. An intermediate matrix F facilitates calculating matrix elements. Using F, it is possible to do calculations on a general potential without storing the potential on the full quadrature grid. We find that surprisingly many intermolecular functions are required. This is due to the importance of coupling between inter- and intra-molecular coordinates. The full G16 symmetry of water dimer is exploited. We calculate, for the first time, monomer excited stretch states and compare P(1) transition frequencies with their experimental counterparts. We also compare with experimental vibrational shifts and tunneling splittings. Surprisingly, we find that the largest tunneling splitting, which does not involve the interchange of the two monomers, is smaller in the asymmetric stretch excited state than in the ground state. Differences between levels we compute and those obtained with a [6+6]D adiabatic approximation [Leforestier et al. J. Chem. Phys. 137 014305 (2012)] are ∼0.6 cm-1 for states without monomer excitation, ∼4 cm-1 for monomer excited bend states, and as large as ∼10 cm-1 for monomer excited stretch states.
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Affiliation(s)
- 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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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] [What about the content of this article? (0)] [Affiliation(s)] [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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Wang XG, Carrington T. Using nondirect product Wigner D basis functions and the symmetry-adapted Lanczos algorithm to compute the ro-vibrational spectrum of CH 4-H 2O. J Chem Phys 2021; 154:124112. [PMID: 33810654 DOI: 10.1063/5.0044010] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
By doing calculations on the methane-water van der Waals complex, we demonstrate that highly converged energy levels and wavefunctions can be obtained using Wigner D basis functions and the Symmetry-Adapted Lanczos (SAL) method. The Wigner D basis is a nondirect product basis and, therefore, efficient when the kinetic energy operator has accessible singularities. The SAL method makes it possible to exploit symmetry to label energy levels and reduce the cost of the calculation, without explicitly using symmetry-adapted basis functions. Line strengths are computed, and new bands are identified. In particular, we find unusually strong transitions between states associated with the isomers of the global minimum and the secondary minimum.
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Affiliation(s)
- 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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Wodraszka R, Carrington T. A rectangular collocation multi-configuration time-dependent Hartree (MCTDH) approach with time-independent points for calculations on general potential energy surfaces. J Chem Phys 2021; 154:114107. [PMID: 33752363 DOI: 10.1063/5.0046425] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We introduce a collocation-based multi-configuration time-dependent Hartree (MCTDH) method that uses more collocation points than basis functions. We call it the rectangular collocation MCTDH (RC-MCTDH) method. It does not require that the potential be a sum of products. RC-MCTDH has the important advantage that it makes it simple to use time-independent collocation points. When using time-independent points, it is necessary to evaluate the potential energy function only once and not repeatedly during an MCTDH calculation. It is inexpensive and straightforward to use RC-MCTDH with combined modes. Using more collocation points than basis functions enables one to reduce errors in energy levels without increasing the size of the single-particle function basis. On the contrary, whenever a discrete variable representation is used, the only way to reduce the quadrature error is to increase the basis size, which then also reduces the basis-set error. We demonstrate that with RC-MCTDH and time-independent points, it is possible to calculate accurate eigenenergies of CH3 and CH4.
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Affiliation(s)
- Robert Wodraszka
- 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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Carrington T. Using collocation to study the vibrational dynamics of molecules. Spectrochim Acta A Mol Biomol Spectrosc 2021; 248:119158. [PMID: 33218875 DOI: 10.1016/j.saa.2020.119158] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2020] [Accepted: 10/26/2020] [Indexed: 06/11/2023]
Abstract
In this paper, I review collocation methods for solving the time-independent and the time-dependent Schroedinger equation. Unlike traditional variational methods, collocation methods do not require integrals and quadrature. Either collocation or quadrature is necessary if the potential does not have a special form. If the basis is a direct product of univariate bases and the quadrature grid is also a direct product, there exist variational methods that do not require quadrature approximations for potential energy matrix elements. These methods, however, do require storing, in computer memory, vectors with as many components as there are quadrature points. For this reason direct-product variational methods are poor for problems with more than five atoms. There are well established ideas for reducing the size of the basis in a variational calculation. Three such ideas are: 1) prune the direct product basis; 2) use basis functions that are products of multivariate functions; 3) optimise the basis functions (e.g. Multiconfiguration time-dependent Hartree). Reducing the basis size, however, is not enough to the make variational methods tractable because, for all three of these ideas, quadrature rears its ugly head. Collocation is an attractive alternative to variational methods.
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Affiliation(s)
- Tucker Carrington
- Department of Chemistry, Queen's University, Kingston, Ontario K7L 3N6, Canada.
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Abstract
The CO2-N2 complex is formed from two key components of Earth's atmosphere, and as such, has received some attention from both experimental and theoretical studies. On the theory side, a potential energy surface (PES) based on high level ab initio data was reported [Nasri et al., J. Chem. Phys., 2015, 142, 174301] and then used in more recently reported rovibrational calculations [Lara-Moreno et al., Phys. Chem. Chem. Phys., 2019, 21, 3550]. Accuracy of about 1 percent was achieved for calculated rotational transitions of the ground vibrational state of the complex, compared with previously reported microwave spectra. However, a very recent measurement of the geared bending mode frequency [Barclay et al., J. Chem. Phys., 2020, 153, 014303] recorded a value of 21.4 cm-1, which is wildly different from the corresponding calculated value of 45.9 cm-1. To provide some insight into this discrepancy, we have constructed a new more accurate PES, and used it to perform highly converged variational rovibrational calculations. Our new results yield a value of 21.1 cm-1 for that bending frequency, in close agreement with the experiment. We also obtain significantly improved predicted rotational transitions. Finally, we note that a very shallow well, previously reported as a distinct second isomer, is not found on our new PES, but rather a transition structure is seen in that location.
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Abstract
We review progress in neural network (NN)-based methods for the construction of interatomic potentials from discrete samples (such as ab initio energies) for applications in classical and quantum dynamics including reaction dynamics and computational spectroscopy. The main focus is on methods for building molecular potential energy surfaces (PES) in internal coordinates that explicitly include all many-body contributions, even though some of the methods we review limit the degree of coupling, due either to a desire to limit computational cost or to limited data. Explicit and direct treatment of all many-body contributions is only practical for sufficiently small molecules, which are therefore our primary focus. This includes small molecules on surfaces. We consider direct, single NN PES fitting as well as more complex methods that impose structure (such as a multibody representation) on the PES function, either through the architecture of one NN or by using multiple NNs. We show how NNs are effective in building representations with low-dimensional functions including dimensionality reduction. We consider NN-based approaches to build PESs in the sums-of-product form important for quantum dynamics, ways to treat symmetry, and issues related to sampling data distributions and the relation between PES errors and errors in observables. We highlight combinations of NNs with other ideas such as permutationally invariant polynomials or sums of environment-dependent atomic contributions, which have recently emerged as powerful tools for building highly accurate PESs for relatively large molecular and reactive systems.
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Affiliation(s)
- Sergei Manzhos
- Centre Énergie Matériaux Télécommunications, Institut National de la Recherche Scientifique, 1650, Boulevard Lionel-Boulet, Varennes, Québec City, Québec J3X 1S2, Canada
| | - Tucker Carrington
- Chemistry Department, Queen's University, Kingston Ontario K7L 3N6, Canada
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Abstract
We report the vibrational energy levels of vinyl radical (VR) that are computed with a Lanczos eigensolver and a contracted basis. Many of the levels of the two previous VR variational calculations differ significantly and differ also from those reported in this paper. We identify the source of and correct symmetry errors on the potential energy surfaces used in the previous calculations. VR has two equivalent equilibrium structures. By plotting wavefunction cuts, we show that two tunneling paths play an important role. Using the computed wavefunctions, it is possible to assign many states and thereby to determine tunneling splittings that are compared with their experimental counterparts. Our computed red shift of the hot band at 2897.23 cm-1, observed by Dong et al. [J Chem. Phys. 128, 044305 (2008)], is 4.47 cm-1, which is close to the experimental value of 4.63 cm-1.
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Affiliation(s)
- 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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Wodraszka R, Carrington T. A collocation-based multi-configuration time-dependent Hartree method using mode combination and improved relaxation. J Chem Phys 2020; 152:164117. [DOI: 10.1063/5.0006081] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Robert Wodraszka
- 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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14
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Simmons J, Wang XG, Carrington T. Computational Study of the Rovibrational Spectra of CH 2D + and CHD 2. J Phys Chem A 2019; 123:10281-10289. [PMID: 31657568 DOI: 10.1021/acs.jpca.9b09045] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In this paper, we present rovibrational energy levels of CH2D+ and CHD2+. They are computed with a large basis and the Lanczos algorithm. CH2D+ and CHD2+ are believed to play an important role in interstellar space, but so far, there are no definitive observations. The predictions of this paper should facilitate detection. For CH2D+, two CH stretch bands have been studied at high resolution. Compared to our calculated energies, the root-mean-square error is 0.08 cm-1. For CHD2+, one CH stretch band has been studied at high resolution. Compared to our calculated energies, the root-mean-square error is 0.5 cm-1. Errors are larger, for both isotopologues, for bend states. We attribute these errors to the potential energy surface. Wave function and probability distribution plots are used to make assignments. The ν1 band of CHD2+ is significantly perturbed, and according to our calculations, the 3ν3 state is closest and might be the most important perturber.
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Affiliation(s)
- Jesse Simmons
- Department of Chemistry , and Department of Physics , Queen's University , Kingston , Ontario K7L 3N6 , Canada
| | - Xiao-Gang Wang
- Department of Chemistry , and Department of Physics , Queen's University , Kingston , Ontario K7L 3N6 , Canada
| | - Tucker Carrington
- Department of Chemistry , and Department of Physics , Queen's University , Kingston , Ontario K7L 3N6 , Canada
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Ku J, Kamath A, Carrington T, Manzhos S. Machine Learning Optimization of the Collocation Point Set for Solving the Kohn–Sham Equation. J Phys Chem A 2019; 123:10631-10642. [DOI: 10.1021/acs.jpca.9b09732] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jonas Ku
- Department of Mechanical Engineering, National University of Singapore, Block EA #07-08, 9 Engineering Drive 1, Singapore 117576, Singapore
| | - Aditya Kamath
- Department of Mechanical Engineering, National University of Singapore, Block EA #07-08, 9 Engineering Drive 1, Singapore 117576, Singapore
| | - Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Sergei Manzhos
- Centre Énergie Matériaux Télécommunications, Institut National de la Recherche Scientifique, 1650, boulevard Lionel-Boulet, Varennes QC J3X 1S2, Canada
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Castro-Juárez E, Wang XG, Carrington T, Quintas-Sánchez E, Dawes R. Computational study of the ro-vibrational spectrum of CO-CO 2. J Chem Phys 2019; 151:084307. [PMID: 31470713 DOI: 10.1063/1.5119762] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An accurate ab initio ground-state intermolecular potential energy surface (PES) was determined for the CO-CO2 van der Waals dimer. The Lanczos algorithm was used to compute rovibrational energies on this PES. For both the C-in and O-in T-shaped isomers, the fundamental transition frequencies agree well with previous experimental results. We confirm that the in-plane states previously observed are geared states. In addition, we have computed and assigned many other vibrational states. The rotational constants we determine from J = 1 energy levels agree well with their experimental counterparts. Planar and out-of-plane cuts of some of the wavefunctions we compute are quite different, indicating strong coupling between the bend and torsional modes. Because the stable isomers are T-shaped, vibration along the out-of-plane coordinates is very floppy. In CO-CO2, when the molecule is out-of-plane, interconversion of the isomers is possible, but the barrier height is higher than the in-plane geared barrier height.
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Affiliation(s)
| | - 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
| | - Ernesto Quintas-Sánchez
- Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
| | - Richard Dawes
- Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
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Wang XG, Carrington T. Using quadrature and an iterative eigensolver to compute fine-structure ro-vibrational levels of Van der Waals complexes: NH(Σ−3)–He, O 2(Σg−3)–Ar, and O 2(Σg−3)–He. J Chem Phys 2019. [DOI: 10.1063/1.5110873] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Affiliation(s)
- 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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Abstract
We show that it is possible to compute vibrational energy levels of polyatomic molecules with a collocation method and a basis of products of one-dimensional harmonic oscillator functions pruned so that it does not include functions for which the indices of many of the one-dimensional functions are nonzero. Functions with many nonzero indices are coupled only by terms that depend simultaneously on many coordinates, and they are typically small. The collocation equation is derived without invoking differences of interpolation operators, which simplifies implementation of the method. This, however, requires inverting a matrix whose elements are values of the pruned basis functions at the collocation points. The collocation points are the points on a Smolyak grid whose size is equal to the size of the pruned basis set. The Smolyak grid is built from symmetrized Leja points. Because both the basis and the grid are not tensor products, the inverse is not straightforward. It can be done by using so-called hierarchical 1-D basis functions. They are defined so that the matrix whose elements are the 1-D hierarchical basis functions evaluated at points is lower triangular. We test the method by applying it to compute 100 energy levels of CH2NH with an iterative eigensolver.
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Affiliation(s)
- Emil J Zak
- 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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19
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Wodraszka R, Carrington T. A pruned collocation-based multiconfiguration time-dependent Hartree approach using a Smolyak grid for solving the Schrödinger equation with a general potential energy surface. J Chem Phys 2019; 150:154108. [DOI: 10.1063/1.5093317] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Robert Wodraszka
- 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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20
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Abstract
Using an accurate 6D water dimer potential energy surface, we compute vibration-rotation-tunnelling levels of HOD dimer, by assuming that the two monomers are rigid. HOD dimer has two isomers, a D-bonded isomer and an H-bonded isomer, and the wavefunctions of both isomers have amplitude in four wells. HOD dimer is important because, unlike the case of H2O dimer or D2O dimer, it is possible to measure the largest tunnelling splitting. Results for HOD dimer, therefore facilitate the testing of H2O dimer potentials. In J. Chem. Phys., 1995, 102, 1114, experimental results were interpreted in terms of 1D models. Experimental splittings of both isomers, obtained by fitting an energy level equation to spectra, are in good agreement with those we compute.
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Affiliation(s)
- Xiao-Gang Wang
- Chemistry Department, Queen's University, Kingston, Ontario K7L 3N6, Canada.
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21
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Manzhos S, Carrington T. Using rectangular collocation with finite difference derivatives to solve electronic Schrödinger equation. J Chem Phys 2018; 149:204105. [DOI: 10.1063/1.5052196] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sergei Manzhos
- Department of Mechanical Engineering, National University of Singapore, Block EA #07-08, 9 Engineering Drive 1, Singapore 117576, Singapore
| | - Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
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22
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Toombs E, Carrington T. Redundant coordinates in quantum mechanics. Chem Phys 2018. [DOI: 10.1016/j.chemphys.2018.07.047] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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23
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Thomas PS, Carrington T, Agarwal J, Schaefer HF. Using an iterative eigensolver and intertwined rank reduction to compute vibrational spectra of molecules with more than a dozen atoms: Uracil and naphthalene. J Chem Phys 2018; 149:064108. [DOI: 10.1063/1.5039147] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Affiliation(s)
- Phillip S. Thomas
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Jay Agarwal
- Center for Computational Chemistry, University of Georgia, Athens, Georgia 30602-0525, USA
| | - Henry F. Schaefer
- Center for Computational Chemistry, University of Georgia, Athens, Georgia 30602-0525, USA
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24
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Kamath A, Vargas-Hernández RA, Krems RV, Carrington T, Manzhos S. Neural networks vs Gaussian process regression for representing potential energy surfaces: A comparative study of fit quality and vibrational spectrum accuracy. J Chem Phys 2018; 148:241702. [DOI: 10.1063/1.5003074] [Citation(s) in RCA: 108] [Impact Index Per Article: 18.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Aditya Kamath
- Department of Mechanical Engineering, National University of Singapore, Block EA, #07-08, 9 Engineering Drive 1, Singapore 117576
| | | | - Roman V. Krems
- Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - Tucker Carrington
- Department of Chemistry, Queen’s University, Chernoff Hall, 90 Bader Lane, Kingston, Ontario K7L 3N6, Canada
| | - Sergei Manzhos
- Department of Mechanical Engineering, National University of Singapore, Block EA, #07-08, 9 Engineering Drive 1, Singapore 117576
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25
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Manzhos S, Wang X, Carrington T. A multimode-like scheme for selecting the centers of Gaussian basis functions when computing vibrational spectra. Chem Phys 2018. [DOI: 10.1016/j.chemphys.2017.10.006] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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26
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Bajaj P, Wang XG, Carrington T, Paesani F. Vibrational spectra of halide-water dimers: Insights on ion hydration from full-dimensional quantum calculations on many-body potential energy surfaces. J Chem Phys 2018; 148:102321. [DOI: 10.1063/1.5005540] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Affiliation(s)
- Pushp Bajaj
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093, USA
| | - Xiao-Gang Wang
- Chemistry Department, Queen’s University, Kingston, Ontario K7L3N6, Canada
| | - Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario K7L3N6, Canada
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, Materials Science and Engineering, and San Diego Supercomputer Center, University of California, San Diego, La Jolla, California 92093, USA
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27
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Wang XG, Carrington T. Using monomer vibrational wavefunctions to compute numerically exact (12D) rovibrational levels of water dimer. J Chem Phys 2018; 148:074108. [DOI: 10.1063/1.5020426] [Citation(s) in RCA: 41] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- 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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28
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Zhao Z, Chen J, Zhang Z, Zhang DH, Wang XG, Carrington T, Gatti F. Computing energy levels of CH4, CHD3, CH3D, and CH3F with a direct product basis and coordinates based on the methyl subsystem. J Chem Phys 2018; 148:074113. [DOI: 10.1063/1.5019323] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zhiqiang Zhao
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
| | - Jun Chen
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
- Collaborative Innovation Center of Chemistry for Energy Materials (iChEM), College of Chemistry and Chemical Engineering, Xiamen University, Siming South Road 422, 361005 Xiamen, China
| | - Zhaojun Zhang
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
| | - Dong H. Zhang
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
| | - 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
| | - Fabien Gatti
- ISMO, Institut des Sciences Moléculaires d’Orsay - UMR 8214 CNRS/Université Paris-Sud, F-91405 Orsay, France
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29
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Wodraszka R, Carrington T. A new collocation-based multi-configuration time-dependent Hartree (MCTDH) approach for solving the Schrödinger equation with a general potential energy surface. J Chem Phys 2018; 148:044115. [DOI: 10.1063/1.5018793] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Robert Wodraszka
- Department of Chemistry, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Department of Chemistry, Queen’s University, Kingston, Ontario K7L 3N6, Canada
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30
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Cybulski H, Henriksen C, Dawes R, Wang XG, Bora N, Avila G, Carrington T, Fernández B. Ab initio study of the CO–N2 complex: a new highly accurate intermolecular potential energy surface and rovibrational spectrum. Phys Chem Chem Phys 2018; 20:12624-12636. [DOI: 10.1039/c8cp01373j] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present a highly accurate ab initio intermolecular potential-energy surface and rovibrational spectrum for the CO–N2 complex.
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Affiliation(s)
- Hubert Cybulski
- Institute of Physics
- Faculty of Physics
- Astronomy and Informatics
- Nicolaus Copernicus University in Torun
- 87-100 Torun
| | - Christian Henriksen
- Department of Applied Mathematics and Computer Science
- Technical University of Denmark
- 2800 Kgs. Lyngby
- Denmark
| | - Richard Dawes
- Missouri University of Science and Technology
- Rolla
- USA
| | | | - Neha Bora
- Chemistry Department
- Queen's University
- Kingston
- Canada
| | - Gustavo Avila
- Chemistry Department
- Queen's University
- Kingston
- Canada
| | | | - Berta Fernández
- Department of Physical Chemistry
- University of Santiago de Compostela
- 15782 Santiago de Compostela
- Spain
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31
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Barclay AJ, McKellar ARW, Moazzen-Ahmadi N, Dawes R, Wang XG, Carrington T. Infrared spectrum and intermolecular potential energy surface of the CO–O2 dimer. Phys Chem Chem Phys 2018; 20:14431-14440. [DOI: 10.1039/c8cp02282h] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The spectrum of the weakly-bound radical complex CO–O2 is studied for the first time.
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Affiliation(s)
- A. J. Barclay
- Department of Physics and Astronomy
- University of Calgary
- Calgary
- Canada
| | | | - N. Moazzen-Ahmadi
- Department of Physics and Astronomy
- University of Calgary
- Calgary
- Canada
| | - Richard Dawes
- Department of Chemistry
- Missouri University of Science and Technology
- Rolla
- USA
| | - Xiao-Gang Wang
- Chemistry Department
- Queen's University
- Ontario K7L 3N6
- Canada
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32
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Affiliation(s)
- Gustavo Avila
- 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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33
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Affiliation(s)
- Gustavo Avila
- 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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34
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Thomas PS, Carrington T. An intertwined method for making low-rank, sum-of-product basis functions that makes it possible to compute vibrational spectra of molecules with more than 10 atoms. J Chem Phys 2017; 146:204110. [PMID: 28571348 PMCID: PMC5451316 DOI: 10.1063/1.4983695] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2017] [Accepted: 05/05/2017] [Indexed: 11/14/2022] Open
Abstract
We propose a method for solving the vibrational Schrödinger equation with which one can compute spectra for molecules with more than ten atoms. It uses sum-of-product (SOP) basis functions stored in a canonical polyadic tensor format and generated by evaluating matrix-vector products. By doing a sequence of partial optimizations, in each of which the factors in a SOP basis function for a single coordinate are optimized, the rank of the basis functions is reduced as matrix-vector products are computed. This is better than using an alternating least squares method to reduce the rank, as is done in the reduced-rank block power method. Partial optimization is better because it speeds up the calculation by about an order of magnitude and allows one to significantly reduce the memory cost. We demonstrate the effectiveness of the new method by computing vibrational spectra of two molecules, ethylene oxide (C2H4O) and cyclopentadiene (C5H6), with 7 and 11 atoms, respectively.
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Affiliation(s)
- Phillip S Thomas
- 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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35
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Wodraszka R, Carrington T. Systematically expanding nondirect product bases within the pruned multi-configuration time-dependent Hartree (MCTDH) method: A comparison with multi-layer MCTDH. J Chem Phys 2017; 146:194105. [PMID: 28527461 DOI: 10.1063/1.4983281] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose a pruned multi-configuration time-dependent Hartree (MCTDH) method with systematically expanding nondirect product bases and use it to solve the time-independent Schrödinger equation. No pre-determined pruning condition is required to select the basis functions. Using about 65 000 basis functions, we calculate the first 69 vibrational eigenpairs of acetonitrile, CH3CN, to an accuracy better than that achieved in a previous pruned MCTDH calculation which required more than 100 000 basis functions. In addition, we compare the new pruned MCTDH method with the established multi-layer MCTDH (ML-MCTDH) scheme and determine that although ML-MCTDH is somewhat more efficient when low or intermediate accuracy is desired, pruned MCTDH is more efficient when high accuracy is required. In our largest calculation, the vast majority of the energies have errors smaller than 0.01 cm-1.
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Affiliation(s)
- Robert Wodraszka
- Department of Chemistry, Queen's University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Department of Chemistry, Queen's University, Kingston, Ontario K7L 3N6, Canada
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36
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Affiliation(s)
- Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario
K7L 3N6, Canada
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37
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Wang XG, Carrington T. Using monomer vibrational wavefunctions as contracted basis functions to compute rovibrational levels of an H2O-atom complex in full dimensionality. J Chem Phys 2017; 146:104105. [DOI: 10.1063/1.4977179] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- 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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38
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Affiliation(s)
- Eduardo Castro
- Chemistry Department, Queen's University , Kingston, Canada
| | - Gustavo Avila
- Chemistry Department, Queen's University , Kingston, Canada
| | - Sergei Manzhos
- Department of Mechanical Engineering, National University of Singapore , Singapore, Singapore
| | - Jay Agarwal
- Center for Computational Quantum Chemistry, University of Georgia , Athens, GA, USA
| | - Henry F. Schaefer
- Center for Computational Quantum Chemistry, University of Georgia , Athens, GA, USA
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39
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Manzhos S, Carrington T. Using an internal coordinate Gaussian basis and a space-fixed Cartesian coordinate kinetic energy operator to compute a vibrational spectrum with rectangular collocation. J Chem Phys 2016; 145:224110. [DOI: 10.1063/1.4971295] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sergei Manzhos
- Department of Mechanical Engineering, National University of Singapore, Block EA #07-08, 9 Engineering Drive 1, 117576 Singapore
| | - Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
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40
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Leclerc A, Thomas PS, Carrington T. Comparison of different eigensolvers for calculating vibrational spectra using low-rank, sum-of-product basis functions. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1249980] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Arnaud Leclerc
- Université de Lorraine , UMR CNRS 7565 SRSMC, Metz, France
| | - Phillip S. Thomas
- Chemistry Department, Queen's University , Kingston, Ontario, Canada
| | - Tucker Carrington
- Chemistry Department, Queen's University , Kingston, Ontario, Canada
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41
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Brown J, Carrington T. Using an expanding nondirect product harmonic basis with an iterative eigensolver to compute vibrational energy levels with as many as seven atoms. J Chem Phys 2016; 145:144104. [DOI: 10.1063/1.4963916] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- James Brown
- 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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42
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Wodraszka R, Carrington T. Using a pruned, nondirect product basis in conjunction with the multi-configuration time-dependent Hartree (MCTDH) method. J Chem Phys 2016; 145:044110. [DOI: 10.1063/1.4959228] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Robert Wodraszka
- Department of Chemistry, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Department of Chemistry, Queen’s University, Kingston, Ontario K7L 3N6, Canada
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43
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Brown J, Carrington T. Assessing the utility of phase-space-localized basis functions: Exploiting direct product structure and a new basis function selection procedure. J Chem Phys 2016; 144:244115. [DOI: 10.1063/1.4954721] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- James Brown
- 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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44
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Affiliation(s)
- 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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45
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Affiliation(s)
- Steve Ndengué
- Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
| | - Richard Dawes
- Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
| | - 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
| | - Zhigang Sun
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China and Center for Advanced Chemical Physics and 2011 Frontier Center for Quantum Science and Technology, University of Science and Technology of China, 96 Jinzhai Road, Hefei 230026, China
| | - Hua Guo
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, USA
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46
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47
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Thomas PS, Carrington T. Using Nested Contractions and a Hierarchical Tensor Format To Compute Vibrational Spectra of Molecules with Seven Atoms. J Phys Chem A 2015; 119:13074-91. [DOI: 10.1021/acs.jpca.5b10015] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Phillip S. Thomas
- 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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48
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Avila G, Carrington T. A multi-dimensional Smolyak collocation method in curvilinear coordinates for computing vibrational spectra. J Chem Phys 2015; 143:214108. [DOI: 10.1063/1.4936294] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gustavo Avila
- 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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49
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Manzhos S, Carrington T, Laverdure L, Mosey N. Computing the Anharmonic Vibrational Spectrum of UF6 in 15 Dimensions with an Optimized Basis Set and Rectangular Collocation. J Phys Chem A 2015; 119:9557-67. [DOI: 10.1021/acs.jpca.5b07627] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Sergei Manzhos
- Department
of Mechanical Engineering, National University of Singapore, Block EA
#07-08, 9 Engineering Drive 1, Singapore 117576
| | - Tucker Carrington
- Department of Chemistry, Queen’s University, Chernoff Hall, 90 Bader Lane, Kingston, ON, Canada K7L 3N6
| | - Laura Laverdure
- Department of Chemistry, Queen’s University, Chernoff Hall, 90 Bader Lane, Kingston, ON, Canada K7L 3N6
| | - Nicholas Mosey
- Department of Chemistry, Queen’s University, Chernoff Hall, 90 Bader Lane, Kingston, ON, Canada K7L 3N6
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50
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Affiliation(s)
- Gustavo Avila
- 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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