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Sharma M, Banik S, Roy TK. Performance of Effective Harmonic Oscillator Approach for the Calculations of Vibrational Transition Energies of Large Molecules. J Phys Chem A 2024; 128:5762-5776. [PMID: 38979981 DOI: 10.1021/acs.jpca.4c01583] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/10/2024]
Abstract
The accuracy and performance of the effective harmonic oscillator approximation for the description of anharmonic vibrational structure calculations are tested for large molecular systems and compared with experimental values along with vibrational self-consistent field and second-order perturbation theories. The effective harmonic oscillator approach is an effective single-particle approximation where the variational parameters are the centroids and widths of the multidimensional Gaussian product functions posited as the vibrational wave functions. A comprehensive calculation for 849 transitions that include the fundamentals, two and three quanta overtone transitions, and several combination bands of three polyaromatic hydrocarbons and one DNA nucleobase with a total of 231 normal modes are assessed. A comparison of EHO results with the experimental values is done for the polyaromatic hydrocarbons, and a close agreement is found between the two results. It also offers anharmonic eigenstates and eigenfunctions that are nearly identical with vibrational self-consistent field theory. An extensive analysis on the resultant wave functions of the excited states is performed. The overall root-mean-square deviation (RMSD) between these two methods for 849 transitions understudy is only about 8.3 cm-1, suggesting the effective harmonic oscillator as a viable alternative for the reliable calculations of transition energies of large molecular systems.
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Affiliation(s)
- Mokshi Sharma
- Department of Chemistry and Chemical Sciences, Central University of Jammu, Rahya-Suchani (Bagla), Jammu, Jammu and Kashmir 181143, India
| | - Subrata Banik
- Department of Chemistry, School of Chemical and Biotechnology, SASTRA Deemed University, Thanjavur, Tamil Nadu 613401, India
| | - Tapta Kanchan Roy
- Department of Chemistry and Chemical Sciences, Central University of Jammu, Rahya-Suchani (Bagla), Jammu, Jammu and Kashmir 181143, India
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Sharma D, Roy TK. Accuracy of Different Electronic Basis Set Families for Anharmonic Molecular Vibrations: A Comprehensive Benchmark Study. J Phys Chem A 2023; 127:7132-7147. [PMID: 37603414 DOI: 10.1021/acs.jpca.3c02874] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/23/2023]
Abstract
In this work, the accuracy and convergence of different electronic basis set families for the computation of anharmonic molecular vibrational spectroscopic calculations are benchmarked. A series of 39 different basis sets from different families following their hierarchy are assessed on VSCF and VSCF-PT2 algorithms with commonly used MP2 and DFT based B3LYP-D potentials for a set of molecular systems. Such an effort has been validated in a previous work ( J. Phys. Chem. A 2020, 124, 9203-9221) with split-valence basis sets for fundamentals and intensities. Here, fundamental transitions, vibrationally excited states, and intensities are compared with the experimental data to estimate the accuracy for a series of Jensen, Dunning, Calendar, Karlsruhe, and Sapporo basis set families. The convergence of basis sets are also compared with the large ANO basis set. Comprehensive statistical error analysis in terms of accuracy and precision was carried out to assess the performance of each basis set. It is observed that the improvement for the calculated harmonic and anharmonic values from the smaller basis sets to the medium (i.e., triple-ξ) is considerable. Beyond this, from medium to large basis sets, the convergence is slow and mostly posits nearly converged values. Basis sets with and without diffuse functions offer characteristically different accuracies and convergence patterns. Finally, recommendations are given on the choice of basis set chosen as black-box which can balance between accuracy and computational time, estimation of the errors, and their selections especially for large molecules.
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Affiliation(s)
- Dhiksha Sharma
- Department of Chemistry and Chemical Sciences, Central University of Jammu, Rahya-Suchani (Bagla), Jammu, J&K 181143 India
| | - Tapta Kanchan Roy
- Department of Chemistry and Chemical Sciences, Central University of Jammu, Rahya-Suchani (Bagla), Jammu, J&K 181143 India
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Palanisamy N, Banik S. An approximation to the vibrational coupled-cluster method for CH-stretching of large molecules: application to naphthalene and anthracene. Phys Chem Chem Phys 2023; 25:20076-20092. [PMID: 37462438 DOI: 10.1039/d3cp01313h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/27/2023]
Abstract
We propose an approximation to the vibrational coupled-cluster method (VCCM) to describe the CH-stretching region of the vibrational spectrum of large molecules. The vibrational modes of a molecule are divided into two sets: the target set and the bath set. The target set includes the CH stretches and the modes that are strongly coupled with the CH stretches and/or involve strong Fermi resonances with a CH stretch fundamental. The rest of the modes are in the bath set. First, the effective harmonic oscillator (EHO) approximation is invoked for the whole system to obtain the zeroth-order frequencies and modified potentials. The effects of interaction between the bath set and the target sets are included in the modified potential from the EHO calculation. The VCCM equations are constructed with the modified potential from the EHO calculations and for the target set only. The transition energies and intensities are calculated using such a truncated VCCM approximation. The proposed method is applied to calculate the IR spectra of naphthalene and anthracene. The results with three different criteria for selecting the modes in the target set are compared with the experimental IR spectra.
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Affiliation(s)
- Nivedhitha Palanisamy
- Department of Chemistry, School of Chemical and Biotechnology, SASTRA Deemed University, Thanjavur, Tamil Nadu, India.
| | - Subrata Banik
- Department of Chemistry, School of Chemical and Biotechnology, SASTRA Deemed University, Thanjavur, Tamil Nadu, India.
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Fayaz A, Banik S, Kanchan Roy T. The importance of electron correlations on vibrational anharmonicities and potential energy surfaces. COMPUT THEOR CHEM 2023. [DOI: 10.1016/j.comptc.2023.114059] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
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Roy TK. Performance of Vibrational Self-Consistent Field Theory for Accurate Potential Energy Surfaces: Fundamentals, Excited States, and Intensities. J Phys Chem A 2022; 126:608-622. [PMID: 35050620 DOI: 10.1021/acs.jpca.1c09989] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The performance of vibrational structure calculations beyond harmonic approximation in the framework of the vibrational self-consistent field method with second-order perturbation corrections (VSCF-PT2) is investigated in conjunction with very accurate potential energy surfaces (PESs) given by various coupled-cluster electronic structure theories. The quality of anharmonic calculations depends on the accuracy of the underlying multidimensional PES obtained from its functional form, which is given by the level of electronic structure theory. Two such highest levels of typical coupled-cluster electronic structure methods, CCSD and the ″gold standard″ CCSD(T), along with their variants such as CCD, CR-CCL (completely renormalized CR-CC(2,3) approach), and CCSD(TQ) are tested for the construction of accurate anharmonic potentials without any fitting or ad hoc scaling and using cc-pVTZ basis sets. The accuracy of VSCF-PT2 theory in comparison to experimental values is tested for a series of 16 molecules with 135 fundamental bands, 64 overtones, and combination bands and also for 39 intensities. It is found that CCD and CCSD bind the potential tighter than CCSD(T) and the computed VSCF-PT2 transitions are more blue-shifted showing higher deviation from the experiment. In general, VSCF-PT2 results computed at the CCSD(T) potential offer a good cost/accuracy ratio, with the mean absolute deviation and the mean absolute percentage error with the experiment being ∼16 cm-1 and 1.38, respectively, for fundamentals. Additionally, while the CR-CCL and CCSD(TQ) methods offer similar levels of accuracies as compared to CCSD(T), the former offers a better accuracy/cost ratio than the latter and is a suitable alternative to CCSD(T).
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Affiliation(s)
- Tapta Kanchan Roy
- Department of Chemistry and Chemical Sciences, Central University of Jammu, Rahya-Suchani (Bagla), Samba, Jammu and Kashmir 181143, India
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Ravichandran L, Banik S. Investigation of the Failure of the MP2 Method to Describe the Out-of-Plane Bending Motions of Carbon-Carbon Double-Bonded Molecules: The Role of Atomic Orbitals. J Phys Chem A 2021; 125:9298-9317. [PMID: 34666490 DOI: 10.1021/acs.jpca.1c06336] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a detailed study on the role of atomic orbitals in the unphysical description of the out-of-plane bending (OOPB) vibrations with the MP2 method. The anharmonicities of the OOPB vibrations are found to be unphysically large for several basis sets with the MP2 method. We find that the inclusion of additional valence s and p orbitals to the basis set leads to the lowering of π* orbitals' energies along with the generation of several spurious low-energy virtual molecular orbitals (VMOs). Such erroneous VMOs create a disbalance between the σ and π correlations for the planar structure of the molecules. Since the OOPB vibrations distort the π* orbitals, the disbalance in the σ and π correlations leads to errors in the derivatives of the correlation energy with respect to the displacement along with OOPB modes. The diffuse functions in the basis set enhance the unphysical anharmonicities of the OOPB modes since these functions are of s- and p-type atomic orbitals. The polarization atomic orbitals of higher angular momentum improve the description of the π* orbitals and thereby reduce the disbalance between the σ and π correlations in the MP2 calculations. We find that the unphysical frequencies for the OOPB modes are significantly eliminated with the d and f orbitals on the C atoms in the basis set.
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Affiliation(s)
| | - Subrata Banik
- Department of Chemistry, School of Chemical and Biotechnology, SASTRA Deemed University, Thanjavur, Tamil Nadu 613401, India
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Yadav S, Banik S, Prasad MD. Understanding of the C-H stretch region of infra-red spectroscopy: an analysis of the final state wavefunctions. Phys Chem Chem Phys 2021; 23:9176-9188. [PMID: 33885051 DOI: 10.1039/d0cp01157f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The nature of the wavefunctions associated with the final states in the CH stretching region of several medium sized molecules is analysed. The number of optically bright transitions is much larger than the number of CH oscillators present in the molecule, and they are spread over a range of about 300 cm-1. Several of them are clustered together within about 5 cm-1 with near equal intensities. The final states of all these transitions are superpositions of multiple zeroth order states. In almost all of such superpositions, no single zeroth order state has more than 50% weight. Several multiquantum states, with three to four quanta of excitation dominate the final states, with the CH chromophore contributing only a small weightage. Thus the band structure of the CH stretch region is due to several optically bright transitions whose final states are superpositions of low frequency multiquantum states with the CH chromophore contributing only a small weight to make them spectroscopically active.
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Affiliation(s)
- Swati Yadav
- School of Chemistry, University of Hyderabad, Hyderabad 500046, India.
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Roy TK, Gerber RB. Dual Basis Approach for Ab Initio Anharmonic Calculations of Vibrational Spectroscopy: Application to Microsolvated Biomolecules. J Chem Theory Comput 2020; 16:7005-7016. [PMID: 32991804 DOI: 10.1021/acs.jctc.0c00725] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A dual electronic basis set approach is introduced for more efficient but accurate calculations of the anharmonic vibrational spectra in the framework of the vibrational self-consistent field (VSCF) theory. In this approach, an accurate basis set is used to compute the vibrational spectra at the harmonic level. The results are used to scale the potential surface from a more modest but much more efficient basis set. The scaling is such that at the harmonic level the new, scaled potential agrees with one of the accurate basis sets. The approach is tested in the application of the microsolvated, protected amino acid Ac-Phe-OMe, using the scaled anharmonic hybrid potential in the VSCF and VSCF-PT2 algorithms. The hybrid potential method yields results that are in good accord with the experiment and very close to those obtained in calculations with the high-level, very costly potential from the large basis set. At the same time, the hybrid potential calculations are considerably less expensive. The results of the hybrid calculations are much more accurate than those computed from the potential surface corresponding to the modest basis set. The results are very encouraging for using the hybrid potential method for inexpensive yet sufficiently accurate anharmonic calculations for the spectra of large biomolecules.
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Affiliation(s)
- Tapta Kanchan Roy
- Department of Chemistry and Chemical Sciences, Central University of Jammu, Rahya-Suchani (Bagla), Dist: Samba Jammu-181143, India
| | - R Benny Gerber
- Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel.,Department of Chemistry, University of California, Irvine, California 92697, United States
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Mitra H, Roy TK. Comprehensive Benchmark Results for the Accuracy of Basis Sets for Anharmonic Molecular Vibrations. J Phys Chem A 2020; 124:9203-9221. [DOI: 10.1021/acs.jpca.0c06634] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Hrishit Mitra
- Department of Chemistry and Chemical Sciences, Central University of Jammu, Rahya-Suchani (Bagla), Jammu, Jammu and Kashmir 181143, India
| | - Tapta Kanchan Roy
- Department of Chemistry and Chemical Sciences, Central University of Jammu, Rahya-Suchani (Bagla), Jammu, Jammu and Kashmir 181143, India
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Dinesh T, Ravichandran L, Prasad MD. An equation of motion approach for the vibrational transition energies in the effective harmonic oscillator formalism: the Random phase approximation. J CHEM SCI 2019. [DOI: 10.1007/s12039-019-1687-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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11
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Lowest order perturbative approximation to vibrational coupled cluster method in bosonic representation. J CHEM SCI 2019. [DOI: 10.1007/s12039-019-1692-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Wang S. Efficiently Calculating Anharmonic Frequencies of Molecular Vibration by Molecular Dynamics Trajectory Analysis. ACS OMEGA 2019; 4:9271-9283. [PMID: 31460016 PMCID: PMC6648323 DOI: 10.1021/acsomega.8b03364] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2018] [Accepted: 05/13/2019] [Indexed: 05/28/2023]
Abstract
Two efficient methods, the Eckart frame algorithm and the multiorder derivative algorithm, for vibrational frequency calculation directly based on the raw data of atomic trajectory from the state-of-the-art first-principles molecular dynamics simulation are presented. The Eckart frame approach is robust to retrieve the full set of anharmonic fundamental frequencies of any molecule from the atomic trajectory for a sufficiently long molecular dynamics simulation at a temperature close to 0 K. In addition to the fundamental vibrational frequencies, the multiorder derivative approach is universal for the calculations of vibrational frequencies based on the molecular dynamics result in a wide range of temperatures. The accuracy, efficiency, and applicability of these two methods are demonstrated through several successful examples in calculating the anharmonic fundamental vibrational frequencies of methane, ethylene, water, and cyclobutadiene.
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Faucheaux JA, Nooijen M, Hirata S. Similarity-transformed equation-of-motion vibrational coupled-cluster theory. J Chem Phys 2018; 148:054104. [PMID: 29421891 DOI: 10.1063/1.5004151] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.
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Affiliation(s)
- Jacob A Faucheaux
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Marcel Nooijen
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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Ravichandran L, Banik S. Anomalous description of the anharmonicity of bending motions of carbon–carbon double bonded molecules with the MP2 method: ethylene as a case study. Phys Chem Chem Phys 2018; 20:27329-27341. [DOI: 10.1039/c8cp04682d] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this work, we report anomalous descriptions of bending modes of the smallest carbon–carbon double bonded molecule ethylene with the MP2 method.
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Affiliation(s)
| | - Subrata Banik
- Department of Chemistry and Chemical Sciences
- Central University of Jammu
- Samba-181143
- India
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Ravichandran L, Banik S. Performance of different density functionals for the calculation of vibrational frequencies with vibrational coupled cluster method in bosonic representation. Theor Chem Acc 2017. [DOI: 10.1007/s00214-017-2177-9] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Banik S, Ravichandran L, Durga Prasad M. Raman spectral calculation by vibrational coupled-cluster method in bosonic representation. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1321153] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Subrata Banik
- Advanced Center for Research in High Energy Materials, University of Hyderabad, Hyderabad, India
| | | | - M. Durga Prasad
- Advanced Center for Research in High Energy Materials, University of Hyderabad, Hyderabad, India
- School of Chemistry, University of Hyderabad, Hyderabad, India
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Chakraborty S, Banik S, Das PK. Anharmonicity in the Vibrational Spectra of Naphthalene and Naphthalene-d8: Experiment and Theory. J Phys Chem A 2016; 120:9707-9718. [DOI: 10.1021/acs.jpca.6b09034] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Shubhadip Chakraborty
- Department
of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore, India
| | - Subrata Banik
- Advanced
Centre for Research in High Energy Materials and School of Chemistry, University of Hyderabad, Hyderabad, India
| | - Puspendu K. Das
- Department
of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore, India
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On the choice electronic structure method to calculate the quartic potential energy surface for the vibrational calculation of polyatomic molecules. Theor Chem Acc 2016. [DOI: 10.1007/s00214-016-1962-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Faucheaux JA, Hirata S. Higher-order diagrammatic vibrational coupled-cluster theory. J Chem Phys 2015; 143:134105. [DOI: 10.1063/1.4931472] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Jacob A. Faucheaux
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA
- CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
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Roy TK, Gerber RB. Vibrational self-consistent field calculations for spectroscopy of biological molecules: new algorithmic developments and applications. Phys Chem Chem Phys 2013; 15:9468-92. [DOI: 10.1039/c3cp50739d] [Citation(s) in RCA: 141] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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