skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory

Journal Article · · The Journal of Chemical Physics
DOI:https://doi.org/10.1063/1.4905120· OSTI ID:1228481
 [1];  [1];  [1]
  1. Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

Sponsoring Organization:
USDOE
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1228481
Journal Information:
The Journal of Chemical Physics, Journal Name: The Journal of Chemical Physics Vol. 142 Journal Issue: 2; ISSN 0021-9606
Publisher:
American Institute of PhysicsCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 24 works
Citation information provided by
Web of Science

References (184)

Pair-correlated coupled cluster theory: An alternative multireference coupled cluster method journal April 2003
On the Hartree-Fock problem journal November 1970
Coupled-Cluster approaches with an approximate account of triply and quadruply excited clusters: Implementation of the orthogonally spin-adaptedCCD +ST(CCD),CCSD +T(CCSD), andACPQ +ST(ACPQ) formalisms journal July 1995
Active-space two-electron reduced-density-matrix method: Complete active-space calculations without diagonalization of the N-electron Hamiltonian journal October 2008
Applicability of coupled-pair theories to quasidegenerate electronic states: A model study journal November 1980
Nonradiative Decay Mechanisms of the Biologically Relevant Tautomer of Guanine journal November 2008
Potential surfaces for the planar cyclopentadienyl radical and cation journal July 1979
A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples journal February 1982
Ability of a coupled electron pair approximation to treat single bond breakings journal June 2010
Theoretical structures for boron-silicon fluorohydrides journal July 1990
Partially linearized, fully size-extensive, and reduced multireference coupled-cluster methods. II. Applications and performance journal April 2008
Complex solutions to simple molecular orbital problems journal March 1988
Electrocyclic Ring Opening ofcis-Bicyclo[m.n.0]alkenes: The Anti-Woodward–Hoffmann Quest journal June 2007
The Usefulness of Exponential Wave Function Expansions Employing One- and Two-Body Cluster Operators in Electronic Structure Theory: The Extended and Generalized Coupled-Cluster Methods journal December 2006
Multireference Ab Initio Density Matrix Renormalization Group (DMRG)-CASSCF and DMRG-CASPT2 Study on the Photochromic Ring Opening of Spiropyran journal September 2013
Self‐consistent molecular orbital methods. XVIII. Constraints and stability in Hartree–Fock theory journal April 1977
PNO–CI (pair natural orbital configuration interaction) and CEPA–PNO (coupled electron pair approximation with pair natural orbitals) calculations of molecular systems. I. Outline of the method for closed‐shell states journal February 1975
Extended Hartree-Fock (EHF) theory in chemical reactions: II. Symmetry properties of the EHF wavefunctions constructed by the magnetically ordered general spin orbitals journal January 1978
Excited‐state reaction pathways for scis buta‐1,3‐diene journal April 1995
Complex molecular orbital method: Open-shell theory journal November 1976
Complex and Unrestricted Hartree‐Fock Wavefunctions journal October 1972
A sequential transformation approach to the internally contracted multireference coupled cluster method journal May 2012
Seniority zero pair coupled cluster doubles theory journal June 2014
Electronic states and wave functions associated with orbital energy crossing journal January 1971
Multireference self-consistent-field energies without the many-electron wave function through a variational low-rank two-electron reduced-density-matrix method journal December 2007
Advances in methods and algorithms in a modern quantum chemistry program package journal January 2006
Electron Correlation in Weakly Coupled Transition Metal Compounds: Poly-Decker Systems journal August 1981
Coupled-cluster approaches with an approximate account of triexcitations and the optimized-inner-projection technique. II. Coupled-cluster results for cyclic-polyene model systems journal August 1990
Photocyclization paths of butadiene. An ab initio MO study journal May 1998
Approximate variational coupled cluster theory journal July 2011
A New Mean-Field Method Suitable for Strongly Correlated Electrons: Computationally Facile Antisymmetric Products of Nonorthogonal Geminals journal February 2013
An efficient and accurate approximation to double substitution coupled cluster wavefunctions journal May 1981
Universal state-selective corrections to multi-reference coupled-cluster theories with single and double excitations journal March 2012
Electrocyclic Ring Opening Reactions of Ethylene Oxides journal September 1977
A linked electron pair functional journal December 2010
Assessment of Orbital-Optimized, Spin-Component Scaled Second-Order Many-Body Perturbation Theory for Thermochemistry and Kinetics journal October 2009
Applicability of the multi-reference double-excitation CI (MRD-CI) method to the calculation of electronic wavefunctions and comparison with related techniques journal March 1978
A size-consistent approach to strongly correlated systems using a generalized antisymmetrized product of nonorthogonal geminals journal January 2013
Approximate account of the connected quadruply excited clusters in the coupled-pair many-electron theory journal November 1984
Isomerizations of Bicyclo[2.1.0]pent-2-ene and Tricyclo[2.1.0.0 2,5 ]pentane into Cyclopenta-1,3-diene:  A Computational Study by DFT and High-Level ab Initio Methods journal January 2004
Molecular orbital theory of the electron structure of organic compounds. XXIV. Geometries and energies of small boron compounds. Comparisons with carbocations journal June 1975
Automated Search for Minimum Energy Conical Intersection Geometries between the Lowest Two Singlet States S 0 /S 1 -MECIs by the Spin-Flip TDDFT Method journal August 2013
Theoretical Study on the Aromaticity of Transition States in Pericyclic Reactions journal May 2006
Symmetry-adapted coupled-pair approach to the many-electron correlation problem. II. Application to the Be atom journal November 1981
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen journal January 1989
Stereochemistry of Electrocyclic Reactions journal January 1965
Orbitally invariant internally contracted multireference unitary coupled cluster theory and its perturbative approximation: Theory and test calculations of second order approximation journal July 2012
On the complex hybridization of orbitals of s and p type journal January 1967
The Density Matrix Renormalization Group in Quantum Chemistry journal May 2011
The instabilities of the Hartree-Fock solutions and the lattice instabilities for conjugated hydrocarbons: The bond-order and bond-length alternations journal September 1976
Projected quasiparticle theory for molecular electronic structure journal September 2011
The shape of the conical intersections of monohydrated pyrimidine bases cytosine, uracil, and thymine: a theoretical study journal February 2011
Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory journal January 2015
Breaking multiple covalent bonds with Hartree–Fock-based quantum chemistry: Quasi-Variational Coupled Cluster theory with perturbative treatment of triple excitations journal January 2012
Chemical bonds and complex wavefunctions journal May 1970
The complete active space SCF (CASSCF) method in a Newton–Raphson formulation with application to the HNO molecule journal February 1981
The perfect quadruples model for electron correlation in a valence active space journal February 2009
A Comparison of the Super-CI and the Newton-Raphson Scheme in the Complete Active Space SCF Method journal January 1980
The Stevens rearrangement: an antiaromatic pericyclic reaction? journal January 1974
Convergence acceleration of iterative sequences. the case of scf iteration journal July 1980
Density‐functional thermochemistry. III. The role of exact exchange journal April 1993
The Complete Active Space Self-Consistent Field Method and its Applications in Electronic Structure Calculations book January 1987
A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach journal May 1980
Unrestricted Hartree-Fock theory and its applications to molecules and chemical reactions journal November 1981
A Valence Bond Analysis of Electronic Degeneracies in Jahn−Teller Systems:  Low-Lying States of the Cyclopentadienyl Radical and Cation journal September 2002
Reaction path following in mass-weighted internal coordinates journal July 1990
On complex molecular orbitals in the extended HF scheme journal August 1973
ImprovedSCF convergence acceleration journal January 1982
Method of complex molecular orbitals: COMPLEX MOLECULAR ORBITALS METHOD journal September 1974
Algorithms and accuracy requirements for computing reaction paths by the method of steepest descent journal March 1988
A size-consistent state-specific multireference coupled cluster theory: Formal developments and molecular applications journal April 1999
Two-body zeroth order Hamiltonians in multireference perturbation theory: The APSG reference state journal January 2002
Symmetry-adapted coupled-pair approach to the many-electron correlation problem. III. Approximate coupled-pair approaches for the Be atom journal November 1981
A fusion of the closed-shell coupled cluster singles and doubles method and valence-bond theory for bond breaking journal September 2012
General properties of the hartree-fock problem demonstrated on the frontier orbital model: II. Analysis of the customary iterative procedure journal September 1975
Projected Hartree–Fock theory journal April 2012
General properties of the Hartree-Fock problem demonstrated on the frontier orbital model: I. Relation among various types of extrema journal September 1975
Application of gradient‐corrected density functional theory to the structures and thermochemistries of ScF 3 , TiF 4 , VF 5 , and CrF 6 journal May 1995
Basis-set convergence of correlated calculations on water journal June 1997
Split‐Shell Molecular Orbitals for Sigma‐Bonded Systems: Hydrogen Halides journal May 1965
The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices journal January 1975
The equivalence of the Piris Natural Orbital Functional 5 (PNOF5) and the antisymmetrized product of strongly orthogonal geminal theory journal January 2013
Stability of a restricted hartree-fock-like wave function under the removal of a symmetry restriction journal January 1968
Accurate thermochemistry from a parameterized coupled-cluster singles and doubles model and a local pair natural orbital based implementation for applications to larger systems journal February 2012
Cyclopentadienyl and related (CH)5+ cations journal August 1973
pCCSD: Parameterized coupled-cluster theory with single and double excitations journal November 2010
Orbital optimization in the density matrix renormalization group, with applications to polyenes and β-carotene journal April 2008
Non-iterative corrections to extended coupled-cluster energies employing the generalized method of moments of coupled-cluster equations journal August 2005
Efficient description of strongly correlated electrons with mean-field cost journal May 2014
Bonding in the ClOO( 2 A″) and BrOO( 2 A″) radical: Nonrelativistic single-reference versus relativistic multi-reference descriptions in density functional theory journal January 2003
Ab initio molecular orbital study of ethylenedione (O.dbd.C.dbd.C.dbd.O) journal April 1975
Tractable spin-pure methods for bond breaking: Local many-electron spin-vector sets and an approximate valence bond model journal February 2009
Wave function constructed from complex hybrids journal May 1969
Geminal model chemistry II. Perturbative corrections journal June 2004
Coupled cluster approaches with an approximate account of triexcitations and the optimized inner projection technique: I. General orthogonally spin-adapted formalism journal January 1990
Orbital-optimized opposite-spin scaled second-order correlation: An economical method to improve the description of open-shell molecules journal April 2007
An efficient internally contracted multiconfiguration–reference configuration interaction method journal November 1988
Electron correlation in one dimension: Coupled cluster approaches to cyclic polyene ?-electron models journal April 1992
The expectation value coupled-cluster method and analytical energy derivatives journal September 1988
Alternate electrocyclic pathways. A quantitative energy evaluation journal March 1968
Quasi-variational coupled cluster theory journal February 2012
Calculations of potential energy surfaces using Monte Carlo configuration interaction journal November 2012
Communication: The distinguishable cluster approximation. II. The role of orbital relaxation journal August 2014
Complex wavefunctions and the conservation of total momentum in the Hartree-Fock theory journal September 1968
The intrinsic reaction coordinate. An a b i n i t i o calculation for HNC→HCN and H +CH 4 →CH 4 +H journal March 1977
Cluster expansion of the wavefunction. Structure of the closed‐shell orbital theory journal November 1978
Biasing reaction pathways with mechanical force journal March 2007
Are atoms intrinsic to molecular electronic wavefunctions? I. The FORS model journal September 1982
Three-state conical intersections in cytosine and pyrimidinone bases journal June 2008
Molecular orbital theory of the electronic structure of organic compounds. XIX. Geometries and energies of C3H5 cations. Energy relations among allyl, vinyl, and cyclopropyl cations journal October 1973
Multireference Nature of Chemistry: The Coupled-Cluster View journal December 2011
Addition by subtraction in coupled-cluster theory: A reconsideration of the CC and CI interface and the nCC hierarchy journal November 2006
Accelerating convergence in the antisymmetric product of strongly orthogonal geminals method journal March 2012
A study of the lowest-lying triplet and singlet states of the cyclopentadienyl cation (c-C5H5+) journal January 1999
Communication: A Jastrow factor coupled cluster theory for weak and strong electron correlation journal November 2013
Quenching of Tryptophan 1 (π,π*) Fluorescence Induced by Intramolecular Hydrogen Abstraction via an Aborted Decarboxylation Mechanism journal June 2002
Altering the Allowed/Forbidden Gap in Cyclobutene Electrocyclic Reactions:  Experimental and Theoretical Evaluations of the Effect of Planarity Constraints journal May 2003
Scaled AMO calculations on the hydrogen molecule II. The 1 s σ 2 p σ 1 ∑ u+ state : THE 1 journal January 1968
An explicitly correlated Mukherjee's state specific coupled cluster method: development and pilot applications journal January 2012
Post-modern valence bond theory for strongly correlated electron spins journal January 2011
Coupled cluster benchmarks of water monomers and dimers extracted from density-functional theory liquid water: The importance of monomer deformations journal September 2009
Cr2 in density-functional theory: approximate spin projection journal October 1995
Strongly orthogonal geminals: size-extensive and variational reference states journal June 2011
Conrotatory and disrotatory stationary points for the electrocyclic isomerization of cyclobutene to cis-butadiene journal March 1984
Excited electronic states from a variational approach based on symmetry-projected Hartree–Fock configurations journal December 2013
Orbital-Optimized Second-Order Perturbation Theory with Density-Fitting and Cholesky Decomposition Approximations: An Efficient Implementation journal May 2014
Single determinant wave functions journal October 1961
Are atoms sic to molecular electronic wavefunctions? II. Analysis of fors orbitals journal September 1982
Behavior of the APSG electronic wavefunction near the electron-electron coalescence point journal April 2004
The influence of orbital rotation on the energy of closed-shell wavefunctions journal January 2014
First Principles Dynamics and Minimum Energy Pathways for Mechanochemical Ring Opening of Cyclobutene journal May 2009
Local spin from strongly orthogonal geminal wavefunctions journal July 2014
Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields journal November 1994
The application of the Woodward–Hoffmann orbital symmetry rules to concerted organic reactions journal January 1968
Locating Multiple Self-Consistent Field Solutions: An Approach Inspired by Metadynamics journal November 2008
Chemiexcitation mechanims. Role of symmetry and spin-orbit coupling in diradicals journal June 1975
Unitary perturbation theory applied to multiconfigurational reference functions journal April 2012
Communication: The distinguishable cluster approximation journal July 2013
Structural and energetic features of fully substituted silylenes, disilenes, and silylsilylenes (SiX2, X2SiSiX2, and XSiSiX3; X = lithium, methyl, and fluorine) journal February 1985
Accurate Theoretical Chemistry with Coupled Pair Models journal May 2009
Quadratic Description of Conical Intersections:  Characterization of Critical Points on the Extended Seam journal March 2007
Locating conical intersections relevant to photochemical reactions journal May 2008
Diradicals, antiaromaticity, and the pseudo-Jahn-Teller effect: Electronic and rovibronic structures of the cyclopentadienyl cation journal July 2007
A geometric approach to direct minimization journal June 2002
The behavior of density functionals with respect to basis set. I. The correlation consistent basis sets journal January 2004
Cr2 revisited journal December 1994
Basis-set convergence of the energy in molecular Hartree–Fock calculations journal March 1999
Theoretical study on the photochemical reactions of butadiene, cyclobutene and bicyclobutane journal March 2000
A tractable and accurate electronic structure method for static correlations: The perfect hextuples model journal July 2010
A geminal model chemistry journal October 2002
Conrotatory and disrotatory pathways in the electrocyclic isomerization of cyclobutene to cis-butadiene: The spin-coupled viewpoint journal December 1997
Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions journal May 1992
The multifacet graphically contracted function method. I. Formulation and implementation journal August 2014
Bondpseudorotation, Jahn-Teller, and pseudo-Jahn-Teller effects in the cyclopentadienyl cation and its pentahalogeno derivatives journal April 2012
Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: Theory and application to the study of chromium dimer journal September 2011
A multireference configuration interaction method based on the separated electron pair wave functions journal January 2005
Ionization energies of water from PNO-CI calculations journal January 1971
The intrinsic reaction coordinate and the rotational barrier in silaethylene journal May 1985
A conical intersection mechanism for the photochemistry of butadiene. A MC-SCF study journal May 1993
Analytic energy gradient for the projected Hartree–Fock method journal May 2014
Coupled Cluster Valence Bond Method: Efficient Computer Implementation and Application to Multiple Bond Dissociations and Strong Correlations in the Acenes journal April 2014
Are atoms intrinsic to molecular electronic wavefunctions? III. Analysis of FORS configurations journal September 1982
The reaction C3H3+ + acetylene and the structural isomers of C5H5+ journal June 1989
Application of an approximate double substitution coupled cluster (ACCD) method to the potential curves of CO and NeHe: Higher order correlation effects in chemically and weakly bonded molecules journal September 1981
The Construction and Interpretation of Mcscf Wavefunctions journal October 1998
Nonradiative Deactivation Mechanisms of Uracil, Thymine, and 5-Fluorouracil: A Comparative ab Initio Study journal December 2011
Radiationless Decay Mechanism of Cytosine:  An Ab Initio Study with Comparisons to the Fluorescent Analogue 5-Methyl-2-pyrimidinone journal April 2007
What is the Preferred Structure of the Singlet Cyclopentadienyl Cation? journal January 1993
Accurate ab initio potential energy curve of O2. II. Core-valence correlations, relativistic contributions, and vibration-rotation spectrum journal February 2010
Extended Hartree-Fock calculations for the helium ground state journal July 1967
General atomic and molecular electronic structure system journal November 1993
Size Consistency Error in the Antisymmetric Geminal Power Wave Function can be Completely Removed journal November 2012
Symmetry breaking in the Hartree-Fock approximation for binuclear transition metal compounds-a theoretical investigation based on a variable model operator: SYMMETRY BREAKING journal August 1983
Multireference many-electron correlation energies from two-electron reduced density matrices computed by solving the anti-Hermitian contracted Schrödinger equation journal November 2007
Singlet and triplet energy surfaces of NiH 2 journal May 1983
Photophysics of xanthine: computational study of the radiationless decay mechanisms journal January 2009
A directCI method with a multiconfigurational reference state journal March 1980
C2V Insertion pathway for BeH2: A test problem for the coupled-cluster single and double excitation model journal March 1983
Rigorously extensive orbital-invariant renormalized perturbative triples corrections from quasi-variational coupled cluster theory journal February 2013
Treating molecules in arbitrary spin states using the parametric two-electron reduced-density-matrix method journal July 2012
Violation of the symmetry rule for the [ 2 + 2 ] addition in the chemisorption of C 2 H 4 on Si(100) journal October 2005
Molecular quadrupole moment functions of HF and N 2 . I. Ab initio linear‐response coupled‐cluster results journal March 1996
A comparative study of single reference correlation methods of the coupled-pair type journal January 2008
On the non-validity of the hartree-fock picture in metallocenes journal November 1981