**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**

*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)`

*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)`