Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

ωB97M-V: A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation

Journal Article · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/1.4952647· OSTI ID:1379385
 [1];  [2]
  1. Univ. of California, Berkeley, CA (United States)
  2. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation is presented in this paper. The final 12-parameter functional form is selected from approximately 10 × 109 candidate fits that are trained on a training set of 870 data points and tested on a primary test set of 2964 data points. The resulting density functional, ωB97M-V, is further tested for transferability on a secondary test set of 1152 data points. For comparison, ωB97M-V is benchmarked against 11 leading density functionals including M06-2X, ωB97X-D, M08-HX, M11, ωM05-D, ωB97X-V, and MN15. Encouragingly, the overall performance of ωB97M-V on nearly 5000 data points clearly surpasses that of all of the tested density functionals. Finally, in order to facilitate the use of ωB97M-V, its basis set dependence and integration grid sensitivity are thoroughly assessed, and recommendations that take into account both efficiency and accuracy are provided.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1379385
Alternate ID(s):
OSTI ID: 1256135
Journal Information:
Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 21 Vol. 144; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

References (134)

The Mechanism of Dihydrogen Activation by Frustrated Lewis Pairs Revisited journal January 2010
Density Functional Theory and Hydrogen Bonds: Are We There Yet? journal February 2015
SG-0: A small standard grid for DFT quadrature on large systems journal January 2006
Semiempirical GGA-type density functional constructed with a long-range dispersion correction journal January 2006
Effect of the damping function in dispersion corrected density functional theory journal March 2011
New accurate benchmark energies for large water clusters: DFT is better than expected journal January 2014
Accurate reaction barrier heights of pericyclic reactions: Surprisingly large deviations for the CBS-QB3 composite method and their consequences in DFT benchmark studies journal February 2015
Heats of formation of platonic hydrocarbon cages by means of high-level thermochemical procedures journal June 2015
Uncertainty quantification in thermochemistry, benchmarking electronic structure computations, and Active Thermochemical Tables journal January 2014
A dataset of highly accurate homolytic NBr bond dissociation energies obtained by Means of W2 theory journal October 2015
Density Functional Calculations of Molecular Bond Energies book January 1987
Correlation energies in the spin-density functional formalism: II. Applications and empirical corrections journal January 1980
The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals journal July 2007
A standard grid for density functional calculations journal July 1993
Assessment of theoretical procedures for a diverse set of isomerization reactions involving double-bond migration in conjugated dienes journal September 2014
Reaction barrier heights for cycloreversion of heterocyclic rings: An Achilles’ heel for DFT and standard ab initio procedures journal September 2015
W4-11: A high-confidence benchmark dataset for computational thermochemistry derived from first-principles W4 data journal July 2011
Benchmark Calculations of Three-Body Intermolecular Interactions and the Performance of Low-Cost Electronic Structure Methods journal June 2015
Benchmark ab Initio Conformational Energies for the Proteinogenic Amino Acids through Explicitly Correlated Methods. Assessment of Density Functional Methods journal December 2015
MN15-L: A New Local Exchange-Correlation Functional for Kohn–Sham Density Functional Theory with Broad Accuracy for Atoms, Molecules, and Solids journal February 2016
What Are the Ground State Structures of C 20 and C 24 ? An Explicitly Correlated Ab Initio Approach journal December 2015
Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parametrization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions journal January 2006
Efficient and Accurate Double-Hybrid-Meta-GGA Density Functionals—Evaluation with the Extended GMTKN30 Database for General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions journal December 2010
Formal Estimation of Errors in Computed Absolute Interaction Energies of Protein−Ligand Complexes journal February 2011
S66: A Well-balanced Database of Benchmark Interaction Energies Relevant to Biomolecular Structures journal July 2011
Extensions of the S66 Data Set: More Accurate Interaction Energies and Angular-Displaced Nonequilibrium Geometries journal October 2011
Advanced Corrections of Hydrogen Bonding and Dispersion for Semiempirical Quantum Mechanical Methods journal December 2011
Why are the Interaction Energies of Charge-Transfer Complexes Challenging for DFT? journal April 2012
Hydrocarbon/Water Interactions: Encouraging Energetics and Structures from DFT but Disconcerting Discrepancies for Hessian Indices journal April 2012
Accuracy of Several Wave Function and Density Functional Theory Methods for Description of Noncovalent Interaction of Saturated and Unsaturated Hydrocarbon Dimers journal June 2012
Exchange–Correlation Functional with Good Accuracy for Both Structural and Energetic Properties while Depending Only on the Density and Its Gradient journal June 2012
Determination of Barrier Heights for Proton Exchange in Small Water, Ammonia, and Hydrogen Fluoride Clusters with G4(MP2)-Type, MP n , and SCS-MP n Procedures—A Caveat journal August 2012
Benchmark Calculations of Noncovalent Interactions of Halogenated Molecules journal September 2012
Long-Range Corrected Hybrid Density Functionals with Improved Dispersion Corrections journal November 2012
Binding in Radical-Solvent Binary Complexes: Benchmark Energies and Performance of Approximate Methods journal February 2013
Halogen Bonds: Benchmarks and Theoretical Analysis journal March 2013
The Performance of Density Functionals for Sulfate–Water Clusters journal February 2013
Describing Noncovalent Interactions beyond the Common Approximations: How Accurate Is the “Gold Standard,” CCSD(T) at the Complete Basis Set Limit? journal April 2013
Assessment of Coupled Cluster Theory and more Approximate Methods for Hydrogen Bonded Systems journal September 2013
On the Reliability of Pure and Hybrid DFT Methods for the Evaluation of Halogen, Chalcogen, and Pnicogen Bonds Involving Anionic and Neutral Electron Donors journal October 2013
Basis Set Convergence of the Post-CCSD(T) Contribution to Noncovalent Interaction Energies journal June 2014
Performance of Density Functional Theory Procedures for the Calculation of Proton-Exchange Barriers: Unusual Behavior of M06-Type Functionals journal July 2014
Halogen Bonding from Dispersion-Corrected Density-Functional Theory: The Role of Delocalization Error journal November 2014
Beyond Energies: Geometries of Nonbonded Molecular Complexes as Metrics for Assessing Electronic Structure Approaches journal March 2015
Accurate Description of Intermolecular Interactions Involving Ions Using Symmetry-Adapted Perturbation Theory journal May 2015
Representative Benchmark Suites for Barrier Heights of Diverse Reaction Types and Assessment of Electronic Structure Methods for Thermochemical Kinetics journal December 2006
Exploring the Limit of Accuracy of the Global Hybrid Meta Density Functional for Main-Group Thermochemistry, Kinetics, and Noncovalent Interactions journal October 2008
Evaluation of B3LYP, X3LYP, and M06-Class Density Functionals for Predicting the Binding Energies of Neutral, Protonated, and Deprotonated Water Clusters journal March 2009
Conformers of Gaseous Cysteine journal May 2009
A General Database for Main Group Thermochemistry, Kinetics, and Noncovalent Interactions − Assessment of Common and Reparameterized ( meta -)GGA Density Functionals journal November 2009
Integration Grid Errors for Meta-GGA-Predicted Reaction Energies: Origin of Grid Errors for the M06 Suite of Functionals journal January 2010
Effectiveness of Diffuse Basis Functions for Calculating Relative Energies by Density Functional Theory journal March 2003
Benchmark Database of Barrier Heights for Heavy Atom Transfer, Nucleophilic Substitution, Association, and Unimolecular Reactions and Its Use to Test Theoretical Methods journal March 2005
Benchmark Database of Barrier Heights for Heavy Atom Transfer, Nucleophilic Substitution, Association, and Unimolecular Reactions and its Use to Test Theoretical Methods journal April 2006
Density Functional for Spectroscopy:  No Long-Range Self-Interaction Error, Good Performance for Rydberg and Charge-Transfer States, and Better Performance on Average than B3LYP for Ground States journal December 2006
Benchmark Structures and Binding Energies of Small Water Clusters with Anharmonicity Corrections journal November 2011
Benchmark Interaction Energies for Biologically Relevant Noncovalent Complexes Containing Divalent Sulfur journal January 2012
Assessment of Theoretical Procedures for Calculating Barrier Heights for a Diverse Set of Water-Catalyzed Proton-Transfer Reactions journal April 2012
The Melatonin Conformer Space: Benchmark and Assessment of Wave Function and DFT Methods for a Paradigmatic Biological and Pharmacological Molecule journal March 2013
What Can We Learn about Dispersion from the Conformer Surface of n -Pentane? journal March 2013
Conformational Equilibria in Butane-1,4-diol: A Benchmark of a Prototypical System with Strong Intramolecular H-bonds journal December 2013
Accurate and Efficient Quantum Chemistry Calculations for Noncovalent Interactions in Many-Body Systems: The XSAPT Family of Methods journal December 2014
Highly Accurate First-Principles Benchmark Data Sets for the Parametrization and Validation of Density Functional and Other Approximate Methods. Derivation of a Robust, Generally Applicable, Double-Hybrid Functional for Thermochemistry and Thermochemical Kinetics journal December 2008
Effects of Heteroatoms on Aromatic π−π Interactions: Benzene−Pyridine and Pyridine Dimer journal February 2009
A Systematic CCSD(T) Study of Long-Range and Noncovalent Interactions between Benzene and a Series of First- and Second-Row Hydrides and Rare Gas Atoms journal February 2009
An Assessment of Theoretical Methods for Nonbonded Interactions: Comparison to Complete Basis Set Limit Coupled-Cluster Potential Energy Curves for the Benzene Dimer, the Methane Dimer, Benzene−Methane, and Benzene−H 2 S journal September 2009
Performance of Ab Initio and Density Functional Methods for Conformational Equilibria of C n H 2 n +2 Alkane Isomers ( n = 4−8) journal October 2009
Benchmark Thermochemistry of the C n H 2 n +2 Alkane Isomers ( n = 2−8) and Performance of DFT and Composite Ab Initio Methods for Dispersion-Driven Isomeric Equilibria journal July 2009
High-Level Ab Initio Electronic Structure Calculations of Water Clusters (H 2 O) 16 and (H 2 O) 17 : A New Global Minimum for (H 2 O) 16 journal October 2010
Generalized Gradient Approximation That Recovers the Second-Order Density-Gradient Expansion with Optimized Across-the-Board Performance journal July 2011
Improving the Accuracy of Hybrid Meta-GGA Density Functionals by Range Separation journal October 2011
M11-L: A Local Density Functional That Provides Improved Accuracy for Electronic Structure Calculations in Chemistry and Physics journal December 2011
Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs journal January 2006
Nonseparable exchange–correlation functional for molecules, including homogeneous catalysis involving transition metals journal January 2015
An accurate benchmark description of the interactions between carbon dioxide and polyheterocyclic aromatic compounds containing nitrogen journal January 2015
Multi-coefficient extrapolated density functional theory for thermochemistry and thermochemical kinetics journal January 2005
Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy journal January 2005
Performance of spin-component-scaled Møller–Plesset theory (SCS-MP2) for potential energy curves of noncovalent interactions journal January 2007
Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections journal January 2008
An improved and broadly accurate local approximation to the exchange–correlation density functional: The MN12-L functional for electronic structure calculations in chemistry and physics journal January 2012
Screened-exchange density functionals with broad accuracy for chemistry and solid-state physics journal January 2012
ωB97X-V: A 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy journal January 2014
MN15: A Kohn–Sham global-hybrid exchange–correlation density functional with broad accuracy for multi-reference and single-reference systems and noncovalent interactions journal January 2016
A new parametrization of exchange–correlation generalized gradient approximation functionals journal April 2001
Hybrid exchange-correlation functional determined from thermochemical data and ab initio potentials journal November 2001
Polarization consistent basis sets: Principles journal November 2001
Polarization consistent basis sets. II. Estimating the Kohn–Sham basis set limit journal May 2002
New exchange-correlation density functionals: The role of the kinetic-energy density journal June 2002
Polarization consistent basis sets. III. The importance of diffuse functions journal November 2002
The van der Waals potentials between all the rare gas atoms from He to Rn journal March 2003
Gaussian basis sets of quadruple zeta valence quality for atoms H–Kr journal December 2003
High-level ab initio calculations for the four low-lying families of minima of (H[sub 2]O)[sub 20]. I. Estimates of MP2/CBS binding energies and comparison with empirical potentials journal January 2004
Development of density functionals for thermochemical kinetics journal August 2004
Prescription for the design and selection of density functional approximations: More constraint satisfaction with fewer fits journal August 2005
Semiempirical hybrid functional with improved performance in an extensive chemical assessment journal September 2005
Exchange-correlation functional with broad accuracy for metallic and nonmetallic compounds, kinetics, and noncovalent interactions journal October 2005
A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions journal November 2006
Avoiding singularity problems associated with meta-GGA (generalized gradient approximation) exchange and correlation functionals containing the kinetic energy density journal December 2007
Systematic optimization of long-range corrected hybrid density functionals journal February 2008
Oscillations in meta-generalized-gradient approximation potential energy surfaces for dispersion-bound complexes journal July 2009
A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu journal April 2010
Property-optimized Gaussian basis sets for molecular response calculations journal October 2010
Nonlocal van der Waals density functional: The simpler the better journal December 2010
Basis set convergence of the coupled-cluster correction, δMP2CCSD(T): Best practices for benchmarking non-covalent interactions and the attendant revision of the S22, NBC10, HBC6, and HSG databases journal November 2011
Communication: A global hybrid generalized gradient approximation to the exchange-correlation functional that satisfies the second-order density-gradient constraint and has broad applicability in chemistry journal November 2011
Density functional calculations of molecular bond energies journal April 1986
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen journal January 1989
Gaussian‐2 theory for molecular energies of first‐ and second‐row compounds journal June 1991
Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions journal May 1992
Fully optimized contracted Gaussian basis sets for atoms Li to Kr journal August 1992
Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon journal January 1993
Density‐functional thermochemistry. III. The role of exact exchange journal April 1993
Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr journal April 1994
Long-range corrected hybrid meta-generalized-gradient approximations with dispersion corrections journal April 2012
Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals journal November 1997
Development and assessment of new exchange-correlation functionals journal October 1998
New generalized gradient approximation functionals journal January 2000
An improved treatment of empirical dispersion and a many-body energy decomposition scheme for the explicit polarization plus symmetry-adapted perturbation theory (XSAPT) method journal July 2013
Exploring the limit of accuracy for density functionals based on the generalized gradient approximation: Local, global hybrid, and range-separated hybrid functionals with and without dispersion corrections journal May 2014
Mapping the genome of meta-generalized gradient approximation density functionals: The search for B97M-V journal February 2015
Thermochemical benchmarking of hydrocarbon bond separation reaction energies: Jacob's ladder is not reversed! journal September 2010
Explicitly correlated benchmark calculations on C 8 H 8 isomer energy separations: how accurate are DFT, double-hybrid, and composite ab initio procedures? journal April 2012
Basis set limit coupled-cluster studies of hydrogen-bonded systems journal February 2015
Advances in molecular quantum chemistry contained in the Q-Chem 4 program package journal September 2014
An assessment of theoretical procedures for π -conjugation stabilisation energies in enones journal December 2014
Can DFT and ab initio methods describe all aspects of the potential energy surface of cycloreversion reactions? journal September 2015
Coulomb-attenuated exchange energy density functionals journal July 1996
Self-Consistent Equations Including Exchange and Correlation Effects journal November 1965
Ground-state correlation energies for atomic ions with 3 to 18 electrons journal May 1993
Accurate and simple analytic representation of the electron-gas correlation energy journal June 1992
Higher-accuracy van der Waals density functional journal August 2010
Ground State of the Electron Gas by a Stochastic Method journal August 1980
Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis journal August 1980
Nonlocal van der Waals density functional: The simpler the better text January 2010

Cited By (63)

Quantum Chemical Modeling of Pressure‐Induced Spin Crossover in Octahedral Metal‐Ligand Complexes journal October 2019
Electron density learning of non-covalent systems journal January 2019
Balancing DFT Interaction Energies in Charged Dimers Precursors to Organic Semiconductors dataset January 2020
The Good, the Bad, and the Ugly: “HiPen”, a New Dataset for Validating (S)QM/MM Free Energy Simulations journal February 2019
Dielectric Screening Meets Optimally Tuned Density Functionals journal April 2018
How reliable is DFT in predicting relative energies of polycyclic aromatic hydrocarbon isomers? comparison of functionals from different rungs of jacob's ladder journal November 2016
W4-17: A diverse and high-confidence dataset of atomization energies for benchmarking high-level electronic structure methods journal July 2017
The reHISS Three-Range Exchange Functional with an Optimal Variation of Hartree-Fock and Its Use in the reHISSB-D Density Functional Theory Method journal September 2018
Fermi-Löwdin orbital self-interaction corrected density functional theory: Ionization potentials and enthalpies of formation: Fermi-Löwdin Orbital Self-interaction Corrected Density Functional Theory: Ionization Potentials and Enthalpies of Formation journal October 2018
ACCDB: A collection of chemistry databases for broad computational purposes: ACCDB: A Collection of Chemistry DataBases for Broad Computational Purposes journal December 2018
Modeling halogen bonding with planewave density functional theory: Accuracy and challenges journal April 2019
Dual‐hybrid direct random phase approximation and second‐order screened exchange with nonlocal van der Waals correlations for noncovalent interactions journal January 2020
Highly accurate equilibrium structure of the C2h symmetric N1-to-O2 hydrogen-bonded uracil-dimer journal March 2018
Fully numerical Hartree‐Fock and density functional calculations. II. Diatomic molecules journal April 2019
Fully numerical Hartree‐Fock and density functional calculations. I. Atoms journal April 2019
Validating additive correction schemes against gradient‐based extrapolations journal April 2019
Modelling Vibrational Dissociation of [H 2 –HCO] + journal September 2019
Advanced models for water simulations journal September 2017
How accurate is density functional theory in predicting spin density? An insight from the prediction of hyperfine coupling constants journal December 2019
Solvents can control solute molecular identity journal May 2018
Machine learning for molecular and materials science journal July 2018
Probing non-covalent interactions with a second generation energy decomposition analysis using absolutely localized molecular orbitals journal January 2016
A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions journal January 2017
How accurate are static polarizability predictions from density functional theory? An assessment over 132 species at equilibrium geometry journal January 2018
Semi-empirical or non-empirical double-hybrid density functionals: which are more robust? journal January 2018
Nature of halogen bonding involving π-systems, nitroxide radicals and carbenes: a highlight of the importance of charge transfer journal January 2018
Electron transfer characteristics of 2′-deoxy-2′-fluoro-arabinonucleic acid, a nucleic acid with enhanced chemical stability journal January 2018
Statistically representative databases for density functional theory via data science journal January 2019
How accurate are approximate quantum chemical methods at modelling solute–solvent interactions in solvated clusters? journal January 2020
Theory and practice of modeling van der Waals interactions in electronic-structure calculations journal January 2019
Low-order many-body interactions determine the local structure of liquid water journal January 2019
A model for dinitrogen binding in the E 4 state of nitrogenase journal January 2019
Chemoselective oxidative addition of vinyl sulfones mediated by palladium complexes bearing picolyl-N-heterocyclic carbene ligands. journal January 2020
Role of exact exchange in thermally-assisted-occupation density functional theory: A proposal of new hybrid schemes journal January 2017
Improving the accuracy of Møller-Plesset perturbation theory with neural networks journal October 2017
The BioFragment Database (BFDb): An open-data platform for computational chemistry analysis of noncovalent interactions journal October 2017
Assessing the performance of the Tao-Mo semilocal density functional in the projector-augmented-wave method journal July 2018
Independent amplitude approximations in coupled cluster valence bond theory: Incorporation of 3-electron-pair correlation and application to spin frustration in the low-lying excited states of a ferredoxin-type tetrametallic iron-sulfur cluster journal October 2018
Fermi-Löwdin orbital self-interaction correction to magnetic exchange couplings journal October 2018
On the geometric dependence of the molecular dipole polarizability in water: A benchmark study of higher-order electron correlation, basis set incompleteness error, core electron effects, and zero-point vibrational contributions journal November 2018
Well-behaved versus ill-behaved density functionals for single bond dissociation: Separating success from disaster functional by functional for stretched H 2 journal March 2019
Towards density functional approximations from coupled cluster correlation energy densities journal June 2019
Two single-reference approaches to singlet biradicaloid problems: Complex, restricted orbitals and approximate spin-projection combined with regularized orbital-optimized Møller-Plesset perturbation theory journal June 2019
Range-separated double-hybrid density-functional theory with coupled-cluster and random-phase approximations journal August 2019
Platinum, gold, and silver standards of intermolecular interaction energy calculations journal August 2019
Interaction between water and carbon nanostructures: How good are current density functional approximations? journal October 2019
From ab initio data to high-dimensional potential energy surfaces: A critical overview and assessment of the development of permutationally invariant polynomial potential energy surfaces for single molecules journal November 2019
Cryogenic ion vibrational predissociation (CIVP) spectroscopy of a gas-phase molecular torsion balance to probe London dispersion forces in large molecules journal December 2019
Making many-body interactions nearly pairwise additive: The polarized many-body expansion approach journal November 2019
Fantasy versus reality in fragment-based quantum chemistry journal November 2019
Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals journal April 2017
Push it to the limit: comparing periodic and local approaches to density functional theory for intermolecular interactions journal June 2018
Theoretical explanation for the DNA cleavage by GO with cation: anti-cooperativity effect among the π⋯π, cation⋯π/σ and H-bonding interactions in cytosine⋯GO⋯M n+ (M n+  = Na + , Mg 2+ , Al 3+ ) journal November 2019
Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals journal January 2020
van der Waals density functional with corrected C 6 coefficients journal May 2019
Delayed catalyst function enables direct enantioselective conversion of nitriles to NH 2 -amines journal April 2019
Towards Density Functional Approximations from Coupled Cluster Correlation Energy Densities journal April 2019
An Overview of Self-Consistent Field Calculations Within Finite Basis Sets journal March 2020
Cryogenic ion vibrational predissociation (CIVP) spectroscopy of a gas-phase molecular torsion balance to probe London dispersion forces in large molecules text January 2019
Fully numerical Hartree-Fock and density functional calculations. I. Atoms text January 2018
Fully numerical Hartree-Fock and density functional calculations. II. Diatomic molecules text January 2018
Two Single-Reference Approaches to Singlet Biradicaloid Problems: Complex, Restricted Orbitals and Approximate Spin-Projection Combined With Regularized Orbital-Optimized Møller-Plesset Perturbation Theory text January 2019
An overview of self-consistent field calculations within finite basis sets text January 2019