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Coupled Electron Pair-Type Approximations for Tensor Product State Wave Functions. J Chem Theory Comput 2022; 18:4856-4864. [PMID: 35878319 DOI: 10.1021/acs.jctc.2c00589] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Size extensivity, defined as the correct scaling of energy with system size, is a desirable property for any many-body method. Traditional configuration interaction (CI) methods are not size extensive, hence the error increases as the system gets larger. Coupled electron pair approximation (CEPA) methods can be constructed as simple extensions of a truncated CI that ensures size extensivity. One of the major issues with the CEPA and its variants is that singularities arise in the amplitude equations when the system starts to be strongly correlated. In this work, we extend the traditional Slater determinant based coupled electron pair approaches like CEPA-0, averaged coupled-pair functional, and average quadratic coupled-cluster to a new formulation based on tensor product states (TPS). We show that a TPS basis can often be chosen such that it removes the singularities that commonly destroy the accuracy of CEPA based methods. A suitable TPS representation can be formed by partitioning the system into separate disjoint clusters and forming the final wave function as the tensor product of the many body states of these clusters. We demonstrate the application of these methods on simple bond breaking systems such as CH4 and F2 where determinant based CEPA methods fail. We further apply the TPS-CEPA approach to stillbene isomerization and few planar π-conjugated systems. Overall, the results show that the TPS-CEPA method can remove the singularities and provide improved numerical results compared to common electronic structure methods.
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2
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Relativistic four-component MRCISD+Q calculations of the six lowest valence states of molecular F[Formula: see text] anion including Breit interactions. J Mol Model 2021; 27:230. [PMID: 34309726 DOI: 10.1007/s00894-021-04846-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2021] [Accepted: 07/05/2021] [Indexed: 10/20/2022]
Abstract
In this study, the potential energy curves of the ground and the excited states of molecular fluorine anion (F[Formula: see text]) were investigated at multireference configuration interaction (MRCISD) with Davidson size-extensivity correction (denoted as +Q) within fully relativistic four-component relativistic framework including Breit interaction. Spectroscopic constants (Re, ωe, ωexe, ωeye, De,D0,Be, αe, βe, γe ), accurate extended Rydberg analytical form and rovibrational levels for ground state X:[Formula: see text] are presented, as well as spectroscopic constants for non dissociative excited states. For most states these spectroscopic constants are presented for the first time in literature and they are of interest for experimental studies, specially regarding electron attachment of F2. Results suggest that inclusion of relativistic effects at 4-component level and correlation effects treated at MRCISD+Q level are needed to obtain reliable results, which we report for X:[Formula: see text] ground state's Re, ωe and De the values of 1.999 Å, 391 cm- 1 and 1.22 eV, respectively.
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Abstract
This paper presents a new theory called multiconfiguration density coherence functional theory (MC-DCFT). This theory provides a new route to define density functionals for multiconfiguration wave functions, in particular by using the one-particle density matrix in the coordinate representation. The theory is illustrated by calculating the dissociation curve of four heteronuclear and homonuclear diatomic molecules, namely, H2, F2, N2, and HF, using density coherence functionals converted from PBE, BLYP, and PW91. By introducing two parameters in the converted density functionals, we are able to calculate bond dissociation energies of comparable accuracy as those calculated by multiconfiguration pair-density functional theory (MC-PDFT) and complete active space second-order perturbation theory (CASPT2). This demonstrates that it would be possible to build a successful multiconfiguration density functional theory based on density coherence.
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4
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Accurate ground state potential of Cu 2 up to the dissociation limit by perturbation assisted double-resonant four-wave mixing. J Chem Phys 2020; 153:244305. [PMID: 33380116 DOI: 10.1063/5.0028908] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Perturbation facilitated double-resonant four-wave mixing is applied to access high-lying vibrational levels of the X 1Σg + (0g +) ground state of Cu2. Rotationally resolved transitions up to v″ = 102 are measured. The highest observed level is at 98% of the dissociation energy. The range and accuracy of previous measurements are significantly extended. By applying the near dissociation equation developed by Le Roy [R. J. Le Roy, J. Quant. Spectrosc. Radiat. Transfer 186, 197 (2017)], a dissociation energy of De = 16 270(7) hc cm-1 is determined, and an accurate potential energy function for the X 1Σg + (0g +) ground state is obtained. Molecular constants are determined from the measured transitions and by solving the radial Schrödinger equation using this function and are compared with results from earlier measurements. In addition, benchmark multi-reference configuration interaction computations are performed using the Douglas-Kroll-Hess Hamiltonian and the appropriate basis of augmented valence quadruple ζ type. Coupled-cluster single, double, and perturbative triple calculations were performed for comparison.
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Long-range-corrected multiconfiguration density functional with the on-top pair density. J Chem Phys 2020; 152:094102. [DOI: 10.1063/1.5138980] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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6
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Reproducing benchmark potential energy curves of molecular bond dissociation with small complete active space aided with density and density-matrix functional corrections. J Chem Phys 2019; 151:164122. [PMID: 31675879 DOI: 10.1063/1.5124948] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Various effects of electron correlation accompany molecular bond dissociation, which makes the efficient calculation of potential energy curves a notoriously difficult problem. In an attempt to reliably reproduce both absolute energies and shapes of the benchmark dissociation curves, calculations with the combined CASΠDFT method are carried out for the prototype molecules H2, BH, F2, and N2. The complete active space (CAS) part of CASΠDFT accounts for long-range nondynamic correlation, while short-range dynamic correlation is accounted for with the corrected Lee-Yang-Parr correlation functional of density functional theory (DFT). The correction represents the suppression of dynamic correlation with nondynamic correlation, and it is a function of the ratio x(r) between the conditional and conventional densities obtained with the CAS on-top pair density Π(r). For the single-bonded molecules H2, BH, and F2, CASΠDFT succeeds in reproducing the shapes and absolute energies (for H2 and BH) of the benchmark curves, while for the triple-bonded N2 molecule, the addition to CASΠDFT of a multibond correction is required. It accounts for the middle-range dynamic correlation of the same-spin electrons in the (symmetrized) high-spin atomic electron configurations of the dissociating N2.
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7
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A simplified account of the correlation effects to bond breaking processes: The Brillouin-Wigner perturbation theory using a multireference formulation. J Chem Phys 2019. [DOI: 10.1063/1.5097657] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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8
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Benchmark of correlation matrix renormalization method in molecule calculations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:195902. [PMID: 30736027 DOI: 10.1088/1361-648x/ab05b3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We report benchmark calculations of the correlation matrix renormalization (CMR) approach for 23 molecules in the well-established G2 molecule set. This subset represents molecules with spin-singlet ground state in a variety of chemical bonding and coordination environments. The QUAsi-atomic minimal basis-set orbitals (QUAMBOs) are used as local orbitals in both CMR and full configuration interaction (FCI) calculations for comparison. The results obtained from the calculations are also compared with available experimental data. It is shown that the CMR method produces binding and dissociation energy curves in good agreement with the QUAMBO-FCI calculations as well as experimental results. The CMR benchmark calculations yield a standard deviation of 0.09 Å for the equilibrium bond length and 0.018 Hartree/atom for the formation energy, with a gain of great computational efficiency which scales like Hartree-Fock method.
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Sum-rule corrections: a route to error cancellations in correlation matrix renormalisation theory. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1278800] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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10
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Correlation Matrix Renormalization Theory: Improving Accuracy with Two-Electron Density-Matrix Sum Rules. J Chem Theory Comput 2016; 12:4806-4811. [DOI: 10.1021/acs.jctc.6b00570] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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11
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Abstract
Hund’s term rules are only valid for isolated atoms, but have no generalization for molecules or clusters of several atoms. We present a benchmark calculation of Al2 and Al3, for which we find the high and low-spin ground states 3Πu and , respectively. We show that the relative stabilities of all the molecular terms of Al2 and Al3 can be described by simple rules pertaining to bonding structures and symmetries, which serve as guiding principles to determine ground state terms of arbitrary multi-atom clusters.
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Relativistic state-specific multireference perturbation theory incorporating improved virtual orbitals: Application to the ground state single-bond dissociation. J Comput Chem 2015; 36:1954-72. [PMID: 26272333 DOI: 10.1002/jcc.24037] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2015] [Revised: 07/01/2015] [Accepted: 07/02/2015] [Indexed: 11/07/2022]
Abstract
Using four-component (4c) relativistic spinors, we present a computationally economical relativistic ab initio method for molecular systems employing our recently proposed second-order state-specific multireference perturbation theory (SSMRPT) incorporating the improved virtual orbital-complete active space configuration interaction (IVO-CASCI) reference wavefunction. The resulting method, 4c-IVO-SSMRPT [calculate one state at a time] is tested in pilot calculations on the homonuclear dimers including Li(2), Na(2), K(2), Rb(2), F(2), Cl(2), and Br(2) through the computations of the ground state potential energy curves (PECs). As SSMRPT curbs intruder effects, 4c-IVO-SSMRPT is numerically stable. To our knowledge, the SSMRPT in the 4c relativistic framework has not been explored in the past. Selective spectroscopic constants that are closely related to the correct shape and accuracy of the energy surfaces have been extracted from the computed PECs. For the halogen molecules, a relativistic destabilization of the bond has been found. Relativistic and electron correlation effects need to be incorporated to get reliable estimates. Our results are in good accordance with reference theoretical and experimental data which manifests the computational accuracy and efficiency of the new 4c-IVO-SSMRPT method. The method opens for an improved description of MR systems containing heavy elements. The inexpensiveness of IVO-CASCI makes 4c-IVO-SSMRPT method promising for studies on large systems of heavy elements.
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State-specific multireference perturbation theory with improved virtual orbitals: Taming the ground state of F2, Be2,and N2. J Comput Chem 2015; 36:907-25. [DOI: 10.1002/jcc.23873] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2014] [Revised: 01/09/2015] [Accepted: 01/11/2015] [Indexed: 11/07/2022]
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14
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Fixed-node diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctions. J Chem Phys 2015; 142:044115. [DOI: 10.1063/1.4905528] [Citation(s) in RCA: 58] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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MR-ccCA: A route for accurate ground and excited state potential energy curves and spectroscopic properties for third-row diatomic molecules. COMPUT THEOR CHEM 2014. [DOI: 10.1016/j.comptc.2014.04.013] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Accurate ab initio potential energy curves and spectroscopic properties of the four lowest singlet states of C2. Theor Chem Acc 2013. [DOI: 10.1007/s00214-013-1425-x] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Abstract
By analysing the properties of the electron density in the structurally simple perhalogenated ethanes, X3C-CY3 (X, Y = F, Cl), a previously overlooked non-covalent attraction between halogens attached to opposite carbon atoms is found. Quantum chemical calculations extrapolated towards the full solution of the Schrödinger equation reveal the complex nature of the interaction. When at least one of the halogens is a chlorine, the strength of the interaction is comparable to that of hydrogen bonds. Further analysis shows that the bond character is quite different from standard non-covalent halogen bonds and hydrogen bonds; no bond critical points are found between the halogens, and the σ-holes of the halogens are not utilised for bonding. Thus, the nature of the intramolecular halogen···halogen bonding studied here appears to be of an unusually strong van der Waals type.
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Accurate Potential Energy Curve for B2. Ab Initio Elucidation of the Experimentally Elusive Ground State Rotation-Vibration Spectrum. J Phys Chem A 2012; 116:1717-29. [DOI: 10.1021/jp210473e] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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21
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On the accuracy of pseudopotentials designed for QMC calculations on molecules of the first row atoms. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2011.11.041] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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22
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Ab Initio Composite Approaches. ACTA ACUST UNITED AC 2012. [DOI: 10.1016/b978-0-444-59440-2.00002-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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23
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Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications. Chem Rev 2011; 112:108-81. [DOI: 10.1021/cr200137a] [Citation(s) in RCA: 470] [Impact Index Per Article: 36.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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24
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Accurateab initiopotential energy curve of O2. II. Core-valence correlations, relativistic contributions, and vibration-rotation spectrum. J Chem Phys 2010; 132:074307. [DOI: 10.1063/1.3298376] [Citation(s) in RCA: 63] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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26
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Perturbative triples corrections in state-specific multireference coupled cluster theory. J Chem Phys 2010; 132:074107. [DOI: 10.1063/1.3305335] [Citation(s) in RCA: 94] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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27
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Accurate ab initio potential energy curve of O2. I. Nonrelativistic full configuration interaction valence correlation by the correlation energy extrapolation by intrinsic scaling method. J Chem Phys 2010; 132:074109. [DOI: 10.1063/1.3298373] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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28
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Resonating valence bond wave function with molecular orbitals: Application to first-row molecules. J Chem Phys 2009; 131:154116. [DOI: 10.1063/1.3249966] [Citation(s) in RCA: 74] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
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29
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Ab initio potential energy curve of F2. IV. Transition from the covalent to the van der Waals region: Competition between multipolar and correlation forces. J Chem Phys 2009; 130:204101. [DOI: 10.1063/1.3139114] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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Electrostatically Embedded Many-Body Approximation for Systems of Water, Ammonia, and Sulfuric Acid and the Dependence of Its Performance on Embedding Charges. J Chem Theory Comput 2009; 5:1573-84. [DOI: 10.1021/ct900095d] [Citation(s) in RCA: 56] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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31
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A companion perturbation theory for state-specific multireference coupled cluster methods. Phys Chem Chem Phys 2009; 11:4728-41. [PMID: 19492126 DOI: 10.1039/b822910d] [Citation(s) in RCA: 62] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
A partitioning scheme is applied to the state-specific Mukherjee multireference coupled cluster method to derive a companion perturbation theory (Mk-MRPT2). A production-level implementation of Mk-MRPT2 is reported. The effectiveness of the Mk-MRPT2 method is demonstrated by application to the classic F(2) dissociation problem and the lowest-lying electronic states of meta-benzyne, including computations with up to 766 atomic orbitals. We show that Mk-MRPT2 theory is particularly useful in multireference focal point extrapolations to determine ab initio limits.
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32
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Multipole polarizabilities and long-range interactions of the fluorine atom. J Chem Phys 2009; 130:124310. [PMID: 19334833 DOI: 10.1063/1.3098320] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The polarizabilities of the ground state of fluorine are determined by the box-based B-spline configuration-interaction method. The ground-state static and tensor polarizabilities are calculated as alpha(d) = 3.49a(0)(3) and alpha(2) = 0.303a(0)(3), respectively. The resulting excitation matrix elements are employed to compute the interatomic dispersion interactions for the HF and F(2) molecules.
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34
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The electronic structure of the F2, Cl2, Br2 molecules: the description of charge-shift bonding within the generalized valence bond ansatz. Theor Chem Acc 2008. [DOI: 10.1007/s00214-008-0484-x] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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35
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Correlation energy and dispersion interaction in the ab initio potential energy curve of the neon dimer. J Chem Phys 2008; 128:214308. [DOI: 10.1063/1.2927302] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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Accurate ab initio potential energy curve of F2. III. The vibration rotation spectrum. J Chem Phys 2008; 127:204313. [PMID: 18052433 DOI: 10.1063/1.2805392] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An analytical expression is found for the accurate ab initio potential energy curve of the fluorine molecule that has been determined in the preceding two papers. With it, the vibrational and rotational energy levels of F(2) are calculated using the discrete variable representation. The comparison of this theoretical spectrum with the experimental spectrum, which had been measured earlier using high-resolution electronic spectroscopy, yields a mean absolute deviation of about 5 cm(-1) over the 22 levels. The dissociation energy with respect to the lowest vibrational energy is calculated within 30 cm(-1) of the experimental value of 12 953+/-8 cm(-1). The reported agreement of the theoretical spectrum and dissociation energy with experiment is contingent upon the inclusion of the effects of core-generated electron correlation, spin-orbit coupling, and scalar relativity. The Dunham analysis [Phys. Rev. 41, 721 (1932)] of the spectrum is found to be very accurate. New values are given for the spectroscopic constants.
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