The Experts below are selected from a list of 153 Experts worldwide ranked by ideXlab platform
Markus Schröder - One of the best experts on this subject based on the ideXlab platform.
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Calculation of Global, High-Dimensional Potential Energy Surface Fits in sum-of-products form Using Monte-Carlo Methods
High Performance Computing in Science and Engineering ' 17, 2020Co-Authors: Markus Schröder, Hans-dieter MeyerAbstract:We have implemented a Monte-Carlo version of the well-known potfit algorithm. With potfit one can transform high-dimensional potential energy surfaces sampled on a grid into a sum-of-products form. More precisely, an fth order general tensor can be transformed into Tucker form. Using Monte-Carlo methods we avoid high-dimensional integrals that are needed to obtain optimal fits and simultaneously introduce importance sampling. The Tucker form is well suited for further use within the Heidelberg MCTDH package for solving the time-dependent as well as the time-independent Schrodinger equation of molecular systems. We demonstrate the power of the Monte-Carlo potfit algorithm by globally fitting the 15-dimensional potential energy surface of the Zundel cation (H5O\(_2^+\)) and subsequently calculating the lowest vibrational eigenstates of the molecule.
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Transforming high-dimensional potential energy surfaces into a canonical polyadic decomposition using Monte Carlo methods
Journal of Chemical Physics, 2020Co-Authors: Markus SchröderAbstract:A Monte Carlo method is proposed for transforming high-dimensional potential energy surfaces evaluated on discrete grid points into a sum-of-products form, more precisely into a Canonical Polyadic Decomposition form. To this end, a modified existing ansatz based on the alternating least squares method is used, in which numerically exact integrals are replaced with Monte Carlo integrals. This largely reduces the numerical cost by avoiding the evaluation of the potential on all grid points and allows the treatment of surfaces with many degrees of freedom. Calculations on the 15D potential of the protonated water dimer (Zundel cation) in a sum-of-products form are presented and compared to the results obtained in a previous work [M. Schroder and H.-D. Meyer, J. Chem. Phys. 147, 064105 (2017)], where a sum-of-products form of the potential was obtained in the Tucker format.A Monte Carlo method is proposed for transforming high-dimensional potential energy surfaces evaluated on discrete grid points into a sum-of-products form, more precisely into a Canonical Polyadic Decomposition form. To this end, a modified existing ansatz based on the alternating least squares method is used, in which numerically exact integrals are replaced with Monte Carlo integrals. This largely reduces the numerical cost by avoiding the evaluation of the potential on all grid points and allows the treatment of surfaces with many degrees of freedom. Calculations on the 15D potential of the protonated water dimer (Zundel cation) in a sum-of-products form are presented and compared to the results obtained in a previous work [M. Schroder and H.-D. Meyer, J. Chem. Phys. 147, 064105 (2017)], where a sum-of-products form of the potential was obtained in the Tucker format.
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Transforming high-dimensional potential energy surfaces into sum-of-products form using Monte Carlo methods.
Journal of Chemical Physics, 2017Co-Authors: Markus Schröder, Hans-dieter MeyerAbstract:We propose a Monte Carlo method, “Monte Carlo Potfit,” for transforming high-dimensional potential energy surfaces evaluated on discrete grid points into a sum-of-products form, more precisely into a Tucker form. To this end we use a variational ansatz in which we replace numerically exact integrals with Monte Carlo integrals. This largely reduces the numerical cost by avoiding the evaluation of the potential on all grid points and allows a treatment of surfaces up to 15-18 degrees of freedom. We furthermore show that the error made with this ansatz can be controlled and vanishes in certain limits. We present calculations on the potential of HFCO to demonstrate the features of the algorithm. To demonstrate the power of the method, we transformed a 15D potential of the protonated water dimer (Zundel cation) in a sum-of-products form and calculated the ground and lowest 26 vibrationally excited states of the Zundel cation with the multi-configuration time-dependent Hartree method.
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Ab initio potential energy and dipole moment surfaces for CS2: determination of molecular vibrational energies.
Journal of Physical Chemistry A, 2012Co-Authors: Ekadashi Pradhan, Markus Schröder, José-luis Carreón-macedo, Javier Cuervo, Alex BrownAbstract:The ground state potential energy and dipole moment surfaces for CS2 have been determined at the CASPT2/C:cc-pVTZ,S:aug-cc-pV(T+d)Z level of theory. The potential energy surface has been fit to a sum-of-products form using the neural network method with exponential neurons. A generic interface between neural network potential energy surface fitting and the Heidelberg MCTDH software package is demonstrated. The potential energy surface has also been fit using the potfit procedure in MCTDH. For fits to the low-energy regions of the potential, the neural network method requires fewer parameters than potfit to achieve high accuracy; global fits are comparable between the two methods. Using these potential energy surfaces, the vibrational energies have been computed for the four most abundant CS2 isotopomers. These results are compared to experimental and previous theoretical data. The current potential energy surfaces are shown to accurately reproduce the low-lying vibrational energies within a few wavenumber...
Hans-dieter Meyer - One of the best experts on this subject based on the ideXlab platform.
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Calculation of Global, High-Dimensional Potential Energy Surface Fits in sum-of-products form Using Monte-Carlo Methods
High Performance Computing in Science and Engineering ' 17, 2020Co-Authors: Markus Schröder, Hans-dieter MeyerAbstract:We have implemented a Monte-Carlo version of the well-known potfit algorithm. With potfit one can transform high-dimensional potential energy surfaces sampled on a grid into a sum-of-products form. More precisely, an fth order general tensor can be transformed into Tucker form. Using Monte-Carlo methods we avoid high-dimensional integrals that are needed to obtain optimal fits and simultaneously introduce importance sampling. The Tucker form is well suited for further use within the Heidelberg MCTDH package for solving the time-dependent as well as the time-independent Schrodinger equation of molecular systems. We demonstrate the power of the Monte-Carlo potfit algorithm by globally fitting the 15-dimensional potential energy surface of the Zundel cation (H5O\(_2^+\)) and subsequently calculating the lowest vibrational eigenstates of the molecule.
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Transforming high-dimensional potential energy surfaces into sum-of-products form using Monte Carlo methods.
Journal of Chemical Physics, 2017Co-Authors: Markus Schröder, Hans-dieter MeyerAbstract:We propose a Monte Carlo method, “Monte Carlo Potfit,” for transforming high-dimensional potential energy surfaces evaluated on discrete grid points into a sum-of-products form, more precisely into a Tucker form. To this end we use a variational ansatz in which we replace numerically exact integrals with Monte Carlo integrals. This largely reduces the numerical cost by avoiding the evaluation of the potential on all grid points and allows a treatment of surfaces up to 15-18 degrees of freedom. We furthermore show that the error made with this ansatz can be controlled and vanishes in certain limits. We present calculations on the potential of HFCO to demonstrate the features of the algorithm. To demonstrate the power of the method, we transformed a 15D potential of the protonated water dimer (Zundel cation) in a sum-of-products form and calculated the ground and lowest 26 vibrationally excited states of the Zundel cation with the multi-configuration time-dependent Hartree method.
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MCTDH study on vibrational states of the CO/Cu(100) system.
Journal of Chemical Physics, 2013Co-Authors: Qingyong Meng, Hans-dieter MeyerAbstract:Full (6D) and reduced (4D and 2D) dimensional multiconfiguration time-dependent Hartree (MCTDH) calculations for the vibrational fundamentals and overtones of the CO/Cu(100) system are carried out using the recently reported [R. Marquardt, F. Cuvelier, R. A. Olsen, E. J. Baerends, J. C. Tremblay, and P. Saalfrank, J. Chem. Phys. 132, 074108 (2010)] SAP potential energy surface (PES). To efficiently perform MCTDH calculations with the Heidelberg package (http://mctdh.uni-hd.de), the SAP-PES is first refitted in a sum-of-products form. Then extensive MCTDH calculations are carefully performed including thorough convergence checks to ensure the accuracy of our results. Full dimensional improved-relaxations and/or block-improved-relaxations are then performed to obtain vibrational ground and excited states of CO/Cu(100). In addition, we investigate the frustrated rotation (R mode) and vertical CO–Cu stretch (S mode), as well as C–O stretch, using a 4D Hamiltonian, which includes the distance between CO and th...
Alex Brown - One of the best experts on this subject based on the ideXlab platform.
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The lowest lying excited electronic states for HFCO including a potential energy surface for S1 in sum-of-products form
Molecular Physics, 2019Co-Authors: Ekadashi Pradhan, Alex BrownAbstract:The vertical excitation energies to the S1 and T1 states for HFCO were determined using multi-reference (CASSCF, CASPT2, CASPT2-F12, MRCI, and MRCI-F12) and the single reference EOM-CCSD methods. T...
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A ground state potential energy surface for HONO based on a neural network with exponential fitting functions
Physical Chemistry Chemical Physics, 2017Co-Authors: Ekadashi Pradhan, Alex BrownAbstract:The minimum energy structures, i.e., trans-HONO, cis-HONO, HNO2, and OH + NO, as well as the corresponding transition states, i.e., TStrans↔cis, TS1,2H-shift, and TS1,3H-shift, on the ground state potential energy surface (PES) of HONO have been characterized at the CCSD(T)-F12/cc-pVTZ-F12 level of theory. Using the same level of theory, a six-dimensional (6D) PES, encompassing the trans- and cis-isomers as well as the associated transition state, is fit in a sum-of-products form using neural network exponential fitting functions. A second PES is developed based on ab initio data from CCSD(T) computations extrapolated to the complete basis set (CBS) limit. The PES fits, based on 90 neurons, are accurate (RMSEs ≈ 10 cm−1) up to 10 000 cm−1 above the energy minimum. The PESs are validated by computing vibrational energies using block improved relaxation with the multi configuration time dependent Hartree (MCTDH) approach. The vibrational frequencies obtained on the PESs are compared to available experimental measurements, previous theoretical computations based on a CCSD(T)/cc-pVQZ(-g functions) PES, and anharmonic frequencies at the MP2/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ levels of theory obtained using second-order vibrational perturbation theory. The results suggest that these are the best available PESs for HONO, and thus, should be suitable for a variety of dynamics studies, including quantum dynamics with MCTDH where the sum-of-products form can be exploited for computational efficiency.
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Fitting potential energy surfaces to sum-of-products form with neural networks using exponential neurons
Journal of Theoretical and Computational Chemistry, 2017Co-Authors: Alex Brown, Ekadashi PradhanAbstract:In this paper, the use of the neural network (NN) method with exponential neurons for directly fitting ab initio data to generate potential energy surfaces (PESs) in sum-of-product form will be discussed. The utility of the approach will be highlighted using fits of CS2, HFCO, and HONO ground state PESs based upon high-level ab initio data. Using a generic interface between the neural network PES fitting, which is performed in MATLAB, and the Heidelberg multi-configuration time-dependent Hartree (MCTDH) software package, the PESs have been tested via comparison of vibrational energies to experimental measurements. The review demonstrates the potential of the PES fitting method, combined with MCTDH, to tackle high-dimensional quantum dynamics problems.
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Vibrational energies for HFCO using a neural network sum of exponentials potential energy surface
Journal of Chemical Physics, 2016Co-Authors: Ekadashi Pradhan, Alex BrownAbstract:A six-dimensional potential energy surface (PES) for formyl fluoride (HFCO) is fit in a sum-of-products form using neural network exponential fitting functions. The ab initio data upon which the fit is based were computed at the explicitly correlated coupled cluster with single, double, and perturbative triple excitations [CCSD(T)-F12]/cc-pVTZ-F12 level of theory. The PES fit is accurate (RMSE = 10 cm−1) up to 10 000 cm−1 above the zero point energy and covers most of the experimentally measured IR data. The PES is validated by computing vibrational energies for both HFCO and deuterated formyl fluoride (DFCO) using block improved relaxation with the multi-configuration time dependent Hartree approach. The frequencies of the fundamental modes, and all other vibrational states up to 5000 cm−1 above the zero-point energy, are more accurate than those obtained from the previous MP2-based PES. The vibrational frequencies obtained on the PES are compared to anharmonic frequencies at the MP2/aug-cc-pVTZ and CCSD...
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Ab initio potential energy and dipole moment surfaces for CS2: determination of molecular vibrational energies.
Journal of Physical Chemistry A, 2012Co-Authors: Ekadashi Pradhan, Markus Schröder, José-luis Carreón-macedo, Javier Cuervo, Alex BrownAbstract:The ground state potential energy and dipole moment surfaces for CS2 have been determined at the CASPT2/C:cc-pVTZ,S:aug-cc-pV(T+d)Z level of theory. The potential energy surface has been fit to a sum-of-products form using the neural network method with exponential neurons. A generic interface between neural network potential energy surface fitting and the Heidelberg MCTDH software package is demonstrated. The potential energy surface has also been fit using the potfit procedure in MCTDH. For fits to the low-energy regions of the potential, the neural network method requires fewer parameters than potfit to achieve high accuracy; global fits are comparable between the two methods. Using these potential energy surfaces, the vibrational energies have been computed for the four most abundant CS2 isotopomers. These results are compared to experimental and previous theoretical data. The current potential energy surfaces are shown to accurately reproduce the low-lying vibrational energies within a few wavenumber...
P.r. Menon - One of the best experts on this subject based on the ideXlab platform.
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On redundant path delay faults in synchronous sequential circuits
IEEE Transactions on Computers, 2000Co-Authors: R. Tekumalla, P.r. MenonAbstract:A path delay fault in a sequential circuit will affect circuit timing only if it can be activated during normal operation of the circuit. Since vector pairs that can be applied to the next-state logic of a nonscan sequential circuit are restricted by the available state transitions, some faults may be impossible to activate. Such faults are redundant and need not be tested. In this paper, we present a method of identifying redundant path delay faults in the next-state logic implemented in a two-level sum of products form and extend it to multilevel realizations. Experimental results on MCNC'91 benchmarks show that large fractions of faults in most of the MCNC'91 benchmarks are redundant.
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VLSI Design - Identifying redundant path delay faults in sequential circuits
Proceedings of 9th International Conference on VLSI Design, 1996Co-Authors: R. Tekumalla, P.r. MenonAbstract:We define a class of faults called redundant path delay faults in sequential circuits, which do not effect circuit delay. A method of identifying redundant path delay faults in the next state logic implemented in a two-level sum-of-products form is presented. The method is extended to circuits with general multi-level realization of the next state logic. Experimental results for MCNC'91 benchmark circuits converted into a restricted factored form are also given.
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Identifying redundant path delay faults in sequential circuits
Proceedings of 9th International Conference on VLSI Design, 1996Co-Authors: R. Tekumalla, P.r. MenonAbstract:We define a class of faults called redundant path delay faults in sequential circuits, which do not effect circuit delay. A method of identifying redundant path delay faults in the next state logic implemented in a two-level sum-of-products form is presented. The method is extended to circuits with general multi-level realization of the next state logic. Experimental results for MCNC'91 benchmark circuits converted into a restricted factored form are also given.
Ekadashi Pradhan - One of the best experts on this subject based on the ideXlab platform.
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The lowest lying excited electronic states for HFCO including a potential energy surface for S1 in sum-of-products form
Molecular Physics, 2019Co-Authors: Ekadashi Pradhan, Alex BrownAbstract:The vertical excitation energies to the S1 and T1 states for HFCO were determined using multi-reference (CASSCF, CASPT2, CASPT2-F12, MRCI, and MRCI-F12) and the single reference EOM-CCSD methods. T...
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A ground state potential energy surface for HONO based on a neural network with exponential fitting functions
Physical Chemistry Chemical Physics, 2017Co-Authors: Ekadashi Pradhan, Alex BrownAbstract:The minimum energy structures, i.e., trans-HONO, cis-HONO, HNO2, and OH + NO, as well as the corresponding transition states, i.e., TStrans↔cis, TS1,2H-shift, and TS1,3H-shift, on the ground state potential energy surface (PES) of HONO have been characterized at the CCSD(T)-F12/cc-pVTZ-F12 level of theory. Using the same level of theory, a six-dimensional (6D) PES, encompassing the trans- and cis-isomers as well as the associated transition state, is fit in a sum-of-products form using neural network exponential fitting functions. A second PES is developed based on ab initio data from CCSD(T) computations extrapolated to the complete basis set (CBS) limit. The PES fits, based on 90 neurons, are accurate (RMSEs ≈ 10 cm−1) up to 10 000 cm−1 above the energy minimum. The PESs are validated by computing vibrational energies using block improved relaxation with the multi configuration time dependent Hartree (MCTDH) approach. The vibrational frequencies obtained on the PESs are compared to available experimental measurements, previous theoretical computations based on a CCSD(T)/cc-pVQZ(-g functions) PES, and anharmonic frequencies at the MP2/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ levels of theory obtained using second-order vibrational perturbation theory. The results suggest that these are the best available PESs for HONO, and thus, should be suitable for a variety of dynamics studies, including quantum dynamics with MCTDH where the sum-of-products form can be exploited for computational efficiency.
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Fitting potential energy surfaces to sum-of-products form with neural networks using exponential neurons
Journal of Theoretical and Computational Chemistry, 2017Co-Authors: Alex Brown, Ekadashi PradhanAbstract:In this paper, the use of the neural network (NN) method with exponential neurons for directly fitting ab initio data to generate potential energy surfaces (PESs) in sum-of-product form will be discussed. The utility of the approach will be highlighted using fits of CS2, HFCO, and HONO ground state PESs based upon high-level ab initio data. Using a generic interface between the neural network PES fitting, which is performed in MATLAB, and the Heidelberg multi-configuration time-dependent Hartree (MCTDH) software package, the PESs have been tested via comparison of vibrational energies to experimental measurements. The review demonstrates the potential of the PES fitting method, combined with MCTDH, to tackle high-dimensional quantum dynamics problems.
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Vibrational energies for HFCO using a neural network sum of exponentials potential energy surface
Journal of Chemical Physics, 2016Co-Authors: Ekadashi Pradhan, Alex BrownAbstract:A six-dimensional potential energy surface (PES) for formyl fluoride (HFCO) is fit in a sum-of-products form using neural network exponential fitting functions. The ab initio data upon which the fit is based were computed at the explicitly correlated coupled cluster with single, double, and perturbative triple excitations [CCSD(T)-F12]/cc-pVTZ-F12 level of theory. The PES fit is accurate (RMSE = 10 cm−1) up to 10 000 cm−1 above the zero point energy and covers most of the experimentally measured IR data. The PES is validated by computing vibrational energies for both HFCO and deuterated formyl fluoride (DFCO) using block improved relaxation with the multi-configuration time dependent Hartree approach. The frequencies of the fundamental modes, and all other vibrational states up to 5000 cm−1 above the zero-point energy, are more accurate than those obtained from the previous MP2-based PES. The vibrational frequencies obtained on the PES are compared to anharmonic frequencies at the MP2/aug-cc-pVTZ and CCSD...
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Ab initio potential energy and dipole moment surfaces for CS2: determination of molecular vibrational energies.
Journal of Physical Chemistry A, 2012Co-Authors: Ekadashi Pradhan, Markus Schröder, José-luis Carreón-macedo, Javier Cuervo, Alex BrownAbstract:The ground state potential energy and dipole moment surfaces for CS2 have been determined at the CASPT2/C:cc-pVTZ,S:aug-cc-pV(T+d)Z level of theory. The potential energy surface has been fit to a sum-of-products form using the neural network method with exponential neurons. A generic interface between neural network potential energy surface fitting and the Heidelberg MCTDH software package is demonstrated. The potential energy surface has also been fit using the potfit procedure in MCTDH. For fits to the low-energy regions of the potential, the neural network method requires fewer parameters than potfit to achieve high accuracy; global fits are comparable between the two methods. Using these potential energy surfaces, the vibrational energies have been computed for the four most abundant CS2 isotopomers. These results are compared to experimental and previous theoretical data. The current potential energy surfaces are shown to accurately reproduce the low-lying vibrational energies within a few wavenumber...
