CFOUR | Main / Calculation Of Molecular Properties

I. Geometry Optimizations

reviews
H.B. Schlegel, Geometry Optimization, in Encyclopedia of Computational Chemistry, Eds.: P.v.R. Schleyer et al. (Wiley, 1998) p. 1136

transition-state search using eigenvector following
C.J. Cerjan and W.H. Miller, On finding transition states, J. Chem. Phys. 75, 2800 (1981)
J. Baker and P.M.W. Gill, An algorithm for the location of branching points on reaction paths, J. Comp. Chem. 9, 465 (1988)
J. Nichols, H. Taylor, P. Schmidt, and J. Simons, Walking on potential energy surfaces, J. Chem. Phys. 92, 340 (1990)

accuracy of calculated molecular geometries
T. Helgaker, J. Gauss, P. Jørgensen, and J. Olsen, The prediction of molecular equilibrium structures by the standard electronic wave functions. J. Chem. Phys. 106, 6430 (1997)
K.L. Bak, J. Gauss, P. Jørgensen, J. Olsen, T. Helgaker, and J.F. Stanton, The accurate determination of molecular equilibrium structures, J. Chem. Phys. 114, 6548 (2001)
S. Coriani, D. Marchesan, J. Gauss C. Hättig, P. Jørgensen, and T. Helgaker, The accuracy of ab initio molecular geometries for systems containing second-row atoms, J. Chem. Phys. 123, 184107 (2005)
M. Heckert, M. Kállay, and J. Gauss, Molecular equilibrium geometries based on coupled-cluster calculations including quadruple excitations, Mol. Phys. 103, 2109 (2005)
M. Heckert, M. Kállay, D.P. Tew, W. Klopper, and J. Gauss, Basis-set extrapolation techniques for the accurate calculation of molecular equilibrium geometries using coupled-cluster theory, J. Chem. Phys. 125, 044108 (2006)

intrinsic reaction coordinate and reaction path hamiltonian
K. Fukui, Formulation of the reaction coordinate, J. Phys. Chem. 74, 4161 (1970)
K. Ishida, K. Morokuma, A. Komornicki, The intrinsic reaction coordinate. An ab initio calculation for HNC→HCN and H−+CH4→CH4+H−, J. Chem. Phys. 66, 2153 (1977)
W. H. Miller, N. C. Handy, and J. E. Adams, Reaction path Hamiltonian for polyatomic-molecules, J. Chem. Phys. 72, 99 (1980)
M. Page, J. W. McIver, On evaluating the reaction path Hamiltonian, J. Chem. Phys. 88, 922 (1988)
H. P. Hratchian, H. B. Schlegel, Accurate reaction paths using a Hessian based predictor–corrector integrator, J. Chem. Phys. 120, 9918 (2004)
H. P. Hratchian, H. B. Schlegel, Using Hessian Updating To Increase the Efficiency of a Hessian Based Predictor-Corrector Reaction Path Following Method, J. Chem. Theory Comput. 1, 61 (2004)

II. Harmonic Force Fields and Vibrational Frequencies

accuracy of calculated harmonic frequencies
D.P. Tew, W. Klopper, M. Heckert, and J. Gauss, Basis set limit CCSD(T) harmonic vibrational frequencies, J. Phys. Chem. A 111, 11242 (2007)
M.H. Cortez, N.R. Brinkmann, W.F. Polik, P.R. Taylor, Y.J. Bomble, and J.F. Stanton, Factors contributing to the accuracy of harmonic force field calculations for water, J. Chem. Theor. Comp. 3, 1267 (2007)

III. Anharmonic Force Fields

general theory for vibrational perturbation theory
I.M. Mills, Vibration-rotation structure in asymmetric- and symmetric-top molecules, in Molecular Spectroscopy: Modern Research, Eds.: K.N. Rao and C.W. Mathews (Academic Press, New York, 1972), p. 115

calculation of cubic and quartic force fields
W. Schneider and W. Thiel, Anharmonic force fields from analytic second derivatives: Method and application to methyl bromide, Chem. Phys. Letters 157, 367 (1989)
J.F. Stanton, C.L. Lopreore, and J. Gauss, The equilibrium structure and fundamental vibrational frequencies of dioxirane, J. Chem. Phys. 108, 7190 (1998)
J.F. Stanton and J. Gauss, Analytic second derivatives in high-order many-body perturbation and coupled-cluster theories: Computational considerations and applications, Int. Rev. Phys. Chem. 19, 61 (2000)

IV. NMR Chemical Shift Calculations

reviews
J. Gauss, Accurate Calculation of NMR Chemical Shifts, Ber. Bunsenges. Phys. Chem. 99, 1001 (1995
T. Helgaker, M. Jaszunski, and K. Ruud, Ab Initio Methods for the Calculation of NMR Shielding and Indirect Spin−Spin Coupling Constants, Chem. Rev. 99, 293 (1999)
J. Gauss and J.F. Stanton, Electron‐correlated approaches for the calculation of NMR chemical shifts, Adv. Chem. Phys. 123, 355 (2002)
J. Gauss and J.F. Stanton, Electron‐correlated methods for the calculation of NMR chemical shifts, in Calculation of NMR and EPR Parameters: Theory and Applications, Eds.: M. Kaupp, M. Bühl and V.G. Malkin (Wiley-VCH, Weinheim, 2004) p.123

gauge-including atomic orbitals (GIAOs)
F. London, Théorie quantique des courants interatomiques dans les combinaisons aromatiques, J. Phys. Radium, 8, 397 (1937)
H.F. Hameka, On the nuclear magnetic shielding in the hydrogen molecule, Mol. Phys. 1, 203 (1958)
H.F. Hameka, Z. Naturforsch. A14, 599 (1959)
R. Ditchfield, Molecular orbital theory of magnetic shielding and magnetic susceptibility, J. Chem. Phys. 56, 5688 (1972)
R. Ditchfield, Self-consistent perturbation theory of diamagnetism. I. A gauge-invariant LCAO method for N.M.R. chemical shifts, Mol. Phys. 27, 789 (1974)
K. Wolinksi, J.F. Hinton, and P. Pulay, Efficient implementation of the gauge-independent atomic orbital method for NMR chemical shift calculations, J. Am. Chem. Soc. 112, 8251 (1990)

GIAO-HF-SCF calculations
K. Wolinski, J.F. Hinton, and P. Pulay,Efficient implementation of the gauge-independent atomic orbital method for NMR chemical shift calculations, J. Am Chem. Soc. 112, 8251 (1990)
M. Häser, R. Ahlrichs, H.P. Baron, P. Weis, and H. Horn, Direct computation of second-order SCF properties of large molecules on workstation computers with an application to large carbon clusters, Theoret. Chim. Acta 83, 455 (1992)

GIAO-MP2 calculations
J. Gauss, Calculation of NMR chemical shifts at second-order many-body perturbation theory using gauge-including atomic orbitals, Chem. Phys. Letters 191, 614 (1992)
J. Gauss, Effects of electron correlation in the calculation of nuclear magnetic resonance chemical shifts, J. Chem. Phys. 99, 3629 (1993)

GIAO-MP3 calculations
J. Gauss, GIAO-MBPT(3) and GIAO-SDQ-MBPT(4) calculations of nuclear magnetic shielding constants, Chem. Phys. Letters 229, 198 (1994)

GIAO-MP4 calculations
J. Gauss and J.F. Stanton, Perturbative treatment of triple excitations in coupled‐cluster calculations of nuclear magnetic shielding constants, J. Chem. Phys. 104, 2574 (1996)

GIAO-CCD, GIAO-QCISD, and GIAO-CCSD calculations
J. Gauss and J.F. Stanton, Gauge‐invariant calculation of nuclear magnetic shielding constants at the coupled–cluster singles and doubles level, J. Chem. Phys. 102, 251 (1995)
J. Gauss and J.F. Stanton, Coupled‐cluster calculations of nuclear magnetic resonance chemical shifts, J. Chem. Phys. 103, 3561 (1995)

GIAO-CC2 calculations
O. Christiansen, J. Gauss, and J.F. Stanton, Nuclear magnetic shielding constants in the CC2 model, Chem. Phys. Letters 266, 53 (1997)

GIAO-CCSD(T) calculations
J. Gauss and J.F. Stanton, Perturbative treatment of triple excitations in coupled‐cluster calculations of nuclear magnetic shielding constants, J. Chem. Phys. 104, 2574 (1996)

GIAO-CCSDT-n (n=1-3) and GIAO-CC3 calculations
J. Gauss and J.F. Stanton, Perturbative treatment of triple excitations in coupled‐cluster calculations of nuclear magnetic shielding consta, Phys. Chem. Chem. Phys. 2, 2047 (2000)

GIAO-CCSDT calculations
J. Gauss, Analytic second derivatives for the full coupled-cluster singles, doubles, and triples model: Nuclear magnetic shielding constants for BH, HF, CO, N2, N2O, and O3 J. Chem. Phys. 116, 4773 (2002)

GIAO calculations for general CC methods
M. Kállay and J. Gauss, Analytic second derivatives for general coupled-cluster and configuration-interaction models, J. Chem. Phys. 120, 6841 (2004)

V. Calculation of Nuclear Spin-Rotation Constants

perturbation-dependent basis functions (rotational London orbitals)
J. Gauss, K. Ruud, and T. Helgaker, Perturbation‐dependent atomic orbitals for the calculation of spin‐rotation constants and rotational g tensors, J. Chem. Phys. 105, 2804 (1996)

coupled-cluster calculations
J. Gauss and D. Sundholm, Coupled-cluster calculations of spin-rotation constants, Mol. Phys. 91, 449 (1997)

VI. Calculation of Magnetizabilities

GIAO calculations at HF-SCF level
K. Ruud, T. Helgaker, K.L. Bak, P. Jørgensen, and H.J.Aa. Jensen, Hartree–Fock limit magnetizabilities from London orbitals, J. Chem. Phys. 99, 3847 (1993)

GIAO calculations at CC/MP levels
J. Gauss, M. Kállay, and K. Ruud, Gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster level , J. Chem. Phys. 127 074101 (2007)

VII. Calculation of Rotational g Tensors

calculations using perturbation-dependent AOs at CC/MP levels
J. Gauss, M. Kállay, and K. Ruud, Gauge-origin independent calculation of magnetizabilities and rotational tensors at the coupled-cluster level, J. Chem. Phys. 127 074101 (2007)

VIII. Calculation of Indirect Spin-Spin Coupling Constants

unrelaxed CCSD and CC3 level
S.A. Perera, M. Nooijen, and R.J. Bartlett, Electron correlation effects on the theoretical calculation of nuclear magnetic resonance spin–spin coupling constants, J. Chem. Phys. 104, 3290 (1996); CCSD
A.A. Auer and J. Gauss, Triple excitation effects in coupled-cluster calculations of indirect spin–spin coupling constants, J. Chem. Phys. 115, 1619 (2001); present analytic CCSD implementation in Cfour
R. Faber, S.P.A. Sauer, and J. Gauss, Importance of Triples Contributions to NMR Spin–Spin Coupling Constants Computed at the CC3 and CCSDT Levels, J. Chem. Theory Comput. 13, 696 (2017); CC3

IX. Calculation of Magnetically Induced Current Densities

J. Jusélius, D. Sundholm, and J. Gauss, Calculation of current densities using gauge-including atomic orbitals, J. Chem. Phys. 121, 3952 (2004) (with GIAOs)

X. Calculation of Electronic g-Tensors

HF-SCF calculations
F. Neese, Prediction of electron paramagnetic resonance g values using coupled perturbed Hartree–Fock and Kohn–Sham theory, J. Chem. Phys. 115, 11080 (2001)

CC calculations
J. Gauss, M. Kállay, and F. Neese, Calculation of Electronic g-Tensors using Coupled Cluster Theory, J. Phys. Chem. A 113, 111541 (2009)

XI. Spin densities and hyperfine coupling constants within the rigorously spin-adapted COS-CC method

CCSD
D. Datta and J. Gauss, Spin densities within a unitary group based spin-adapted open-shell coupled-cluster theory: Analytic evaluation of isotropic hyperfine-coupling constants for the combinatoric open-shell coupled-cluster scheme, J. Chem. Phys. 143, 011101 (2015); implementation in CFour

CCSD(T)
D. Datta and J. Gauss, Accurate prediction of hyperfine coupling tensors for main group elements using a unitary group based rigorously spin-adapted coupled-cluster theory, J. Chem. Theory Comput. 15, 1572 (2019); implementation in CFour

XII. Frequency-Dependent Properties

CCSD frequency-dependent polarizabilities
R. Kobayashi, H. Koch, and P. Jørgensen, Calculation of frequency-dependent polarizabilities using coupled-cluster response theory, Chem. Phys. Letters 219, 30 (1994)

CC3 frequency-dependent polarizabilities
O. Christiansen, J. Gauss, and J.F. Stanton, The effect of triple excitations in coupled cluster calculations of frequency-dependent polarizabilities, Chem. Phys. Letters 292, 437 (1998)

general CC frequency-dependent polarizabilities
M. Kállay and J. Gauss, Calculation of frequency-dependent polarizabilities using general coupled-cluster models, J. Mol. Struct. (THEOCHEM), 768, 71 (2006)

CCSD frequency-dependent first hyperpolarizabilities
C. Hättig, O. Christiansen, and P. Jørgensen, Frequency-dependent first hyperpolarizabilities using coupled cluster quadratic response theory, Chem. Phys. Letters 269, 428 (1997)

CC3 frequency-dependent first hyperpolarizabilities
J. Gauss, O. Christiansen, and J.F. Stanton, Triple excitation effects in coupled-cluster calculations of frequency-dependent hyperpolarizabilities, Chem. Phys. Letters 296, 117 (1998)

general CC frequency-dependent hyperpolarizabilities
D.P. O'Neill, M. Kállay, and J. Gauss, Calculation of frequency-dependent hyperpolarizabilities using general coupled-cluster models, J. Chem. Phys. 127, 134109 (2007)

Mk-MRCCSD frequency-dependent polarizabilities
T.-C. Jagau and J. Gauss, Linear-response theory for Mukherjee's multireference coupled-cluster method: static and dynamic polarizabilities, J. Chem. Phys. 137, 044115 (2012)

XIII. Verdet constants

S. Coriani, C. Hättig, P. Jørgensen, A. Halkier, and A. Rizzo, Coupled cluster calculations of Verdet constants, Chem. Phys. Letters 281, 445 (1997)

S. Coriani, P. Jørgensen, O. Christiansen, and J. Gauss, Triple excitation effects in coupled cluster calculations of Verdet constants, Chem. Phys. Letters 330, 463 (2000)

XIV. Raman Intensities (Polarizability Derivatives)

D.P. O'Neill, M. Kállay, and J. Gauss, Analytic evaluation of Raman intensities in coupled-cluster theory, Mol. Phys. 105, 2447 (2007)

XV. Dipole Hessians (Electrical Anharmonicities)

T.-C. Jagau, J. Gauss, and K. Ruud, Analytic evaluation of the dipole Hessian matrix in coupled-cluster theory, J. Chem. Phys. 139, 154106 (2013)

XVI. Vibrational Contribution to Molecular Properties

review
T.A. Ruden and K. Ruud, Ro‐Vibrational corrections to NMR parameters, in Calculation of NMR and EPR parameters: Theory and applications, Eds.: M. Kaupp, M. Bühl, and V.G. Malkin (Wiley-VCH, Weinheim, 2004) p.153

implementation into Cfour
A.A. Auer, J. Gauss, and J.F. Stanton, Quantitative prediction of gas-phase 13C nuclear magnetic shielding constants, J. Chem. Phys. 118, 10407 (2003)