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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] [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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2
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Manzhos S, Ihara M. The loss of the property of locality of the kernel in high-dimensional Gaussian process regression on the example of the fitting of molecular potential energy surfaces. J Chem Phys 2023; 158:044111. [PMID: 36725493 DOI: 10.1063/5.0136156] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
Kernel-based methods, including Gaussian process regression (GPR) and generally kernel ridge regression, have been finding increasing use in computational chemistry, including the fitting of potential energy surfaces and density functionals in high-dimensional feature spaces. Kernels of the Matern family, such as Gaussian-like kernels (basis functions), are often used which allow imparting to them the meaning of covariance functions and formulating GPR as an estimator of the mean of a Gaussian distribution. The notion of locality of the kernel is critical for this interpretation. It is also critical to the formulation of multi-zeta type basis functions widely used in computational chemistry. We show, on the example of fitting of molecular potential energy surfaces of increasing dimensionality, the practical disappearance of the property of locality of a Gaussian-like kernel in high dimensionality. We also formulate a multi-zeta approach to the kernel and show that it significantly improves the quality of regression in low dimensionality but loses any advantage in high dimensionality, which is attributed to the loss of the property of locality.
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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
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Graubner T, Karttunen AJ, Kraus F. A Computational Study on Closed-Shell Molecular Hexafluorides MF 6 (M=S, Se, Te, Po, Xe, Rn, Cr, Mo, W, U) - Molecular Structure, Anharmonic Frequency Calculations, and Prediction of the NdF 6 Molecule. Chemphyschem 2023; 24:e202200903. [PMID: 36688413 DOI: 10.1002/cphc.202200903] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2022] [Revised: 01/23/2023] [Accepted: 01/23/2023] [Indexed: 01/24/2023]
Abstract
Quantum chemical methods were used to study the molecular structure and anharmonic IR spectra of the experimentally known closed-shell molecular hexafluorides MF6 (M=S, Se, Te, Xe, Mo, W, U). First, the molecular structures and harmonic frequencies were investigated using Density Functional Theory (DFT) with all-electron basis sets and explicitly considering the influence of spin-orbit coupling. Second, anharmonic frequencies and IR intensities were calculated with the CCSD(T) coupled cluster method and compared, where available, with IR spectra recorded by us. These comparisons showed satisfactory results. The anharmonic IR spectra provide means for identifying experimentally too little studied or unknown MF6 molecules with M=Cr, Po, Rn. To the best of our knowledge, we predict the NdF6 molecule for the first time and show it to be a true local minimum on the potential energy surface. We used intrinsic bond orbital (IBO) analyses to characterize the bonding situation in comparison with the UF6 molecule.
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Affiliation(s)
- Tim Graubner
- Fluorchemie, Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032, Marburg, Germany
| | - Antti J Karttunen
- Department of Chemistry and Materials Science, Aalto University, 00076, Espoo, Finland
| | - Florian Kraus
- Fluorchemie, Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Straße 4, 35032, Marburg, Germany
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Ghosh A, Jonnalgadda PN. Ab initio and DFT benchmark study for the calculations of isotopic shifts of fundamental frequencies for 2,3-dihydropyran. Struct Chem 2022. [DOI: 10.1007/s11224-021-01829-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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5
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Manzhos S, Sasaki E, Ihara M. Easy representation of multivariate functions with low-dimensional terms via Gaussian process regression kernel design: applications to machine learning of potential energy surfaces and kinetic energy densities from sparse data. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2022. [DOI: 10.1088/2632-2153/ac4949] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Abstract
We show that Gaussian process regression (GPR) allows representing multivariate functions with low-dimensional terms via kernel design. When using a kernel built with high-dimensional model representation (HDMR), one obtains a similar type of representation as the previously proposed HDMR-GPR scheme while being faster and simpler to use. We tested the approach on cases where highly accurate machine learning is required from sparse data by fitting potential energy surfaces and kinetic energy densities.
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Manzhos S, Ihara M. Computational vibrational spectroscopy of molecule-surface interactions: what is still difficult and what can be done about it. Phys Chem Chem Phys 2022; 24:15158-15172. [DOI: 10.1039/d2cp01389d] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Interactions of molecules with solid surfaces are responsible for key functionalities for a range of currently actively pursued technologies, including heterogeneous catalysis for synthesis or decomposition of molecules, sensitization, surface...
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Pototschnig JV, Papadopoulos A, Lyakh DI, Repisky M, Halbert L, Severo Pereira Gomes A, Jensen HJA, Visscher L. Implementation of Relativistic Coupled Cluster Theory for Massively Parallel GPU-Accelerated Computing Architectures. J Chem Theory Comput 2021; 17:5509-5529. [PMID: 34370471 PMCID: PMC8444343 DOI: 10.1021/acs.jctc.1c00260] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
In this paper, we report reimplementation of the core algorithms of relativistic coupled cluster theory aimed at modern heterogeneous high-performance computational infrastructures. The code is designed for parallel execution on many compute nodes with optional GPU coprocessing, accomplished via the new ExaTENSOR back end. The resulting ExaCorr module is primarily intended for calculations of molecules with one or more heavy elements, as relativistic effects on the electronic structure are included from the outset. In the current work, we thereby focus on exact two-component methods and demonstrate the accuracy and performance of the software. The module can be used as a stand-alone program requiring a set of molecular orbital coefficients as the starting point, but it is also interfaced to the DIRAC program that can be used to generate these. We therefore also briefly discuss an improvement of the parallel computing aspects of the relativistic self-consistent field algorithm of the DIRAC program.
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Affiliation(s)
- Johann V Pototschnig
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, de Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Anastasios Papadopoulos
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, de Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Dmitry I Lyakh
- National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Michal Repisky
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Loïc Halbert
- Universite de Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers, Atomes et Molecules, F-59000 Lille, France
| | - André Severo Pereira Gomes
- Universite de Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers, Atomes et Molecules, F-59000 Lille, France
| | - Hans Jørgen Aa Jensen
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
| | - Lucas Visscher
- Department of Chemistry and Pharmaceutical Sciences, Faculty of Science, Vrije Universiteit Amsterdam, de Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
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Rey M, Chizhmakova IS, Nikitin AV, Tyuterev VG. Towards a complete elucidation of the ro-vibrational band structure in the SF 6 infrared spectrum from full quantum-mechanical calculations. Phys Chem Chem Phys 2021; 23:12115-12126. [PMID: 34032236 DOI: 10.1039/d0cp05727d] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
The first accurate and complete theoretical room-temperature rotationally resolved spectra in the range 300-3000 cm-1 are reported for the three most abundant isotopologues (32SF6, 33SF6 and 34SF6) of the sulfur hexafluoride molecule. The literature reports that SF6 is widely used as a prototype molecule for studying the multi-photon excitation processes with powerful lasers in the infrared range. On the other hand, SF6 is an important greenhouse molecule with a very long lifetime in the atmosphere. Because of relatively low vibrational frequencies, the hot bands of this molecule contribute significantly to the absorption infrared spectra even at room temperature. This makes the calculation of complete rovibrational line lists required for fully converged opacity modeling extremely demanding. In order to reduce the computational costs, symmetry was exploited at all stages of the first global variational nuclear motion calculations by means of irreducible tensor operators. More than 2600 new vibrational band centers were predicted using our empirically refined ab initio potential energy surface. Highly excited rotational states were calculated up to J = 121, resulting in 6 billion transitions computed from an ab initio dipole moment surface and distributed over more than 500 cold and hot bands. The final line lists are made available through the TheoReTS information system (http://theorets.univ-reims.fr, http://theorets.tsu.ru). For the first time, the major (ro)vibrational band structures in the wavenumber range corresponding to the strongest absorption in the infra-red are completely elucidated for a seven-atom molecule, providing excellent agreement with the observed spectral patterns. It is shown that the obtained results are more complete than all available line lists, permitting reliable modelling of the temperature dependence of the molecular opacity.
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Affiliation(s)
- Michaël Rey
- Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 7331, BP 1039, F-51687, Reims Cedex 2, France.
| | - Iana S Chizhmakova
- Laboratory of Quantum Mechanics of Molecules and Radiative Processes, Tomsk State University, 36 Lenin Avenue, 634050 Tomsk, Russia
| | - Andrei V Nikitin
- V.E. Zuev Institute of Atmospheric Optics, Russian Academy of Sciences, 1, Akademichesky Avenue, 634055 Tomsk, Russian Federation
| | - Vladimir G Tyuterev
- Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 7331, BP 1039, F-51687, Reims Cedex 2, France. and Laboratory of Quantum Mechanics of Molecules and Radiative Processes, Tomsk State University, 36 Lenin Avenue, 634050 Tomsk, Russia
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Carrington T. Using collocation to study the vibrational dynamics of molecules. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 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] [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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Manzhos S, Carrington T. Neural Network Potential Energy Surfaces for Small Molecules and Reactions. Chem Rev 2020; 121:10187-10217. [PMID: 33021368 DOI: 10.1021/acs.chemrev.0c00665] [Citation(s) in RCA: 119] [Impact Index Per Article: 29.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
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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Boussaidi MA, Ren O, Voytsekhovsky D, Manzhos S. Random Sampling High Dimensional Model Representation Gaussian Process Regression (RS-HDMR-GPR) for Multivariate Function Representation: Application to Molecular Potential Energy Surfaces. J Phys Chem A 2020; 124:7598-7607. [DOI: 10.1021/acs.jpca.0c05935] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Mohamed Ali Boussaidi
- Centre Énergie Matériaux Télécommunications, Institut National de la Recherche Scientifique, 1650 boulevard Lionel-Boulet, Varennes QC J3X 1S2, Canada
- Ecole Nationale d’Ingénieurs de Tunis, Rue Béchir Salem Belkhiria Campus universitaire, BP 37, 1002, Le Bélvédère, Tunis, Tunisia
| | - Owen Ren
- Centre Énergie Matériaux Télécommunications, Institut National de la Recherche Scientifique, 1650 boulevard Lionel-Boulet, Varennes QC J3X 1S2, Canada
- Purefacts Inc., 48 Yonge Street, Suite 400, Toronto, ON M5E 1G6, 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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12
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Nikitin AV, Rey M, Chizhmakova IS, Tyuterev VG. First Full-Dimensional Potential Energy and Dipole Moment Surfaces of SF6. J Phys Chem A 2020; 124:7014-7023. [DOI: 10.1021/acs.jpca.0c02733] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Andrei V. Nikitin
- V.E. Zuev Institute of Atmospheric Optics, Russian Academy of Sciences, 1, Akademichesky Avenue, 634055 Tomsk, Russian Federation
| | - Michael Rey
- Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 6089, Université de Reims, U.F.R. Sciences, B.P. 1039, 51687 Reims Cedex 2, France
| | - Iana S. Chizhmakova
- Institute of Monitoring of Climatic and Ecological Systems, Russian Academy of Sciences, 10/3, Academichesky Avenue, 634055 Tomsk, Russian Federation
- QUAMER Laboratory, Tomsk State University, 36 Lenin Avenue, 634050 Tomsk, Russian Federation
| | - Vladimir G. Tyuterev
- Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 6089, Université de Reims, U.F.R. Sciences, B.P. 1039, 51687 Reims Cedex 2, France
- QUAMER Laboratory, Tomsk State University, 36 Lenin Avenue, 634050 Tomsk, Russian Federation
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Tian T, Xu T, Kirk SR, Rongde IT, Tan YB, Manzhos S, Shigeta Y, Jenkins S. Intramolecular mode coupling of the isotopomers of water: a non-scalar charge density-derived perspective. Phys Chem Chem Phys 2020; 22:2509-2520. [DOI: 10.1039/c9cp05879f] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
Left: The BCP trajectories T(s) for H2O for the bending (Q1) mode, the axes labels of the trajectory T(s). The green spheres correspond to the bond critical point (BCPs). Right: The corresponding T(s) for H2O for the symmetric-stretch (Q2) mode.
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Affiliation(s)
- Tian Tian
- Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research and Key Laboratory of Resource National and Local Joint Engineering Laboratory for New Petro-chemical Materials and Fine Utilization of Resources
- College of Chemistry and Chemical Engineering
- Hunan Normal University
- Changsha
- China
| | - Tianlv Xu
- Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research and Key Laboratory of Resource National and Local Joint Engineering Laboratory for New Petro-chemical Materials and Fine Utilization of Resources
- College of Chemistry and Chemical Engineering
- Hunan Normal University
- Changsha
- China
| | - Steven R. Kirk
- Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research and Key Laboratory of Resource National and Local Joint Engineering Laboratory for New Petro-chemical Materials and Fine Utilization of Resources
- College of Chemistry and Chemical Engineering
- Hunan Normal University
- Changsha
- China
| | - Ian Tay Rongde
- Department of Mechanical Engineering
- National University of Singapore
- Singapore
| | - Yong Boon Tan
- Department of Mechanical Engineering
- National University of Singapore
- Singapore
| | - Sergei Manzhos
- Centre Énergie Matériaux Télécommunications
- Institut National de la Recherche Scientifique
- 1650 boulevard Lionel-Boulet
- Varennes QC J3X1S2
- Canada
| | - Yasuteru Shigeta
- Center for Computational Sciences
- University of Tsukuba
- Tsukuba 305-8577
- Japan
| | - Samantha Jenkins
- Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research and Key Laboratory of Resource National and Local Joint Engineering Laboratory for New Petro-chemical Materials and Fine Utilization of Resources
- College of Chemistry and Chemical Engineering
- Hunan Normal University
- Changsha
- China
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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] [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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Tan YB, Tay IR, Loy LY, Aw KF, Ong ZL, Manzhos S. A Scheme for Ultrasensitive Detection of Molecules with Vibrational Spectroscopy in Combination with Signal Processing. Molecules 2019; 24:molecules24040776. [PMID: 30795561 PMCID: PMC6413196 DOI: 10.3390/molecules24040776] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2018] [Revised: 02/04/2019] [Accepted: 02/18/2019] [Indexed: 11/16/2022] Open
Abstract
We show that combining vibrational spectroscopy with signal processing can result in a scheme for ultrasensitive detection of molecules. We consider the vibrational spectrum as a signal on the energy axis and apply a matched filter on that axis. On the example of a nerve agent molecule, we show that this allows detection of a molecule by its vibrational spectrum, even when the recorded spectrum is completely buried in noise when conventional spectroscopic detection is impossible. Detection is predicted to be possible with signal-to-noise ratios in the recorded spectra as low as 0.1. We have studied the importance of the spectral range used for detection as well as of the quality of the computed spectrum used to program the filter, specifically, the role of anharmonicity, of the exchange correlation functional, and of the basis set. The use of the full spectral range rather than of a narrow spectral window with key vibrations is shown to be advantageous, as well as accounting for anharmonicity.
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Affiliation(s)
- Yong Boon Tan
- Raffles Institution, One Raffles Institution Lane, Singapore 575954, Singapore.
| | - Ian Rongde Tay
- Raffles Institution, One Raffles Institution Lane, Singapore 575954, Singapore.
| | - Liang Yi Loy
- NUS High School of Mathematics and Science, 20 Clementi Avenue 1, Singapore 129957, Singapore.
| | - Ke Fun Aw
- NUS High School of Mathematics and Science, 20 Clementi Avenue 1, Singapore 129957, Singapore.
| | - Zhi Li Ong
- NUS High School of Mathematics and Science, 20 Clementi Avenue 1, Singapore 129957, Singapore.
| | - Sergei Manzhos
- Department of Mechanical Engineering, National University of Singapore, Block EA #07-08, 9 Engineering Drive 1, Singapore 117576, Singapore.
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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] [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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Inverse Multiquadratic Functions as the Basis for the Rectangular Collocation Method to Solve the Vibrational Schrödinger Equation. MATHEMATICS 2018. [DOI: 10.3390/math6110253] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
We explore the use of inverse multiquadratic (IMQ) functions as basis functions when solving the vibrational Schrödinger equation with the rectangular collocation method. The quality of the vibrational spectrum of formaldehyde (in six dimensions) is compared to that obtained using Gaussian basis functions when using different numbers of width-optimized IMQ functions. The effects of the ratio of the number of collocation points to the number of basis functions and of the choice of the IMQ exponent are studied. We show that the IMQ basis can be used with parameters where the IMQ function is not integrable. We find that the quality of the spectrum with IMQ basis functions is somewhat lower that that with a Gaussian basis when the basis size is large, and for a range of IMQ exponents. The IMQ functions are; however, advantageous when a small number of functions is used or with a small number of collocation points (e.g., when using square collocation).
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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] [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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Carrington T. Perspective: Computing (ro-)vibrational spectra of molecules with more than four atoms. J Chem Phys 2017; 146:120902. [DOI: 10.1063/1.4979117] [Citation(s) in RCA: 67] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario
K7L 3N6, Canada
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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] [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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Wu F, Ren Y, Bian W. The hydrogen tunneling splitting in malonaldehyde: A full-dimensional time-independent quantum mechanical method. J Chem Phys 2016; 145:074309. [DOI: 10.1063/1.4960789] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Feng Wu
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yinghui Ren
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Wensheng Bian
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
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