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Josef Paldus - One of the best experts on this subject based on the ideXlab platform.
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Symmetry breaking in spin‐Restricted, open‐shell Hartree–Fock wave functions
International Journal of Quantum Chemistry, 2020Co-Authors: Xiangzhu Li, Josef PaldusAbstract:Relying on a unitary group approach (UGA) to coupled-cluster (CC) theory for Open-Shell systems we formulate a spin-free analogue of Thouless' theorem and derive stability conditions for spin-Restricted, Open-Shell Hartree–Fock (ROHF) solutions. The formalism is illustrated on the ground states of the oxygen and boron molecules. For the O2 molecule, the broken-space-symmetry solution appears already for a slightly stretched OO bond. For the B2 molecule we find a broken-symmetry solution even at the equilibrium geometry and, in fact, in almost an entire region of intermolecular separations. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009
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Multireference coupled-cluster study of the symmetry breaking in the C2B radical.
Journal of Chemical Physics, 2011Co-Authors: Xiangzhu Li, Josef PaldusAbstract:The potential energy surfaces (PESs) for both the ground and the excited electronic states of the C2B radical are investigated using various multireference (MR) coupled-cluster (CC) approaches. In the ground state case we employ the reduced MR (RMR) CC approach with singles (S) and doubles (D), the RMR CCSD method, as well as its RMR CCSD(T) version corrected for secondary triples, relying on various model spaces and basis sets. The reliability of this approach is also tested against the benchmark full configuration interaction results obtained for a small Dunning–Hay (DH) basis set. The results imply a clear preference for a cyclic structure which, however, breaks the C2v symmetry. This symmetry breaking manifests itself strongly at the level of the independent particle model, as represented by the Restricted Open-Shell Hartree–Fock approximation, but the tendency toward symmetry breaking diminishes with the increasing size of the basis set employed as well as with the enhanced account of the correlation...
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unitary group based state specific open shell singlet coupled cluster method application to ozone and comparison with hilbert and fock space theories
Journal of Chemical Physics, 1995Co-Authors: Xiangzhu Li, Josef PaldusAbstract:Recently introduced state‐specific coupled‐cluster method, which exploits the formalism of the unitary group approach to the many‐electron correlation problem and enables a properly spin‐adapted treatment of open‐shell states, is applied to several low lying singlet and triplet electronic states of ozone at the double‐zeta plus polarization level of approximation. The method employs a nonstandard cluster Ansatz, based on a single spin‐free reference built from either the ground state Restricted Hartree–Fock orbitals or from the Restricted open‐shell Hartree–Fock orbitals, specific for each excited state. The results are compared with available experimental data and with other ab initio calculations, particularly with those employing spin‐orbital based, spin nonadapted multireference coupled‐cluster approaches of both state universal and valence universal types, as well as equation‐of‐motion coupled‐cluster method. The general agreement is satisfactory except for the B2 states, where the difference between...
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Unitary group based state specific open‐shell‐singlet coupled‐cluster method: Application to ozone and comparison with Hilbert and Fock space theories
Journal of Chemical Physics, 1995Co-Authors: Xiangzhu Li, Josef PaldusAbstract:Recently introduced state‐specific coupled‐cluster method, which exploits the formalism of the unitary group approach to the many‐electron correlation problem and enables a properly spin‐adapted treatment of open‐shell states, is applied to several low lying singlet and triplet electronic states of ozone at the double‐zeta plus polarization level of approximation. The method employs a nonstandard cluster Ansatz, based on a single spin‐free reference built from either the ground state Restricted Hartree–Fock orbitals or from the Restricted open‐shell Hartree–Fock orbitals, specific for each excited state. The results are compared with available experimental data and with other ab initio calculations, particularly with those employing spin‐orbital based, spin nonadapted multireference coupled‐cluster approaches of both state universal and valence universal types, as well as equation‐of‐motion coupled‐cluster method. The general agreement is satisfactory except for the B2 states, where the difference between...
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Spin‐adapted open‐shell state‐selective coupled cluster approach and doublet stability of its Hartree–Fock reference
Journal of Chemical Physics, 1995Co-Authors: Xiangzhu Li, Josef PaldusAbstract:The performance of the unitary group based state‐selective coupled cluster approach, in both linear and quadratic approximations, is examined for the case of doublet ground states of the first two alkaline earth hydrides in the whole range of internuclear separation. It is shown that the doublet instability of the Restricted open‐shell Hartree–Fock wave functions is responsible for the singular behavior of the linear coupled cluster potential energy curves, as well as for slight discontinuity in these curves when the bilinear terms are included. The effect of using different types of orbitals is investigated and the results are compared with full or very precise limited configuration interaction results as well as with the coupled cluster results employing the unRestricted Hartree–Fock reference, which is free of the instability problems in open shell systems.
Xiangzhu Li - One of the best experts on this subject based on the ideXlab platform.
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Symmetry breaking in spin‐Restricted, open‐shell Hartree–Fock wave functions
International Journal of Quantum Chemistry, 2020Co-Authors: Xiangzhu Li, Josef PaldusAbstract:Relying on a unitary group approach (UGA) to coupled-cluster (CC) theory for Open-Shell systems we formulate a spin-free analogue of Thouless' theorem and derive stability conditions for spin-Restricted, Open-Shell Hartree–Fock (ROHF) solutions. The formalism is illustrated on the ground states of the oxygen and boron molecules. For the O2 molecule, the broken-space-symmetry solution appears already for a slightly stretched OO bond. For the B2 molecule we find a broken-symmetry solution even at the equilibrium geometry and, in fact, in almost an entire region of intermolecular separations. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009
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Multireference coupled-cluster study of the symmetry breaking in the C2B radical.
Journal of Chemical Physics, 2011Co-Authors: Xiangzhu Li, Josef PaldusAbstract:The potential energy surfaces (PESs) for both the ground and the excited electronic states of the C2B radical are investigated using various multireference (MR) coupled-cluster (CC) approaches. In the ground state case we employ the reduced MR (RMR) CC approach with singles (S) and doubles (D), the RMR CCSD method, as well as its RMR CCSD(T) version corrected for secondary triples, relying on various model spaces and basis sets. The reliability of this approach is also tested against the benchmark full configuration interaction results obtained for a small Dunning–Hay (DH) basis set. The results imply a clear preference for a cyclic structure which, however, breaks the C2v symmetry. This symmetry breaking manifests itself strongly at the level of the independent particle model, as represented by the Restricted Open-Shell Hartree–Fock approximation, but the tendency toward symmetry breaking diminishes with the increasing size of the basis set employed as well as with the enhanced account of the correlation...
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unitary group based state specific open shell singlet coupled cluster method application to ozone and comparison with hilbert and fock space theories
Journal of Chemical Physics, 1995Co-Authors: Xiangzhu Li, Josef PaldusAbstract:Recently introduced state‐specific coupled‐cluster method, which exploits the formalism of the unitary group approach to the many‐electron correlation problem and enables a properly spin‐adapted treatment of open‐shell states, is applied to several low lying singlet and triplet electronic states of ozone at the double‐zeta plus polarization level of approximation. The method employs a nonstandard cluster Ansatz, based on a single spin‐free reference built from either the ground state Restricted Hartree–Fock orbitals or from the Restricted open‐shell Hartree–Fock orbitals, specific for each excited state. The results are compared with available experimental data and with other ab initio calculations, particularly with those employing spin‐orbital based, spin nonadapted multireference coupled‐cluster approaches of both state universal and valence universal types, as well as equation‐of‐motion coupled‐cluster method. The general agreement is satisfactory except for the B2 states, where the difference between...
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Unitary group based state specific open‐shell‐singlet coupled‐cluster method: Application to ozone and comparison with Hilbert and Fock space theories
Journal of Chemical Physics, 1995Co-Authors: Xiangzhu Li, Josef PaldusAbstract:Recently introduced state‐specific coupled‐cluster method, which exploits the formalism of the unitary group approach to the many‐electron correlation problem and enables a properly spin‐adapted treatment of open‐shell states, is applied to several low lying singlet and triplet electronic states of ozone at the double‐zeta plus polarization level of approximation. The method employs a nonstandard cluster Ansatz, based on a single spin‐free reference built from either the ground state Restricted Hartree–Fock orbitals or from the Restricted open‐shell Hartree–Fock orbitals, specific for each excited state. The results are compared with available experimental data and with other ab initio calculations, particularly with those employing spin‐orbital based, spin nonadapted multireference coupled‐cluster approaches of both state universal and valence universal types, as well as equation‐of‐motion coupled‐cluster method. The general agreement is satisfactory except for the B2 states, where the difference between...
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Spin‐adapted open‐shell state‐selective coupled cluster approach and doublet stability of its Hartree–Fock reference
Journal of Chemical Physics, 1995Co-Authors: Xiangzhu Li, Josef PaldusAbstract:The performance of the unitary group based state‐selective coupled cluster approach, in both linear and quadratic approximations, is examined for the case of doublet ground states of the first two alkaline earth hydrides in the whole range of internuclear separation. It is shown that the doublet instability of the Restricted open‐shell Hartree–Fock wave functions is responsible for the singular behavior of the linear coupled cluster potential energy curves, as well as for slight discontinuity in these curves when the bilinear terms are included. The effect of using different types of orbitals is investigated and the results are compared with full or very precise limited configuration interaction results as well as with the coupled cluster results employing the unRestricted Hartree–Fock reference, which is free of the instability problems in open shell systems.
Jürgen Gauss - One of the best experts on this subject based on the ideXlab platform.
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accurate prediction of hyperfine coupling tensors for main group elements using a unitary group based rigorously spin adapted coupled cluster theory
Journal of Chemical Theory and Computation, 2019Co-Authors: Dipayan Datta, Jürgen GaussAbstract:We present the development of a perturbative triples correction scheme for the previously reported unitary group based spin-adapted combinatoric Open-Shell coupled-cluster (CC) singles and doubles (COS-CCSD) approach and report on the applications of the newly developed method, termed “COS-CCSD(T)”, to the calculation of hyperfine coupling (HFC) tensors for radicals consisting of hydrogen, second- and third-row elements. The COS-CCSD(T) method involves a single noniterative step with N7 scaling of the computational cost for the calculation of triples corrections to the energy. The key feature of this development is the use of spatial semicanonical orbitals generated from standard Restricted Open-Shell Hartree–Fock (ROHF) orbitals, which allows the unperturbed Hamiltonian operator to be defined in terms of a diagonal spin-free Fock operator. The HFC tensors are computed as a first-order property via implementation of an analytic derivative scheme. The required one-particle spin density matrix is computed b...
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Assessment of the accuracy of coupled cluster perturbation theory for Open-Shell systems. II. Quadruples expansions
Journal of Chemical Physics, 2016Co-Authors: Janus J. Eriksen, Devin A. Matthews, Poul Jørgensen, Jürgen GaussAbstract:The accuracy at which total energies of Open-Shell atoms and organic radicals may be calculated is assessed for selected coupled cluster perturbative triples expansions, all of which augment the coupled cluster singles and doubles (CCSD) energy by a non-iterative correction for the effect of triple excitations. Namely, the second- through sixth-order models of the recently proposed CCSD(T–n) triples series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)] are compared to the acclaimed CCSD(T) model for both unRestricted as well as Restricted Open-Shell Hartree-Fock (UHF/ROHF) reference determinants. By comparing UHF- and ROHF-based statistical results for a test set of 18 modest-sized Open-Shell species with comparable RHF-based results, no behavioral differences are observed for the higher-order models of the CCSD(T–n) series in their correlated descriptions of closed- and Open-Shell species. In particular, we find that the convergence rate throughout the series towards the coupled cluster single...
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Analytic first derivatives for a spin-adapted Open-Shell coupled cluster theory: Evaluation of first-order electrical properties
Journal of Chemical Physics, 2014Co-Authors: Dipayan Datta, Jürgen GaussAbstract:An analytic scheme is presented for the evaluation of first derivatives of the energy for a unitary group based spin-adapted coupled cluster (CC) theory, namely, the combinatoric Open-Shell CC (COSCC) approach within the singles and doubles approximation. The widely used Lagrange multiplier approach is employed for the derivation of an analytical expression for the first derivative of the energy, which in combination with the well-established density-matrix formulation, is used for the computation of first-order electrical properties. Derivations of the spin-adapted lambda equations for determining the Lagrange multipliers and the expressions for the spin-free effective density matrices for the COSCC approach are presented. Orbital-relaxation effects due to the electric-field perturbation are treated via the Z-vector technique. We present calculations of the dipole moments for a number of doublet radicals in their ground states using Restricted Open-Shell Hartree-Fock (ROHF) and quasi-Restricted HF (QRHF)...
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Coupled‐cluster methods with noniterative triple excitations for Restricted open‐shell Hartree–Fock and other general single determinant reference functions. Energies and analytical gradients
Journal of Chemical Physics, 1993Co-Authors: John D. Watts, Jürgen Gauss, Rodney J. BartlettAbstract:A new, noniterative triples correction to the coupled‐cluster singles and doubles (CCSD), method, for general single determinant reference functions is proposed and investigated numerically for various cases, including non‐Hartree–Fock (non‐HF) reference functions. It is correct through fourth‐order of perturbation theory for non‐HF references, and unlike other such methods, retains the usual invariance properties common to CC methods, while requiring only a single N7 step. In the canonical Hartree–Fock case, the method is equivalent to the usual CCSD(T) method, but now permits the use of Restricted open‐shell Hartree‐Fock (ROHF) and quasiRestricted Hartree–Fock (QRHF) reference determinants, along with many others. Comparisons with full configuration interaction (FCI) results are presented for CH2, CH2+, CH3, NH2, and SiH2. The paper also reports the derivation and initial computational implementation of analytical gradients for the ROHF‐CCSD(T) method, which includes unRestricted Hartree–Fock (UHF) CCSD...
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Analytic ROHF–MBPT(2) second derivatives
Journal of Chemical Physics, 1992Co-Authors: Jürgen Gauss, John F. Stanton, Rodney J. BartlettAbstract:The theory and a first implementation of analytic second derivatives for the second‐order energy within many‐body perturbation theory [MBPT(2)] based on a Restricted open‐shell Hartree–Fock (ROHF) reference function are presented. The applicability of the method is demonstrated by calculating harmonic frequency and infrared intensities for the 2B1 state of the CH2N molecule, which suffers from appreciable spin contamination.
Rodney J. Bartlett - One of the best experts on this subject based on the ideXlab platform.
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Theoretical study of the electronic structure of MCH(2)(+)(M=Fe,Co,Ni).
Journal of Chemical Physics, 2007Co-Authors: Sébastien Villaume, Alain Strich, Cherif A. A. Ndoye, Chantal Daniel, S. Ajith Perera, Rodney J. BartlettAbstract:State of the art coupled cluster (CC) methods are applied to accurately characterize the ground state electronic structure and photoelectron spectra of transition metal carbene ions MCH2+ (M=Fe, Co, and Ni). The geometries and energies of the lowest energy quartet, triplet, and doublet electronic states as well as several low-lying vertical excitation energies of FeCH2+, CoCH2+, and NiCH2+ are reported. The excitation energies are computed using the equation-of-motion CC and for states of different symmetries, by the energy differences of single reference ground and excited states (Δ-CC). The latter employ several reference states; the unRestricted Hartree-Fock, Restricted open shell Hartree-Fock, and unRestricted Kohn-Sham. We conclude that the A12 electronic ground state of NiCH2+ is separated by about 30.0kJ∕mol from the next highest state, and the lowest B14 and B24 states of FeCH2+ as well as the A23 and A13 states of CoCH2+ are nearly degenerate. The presence of metal-πMCH2* charge transfer states w...
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Analytic energy gradients with frozen molecular orbitals in coupled-cluster and many-body perturbation theory methods: Systematic study of the magnitude and trends of the effects of frozen molecular orbitals
Journal of Chemical Physics, 1997Co-Authors: Kyoung Koo Baeck, John D. Watts, Rodney J. BartlettAbstract:Analytic coupled-cluster (CC) and many-body perturbation theory (MBPT) energy gradient methods with Restricted Hartree–Fock (RHF), unRestricted Hartree–Fock (UHF), Restricted Open-Shell Hartree–Fock (ROHF), and quasi-RHF(QRHF) reference functions are extended to permit dopping core and excited orbitals. By using the canonical property of the semicanonical ROHF orbitals and the RHF orbitals from which the QRHF reference function is constructed, it is shown that a general procedure can be established not only for RHF and UHF, but also for ROHF and QRHF reference functions. The basic theory and implementation are reported. To provide a systematic study of the trends and magnitudes of the effects of dropped molecular orbitals (MOs) on the structures, harmonic frequencies, and ir intensities, we study HCN, C2H2, CO2, HO2, and C2H4 at increasing levels of correlation and basis sets. The effects of the dropped MOs with the largest basis sets are about 0.003 A and 0.1° in structures and about 1% on harmonic frequ...
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Radical hydrogen transfer reactions: benchmark calculations on the C2H4…H…C2H4 transition state
Chemical Physics Letters, 1996Co-Authors: John D. Watts, James A. Franz, Rodney J. BartlettAbstract:Abstract High level ab initio calculations using coupled-cluster (CC) methods have been applied to calculate the barrier height of the prototypical hydrocarbon radical hydrogen transfer reaction between C 2 H 4 and C 2 H 5 . The barrier at 298 K is estimated to be 27.7–30.7 kcal mol −1 . Second-order perturbation theory based on a Restricted Open-Shell Hartree-Fock reference, unlike spin contaminated UHF-MBPT(2), provides reasonable agreement with the CC calculations, and may be of use in studies of the RHT reaction of larger systems.
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Coupled‐cluster methods with noniterative triple excitations for Restricted open‐shell Hartree–Fock and other general single determinant reference functions. Energies and analytical gradients
Journal of Chemical Physics, 1993Co-Authors: John D. Watts, Jürgen Gauss, Rodney J. BartlettAbstract:A new, noniterative triples correction to the coupled‐cluster singles and doubles (CCSD), method, for general single determinant reference functions is proposed and investigated numerically for various cases, including non‐Hartree–Fock (non‐HF) reference functions. It is correct through fourth‐order of perturbation theory for non‐HF references, and unlike other such methods, retains the usual invariance properties common to CC methods, while requiring only a single N7 step. In the canonical Hartree–Fock case, the method is equivalent to the usual CCSD(T) method, but now permits the use of Restricted open‐shell Hartree‐Fock (ROHF) and quasiRestricted Hartree–Fock (QRHF) reference determinants, along with many others. Comparisons with full configuration interaction (FCI) results are presented for CH2, CH2+, CH3, NH2, and SiH2. The paper also reports the derivation and initial computational implementation of analytical gradients for the ROHF‐CCSD(T) method, which includes unRestricted Hartree–Fock (UHF) CCSD...
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Analytic ROHF–MBPT(2) second derivatives
Journal of Chemical Physics, 1992Co-Authors: Jürgen Gauss, John F. Stanton, Rodney J. BartlettAbstract:The theory and a first implementation of analytic second derivatives for the second‐order energy within many‐body perturbation theory [MBPT(2)] based on a Restricted open‐shell Hartree–Fock (ROHF) reference function are presented. The applicability of the method is demonstrated by calculating harmonic frequency and infrared intensities for the 2B1 state of the CH2N molecule, which suffers from appreciable spin contamination.
Ernest R. Davidson - One of the best experts on this subject based on the ideXlab platform.
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Koopmans’s theorem in the Restricted Open-Shell Hartree–Fock method. II. The second canonical set for orbitals and orbital energies
Journal of Chemical Physics, 2010Co-Authors: Ernest R. Davidson, Boris N. PlakhutinAbstract:A treatment of the validity of Koopmans’s theorem (KT) in the Restricted Open-Shell Hartree–Fock (ROHF) method can be separated into two essentially different cases. The first of them involves the one-electron processes X→Xj± in which the spin state of an ion Xj± having a hole or an extra electron in the closed, open or virtual orbital ϕj is correctly described by a one-determinant wave function. This case was analyzed using different methods by Plakhutin et al. [J. Chem. Phys. 125, 204110 (2006)] and by Plakhutin and Davidson [J. Phys. Chem. A 113, 12386 (2009)]. In the present work we analyze more complex processes where the state of an ion cannot be described by a single determinant. An example of such processes is the removal of an alpha electron from the closed shell of a high-spin half-filled Open-Shell system X. For this case we give a slightly generalized formulation of KT in both the “frozen” orbital approximation (i.e., within the canonical ROHF method) and the limited configuration interaction ...
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Koopmans' theorem in the Restricted Open-Shell Hartree-Fock method. 1. A variational approach.
Journal of Physical Chemistry A, 2009Co-Authors: Boris N. Plakhutin, Ernest R. DavidsonAbstract:A general formulation of Koopmans’ theorem is derived for high-spin half-filled open shells in the Restricted Open-Shell Hartree−Fock (ROHF) method based on a variational treatment of both the initial (nonionized) Open-Shell system under study, e.g., X, and the corresponding high-spin ions Xk+, Xm+, and Xv− having a hole or an extra electron in the closed, open, and virtual shell, respectively. The ions are treated within a FCI-RAS (full CI in the Restricted active space) method with a use of arbitrary ROHF orbitals optimal for the initial system. We show that the desired canonical ROHF orbitals and orbital energies satisfying Koopmans’ theorem, first defined within the canonical ROHF treatment [Plakhutin; et al. J. Chem. Phys. 2006, 125, 204110], generally appear as the natural CI orbitals and the eigenvalues of CI matrices for the respective ions X±. A comparison is performed between the results derived with the present CI approach and the canonical ROHF method for the specific case where the canonical ...
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Electron spin resonance studies of 45Sc17O, 89Y17O, and 139La17O in rare gas matrices: Comparison with ab initio electronic structure and nuclear hyperfine calculations
Journal of Chemical Physics, 1999Co-Authors: Lon B. Knight, John G. Kaup, Benjamin Petzoldt, Ramzi Ayyad, Tapan K. Ghanty, Ernest R. DavidsonAbstract:The first nuclear hyperfine measurements of 17O (I=5/2) have been made for Sc17O, Y17O and La17O in their X 2Σ ground electronic states. These metal oxide radicals were generated by the pulsed-laser vaporization of the metals in the presence of 16O2/17O2 and trapped in neon and argon matrices for electron spin resonance investigations. The fully resolved A tensors of the metal and 17O were compared with ab initio theoretical calculations—a comparison previously reported only for the ScO radical. The computational methods employed were unRestricted Hartree–Fock, density functional theory (DFT), and Restricted Open-Shell Hartree–Fock. Having the metal and 17O hyperfine interactions available has permitted a more thorough description of the electronic structure and charge distribution in these metal oxide molecules. An electronic structure comparison with the AlO, GaO, and InO radicals has also been made. Reasonably good agreement between the observed and calculated values of Aiso and Adip were achieved with...
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Electron spin resonance matrix isolation studies of 27Al16,17O, 69,71Ga16,17O and 115In16,17O: Observed hyperfine interactions compared with ab initio theoretical results
Journal of Chemical Physics, 1997Co-Authors: Lon B. Knight, Thomas J. Kirk, John O. Herlong, John G. Kaup, Ernest R. DavidsonAbstract:Electron spin resonance (ESR) studies are reported for Al16,17O, Ga16,17O, and In16,17O isolated in neon matrices at 4 K. Except for Al16O, no previous ESR measurements have been reported for these X 2Σ diatomic radicals. The pulsed laser vaporization of the metals in the presence of 16O2 and 17O2 produced high quality ESR spectra of these metal oxide radicals whose nuclear hyperfine interactions (A tensors) were fully resolved for both the metal and oxygen nuclei. An analysis of the experimental spin densities in combination with different types of theoretical calculations provided detailed information concerning the electronic structure trends going down this metal oxide group. Increased p-orbital spin density on oxygen was observed for the heavier metal oxide radicals. Nonrelativistic ab initio calculations with an extended basis set and the UB3LYP method reproduced the trends in the isotropic and dipolar hyperfine interactions. All-electron CI calculations, Restricted Open-Shell Hartree–Fock (ROHF) wa...
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Perturbation theory for open shell systems
Chemical Physics Letters, 1991Co-Authors: Christopher W. Murray, Ernest R. DavidsonAbstract:Abstract Two new forms of perturbation theory are presented that are applicable to open shell systems. They are based entirely on the Restricted open shell Hartree-Fock formalism and can be used on the lowest energy of a given symmetry at that geometry. The methods are compared with other approaches and some test cases are presented.