[1] R. Ahlrichs; M. Bär; M. Häser; H. Horn; C. Kölmel. Electronic structure calculations on workstation computers: The program system Turbomole. Chem. Phys. Lett., 162(3), 165–169, (1989).
[2] A. Schäfer; H. Horn; R. Ahlrichs. Fully optimized contracted Gaussian basis sets for atoms Li to Kr. J. Chem. Phys., 97(4), 2571–2577, (1992).
[3] A. Schäfer; C. Huber; R. Ahlrichs. Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr. J. Chem. Phys., 100(8), 5829–5835, (1994).
[4] K. Eichkorn; F. Weigend; O. Treutler; R. Ahlrichs. Auxiliary basis sets for main row atoms and transition metals and their use to approximate Coulomb potentials. Theor. Chem. Acc., 97(1–4), 119–124, (1997).
[5] F. Weigend; F. Furche; R. Ahlrichs. Gaussian basis sets of quadruple zeta valence quality for atoms H–Kr. J. Chem. Phys., 119(24), 12753–12762, (2003).
[6] F. Weigend; R. Ahlrichs. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. Phys. Chem. Chem. Phys., 7(18), 3297–3305, (2005).
[7] A. K. Rappé; C. J. Casewit; K. S. Colwell; W. A. Goddard III; W. M. Skiff. UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. J. Am. Chem. Soc., 114(25), 10024–10035, (1992).
[8] C. Hättig; F. Weigend. CC2 excitation energy calculations on large molecules using the resolution of the identity approximation. J. Chem. Phys., 113(13), 5154–5161, (2000).
[9] C. Hättig; K. Hald. Implementation of RI-CC2 for triplet excitation energies with an application to trans-azobenzene. Phys. Chem. Chem. Phys., 4(11), 2111–2118, (2002).
[10] C. Hättig; A. Köhn; K. Hald. First–order properties for triplet excited states in the approximated coupled cluster model CC2 using an explicitly spin coupled basis. J. Chem. Phys., 116(13), 5401–5410, (2002).
[11] C. Hättig. Geometry optimizations with the coupled-cluster model CC2 using the resolution-of-the-identity approximation. J. Chem. Phys., 118(17), 7751–7761, (2003).
[12] A. Köhn; C. Hättig. Analytic gradients for excited states in the coupled-cluster model CC2 employing the resolution-of-the-identity approximation. J. Chem. Phys., 119(10), 5021–5036, (2003).
[13] C. Hättig; A. Hellweg; A. Köhn. Distributed memory parallel implementation of energies and gradients for second-order Møller-Plesset perturbation theory with the resolution-of-the-identity approximation. Phys. Chem. Chem. Phys., 8(10), 1159–1169, (2006).
[14] A. Hellweg; S. Grün; C. Hättig. Benchmarking the performance of spin–component scaled CC2 in ground and electronically excited states. Phys. Chem. Chem. Phys., 10, 1159–1169, (2008).
[15] N. O. C. Winter; C. Hättig. Scaled opposite-spin CC2 for ground and excited states with fourth order scaling computational costs. J. Chem. Phys., 134, 184101, (2011).
[16] R. A. Bachorz; F. A. Bischoff; A. Glöß; C. Hättig; S. Höfener; W. Klopper; D. P. Tew. The mp2-f12 method in the turbomole programm package. J. Comput. Chem., 32, 2492–2513, (2011).
[17] D. P. Tew; W. Klopper; C. Neiss; C. Hättig. Quintuple-ζ quality coupled-cluster correlation energies with triple-ζ basis sets. Phys. Chem. Chem. Phys., 9, 1921–1930, (2007).
[18] C. Hättig; D. P. Tew; A. Köhn. Accurate and efficient approximations to explicitly correlated coupled-cluster singles and doubles, CCSD-F12. J. Chem. Phys., 132, 231102, (2010).
[19] D. P. Tew; W. Klopper. Open-shell explicitly correlated f12 methods. Mol. Phys., 108, 315–325, (2010).
[20] G. Schmitz; B. Helmich; C. Hättig. A ≀(\3)-scaling PNO-MP2 method using a hybrid OSV-PNO approach with an iterative direct generation of OSVs. Mol. Phys., 111, 2463–2473, (2013).
[21] G. Schmitz; C. Hättig; D. Tew. Explicitly correlated pno-mp2 and pno-ccsd and its application to the s66 set and large molecular systems. Phys. Chem. Chem. Phys., 16, 22167–22178, (2014).
[22] R. Bauernschmitt; R. Ahlrichs. Treatment of electronic excitations within the adiabatic approximation of time dependent density functional theory. Chem. Phys. Lett., 256(4–5), 454–464, (1996).
[23] R. Bauernschmitt; R. Ahlrichs. Stability analysis for solutions of the closed shell Kohn-Sham equation. J. Chem. Phys., 104(22), 9047–9052, (1996).
[24] F. Furche; R. Ahlrichs. Adiabatic time-dependent density functional methods for excited state properties. J. Chem. Phys., 117(16), 7433–7447, (2002).
[25] M. Kollwitz; J. Gauss. A direct implementation of the GIAO-MBPT(2) method for calculating NMR chemical shifts. Application to the naphthalenium and and anthracenium ions. Chem. Phys. Lett., 260(5–6), 639–646, (1996).
[26] C. van Wüllen. Shared-memory parallelization of the TURBOMOLE programs AOFORCE, ESCF, and EGRAD: How to quickly parallelize legacy code. J. Comp. Chem., 32, 1195–1201, (2011).
[27] M. von Arnim; R. Ahlrichs. Geometry optimization in generalized natural internal coordinates. J. Chem. Phys., 111(20), 9183–9190, (1999).
[28] P. Pulay; G. Fogarasi; F. Pang; J. E. Boggs. Systematic ab initio gradient calculation of molecular geometries, force constants, and dipole moment derivatives. J. Am. Chem. Soc., 101(10), 2550–2560, (1979).
[29] M. Dolg; U. Wedig; H. Stoll; H. Preuß. Energy-adjusted ab initio pseudopotentials for the first row transition elements. J. Chem. Phys., 86(2), 866–872, (1986).
[30] C. C. J. Roothaan. Self-consistent field theory for open shells of electronic systems. Rev. Mod. Phys., 32(2), 179–185, (1960).
[31] R. Ahlrichs; F. Furche; S. Grimme. Comment on “Assessment of exchange correlation functionals”. Chem. Phys. Lett., 325(1–3), 317–321, (2000).
[32] M. Sierka; A. Hogekamp; R. Ahlrichs. Fast evaluation of the Coulomb potential for electron densities using multipole accelerated resolution of identity approximation. J. Chem. Phys., 118(20), 9136–9148, (2003).
[33] F. Weigend. A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency. Phys. Chem. Chem. Phys., 4(18), 4285–4291, (2002).
[34] R. Fletcher. Practical Methods of Optimization. Unconstrained Optimization. Band 1. Wiley: New York, 1980.
[35] T. Helgaker. Transition-state optimizations by trust-region image minimization. Chem. Phys. Lett., 182(5), 503–510, (1991).
[36] F. Jensen. Locating transition structures by mode following: A comparison of six methods on the Ar8 Lennard-Jones potential. J. Chem. Phys., 102(17), 6706–6718, (1995).
[37] P. Császár; P. Pulay. Geometry optimization by direct inversion in the iterative subspace. J. Mol. Struct., 114, 31–34, (1984).
[38] R. Fletcher. A new approach to variable metric algorithms. Comput. J., 13(3), 317–322, (1970).
[39] H. B. Schlegel. Optimization of equilibrium geometries and transition structures. J. Comput. Chem., 3(2), 214–218, (1982).
[40] H. B. Schlegel. Estimating the hessian for gradient-type geometry optimizations. Theor. Chim. Acta, 66(5), 333–340, (1984).
[41] M. Ehrig. Diplomarbeit. Master’s thesis, Universität Karlsruhe, 1990.
[42] T. Koga; H. Kobayashi. Exponent optimization by uniform scaling technique. J. Chem. Phys., 82(3), 1437–1439, (1985).
[43] A. K. Rappé; W. A. Goddard III. Charge equilibration for molecular dynamics simulations. J. Phys. Chem., 95(8), 3358–3363, (1991).
[44] C. G. Broyden. The convergence of a class of double-rank minimization algorithms 1. General considerations. J. Inst. Math. Appl., 6(1), 76–90, (1970).
[45] D. Goldfarb. A family of variable-metric methods derived by variational means. Math. Comput., 24(109), 23–26, (1970).
[46] D. F. Shanno. Conditioning of quasi-newton methods for function minimization. Math. Comput., 24(111), 647–656, (1970).
[47] P. Pulay. Convergence acceleration of iterative sequences. the case of SCF iteration. Chem. Phys. Lett., 73(2), 393–398, (1980).
[48] M. P. Allen; D. J. Tildesley. Computer Simulation of Liquids. Oxford University Press: Oxford, 1987.
[49] M. Sierka. Synergy between theory and experiment in structure resolution of low-dimensional oxides. Prog. Surf. Sci., 85, 398–434, (2010).
[50] T. Halgren; W. Lipscomb. Synchronous-transit method for determining reaction pathways and locating molecular transition-states. Chem. Phys. Lett., 49(2), 225–232, (1977).
[51] R. Elber; M. Karplus. A method for determining reaction paths in large molecules - application to myoglobin. Chem. Phys. Lett., 139(5), 375–380, (1987).
[52] M. G; H. Jonsson. Quantum and thermal effects in h-2 dissociative adsorption - evaluation of free-energy barriers in multidimensional quantum-systems. Phys. Rev. Lett., 72(7), 1124–1127, (1994).
[53] G. Henkelman; H. Jonsson. J. Chem. Phys., 113(22), 9978–9985, (2000).
[54] E. Weinan; W. Ren; E. Vanden-Eijnden. Phys. Rev. B, 66(5), 052301, (2002).
[55] P. Plessow. Reaction Path Optimization without NEB Springs or Interpolation Algorithms. J. Chem. Theory Comput., 9(3), 1305–1310, (2013).
[56] K. Eichkorn; O. Treutler; H. Öhm; M. Häser; R. Ahlrichs. Auxiliary basis sets to approximate Coulomb potentials (erratum, 1995, 242, 283). Chem. Phys. Lett., 242(6), 652–660, (1995).
[57] J. A. Pople; R. K. Nesbet. Self-consistent orbitals for radicals. J. Chem. Phys., 22(3), 571–572, (1954).
[58] J. Čižek; J. Paldus. Stability conditions for solutions of Hartree-Fock equations for atomic and molecular systems. application to pi-electron model of cyclic plyenes. J. Chem. Phys., 47(10), 3976–3985, (1967).
[59] F. Neese; F. Wennmohs; A. Hansen; U. Becker. Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. A ’chain-of-spheres’ algorithm for the Hartree–Fock exchange. Chem. Phys., 356, 98–109, (2009).
[60] U. Ekström; L. Visscher; R. Bast; A. J. Thorvaldsen; K. Ruud. Arbitrary-order density functional response theory from automatic differentiation. J. Chem. Theory Comput., 6, 1971–1980, (2010).
[61] Y. Zhao; D. G. Truhlar. 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. Theor. Chem. Acc., 120, 215–241, (2008).
[62] P. A. M. Dirac. Quantum mechanics of many-electron systems. Proc. Royal Soc. (London) A, 123(792), 714–733, (1929).
[63] J. C. Slater. A simplification of the Hartree-Fock method. Phys. Rev., 81(3), 385–390, (1951).
[64] S. Vosko; L. Wilk; M. Nusair. Accurate spin-dependent electron-liquid correlation energies for local spin density calculations: a critical analysis. Can. J. Phys., 58(8), 1200–1211, (1980).
[65] J. P. Perdew; Y. Wang. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B, 45(23), 13244–13249, (1992).
[66] A. D. Becke. Density-functional exchange-energy approximation with correct asymptotic behaviour. Phys. Rev. A, 38(6), 3098–3100, (1988).
[67] C. Lee; W. Yang; R. G. Parr. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B, 37(2), 785–789, (1988).
[68] J. P. Perdew. Density-functional approximation for the correlation-energy of the inhomogenous electron gas. Phys. Rev. B, 33(12), 8822–8824, (1986).
[69] J. P. Perdew; K. Burke; M. Ernzerhof. Generalized gradient approximation made simple. Phys. Rev. Lett., 77(18), 3865–3868, (1996).
[70] J. Tao; J. P. Perdew; V. N. Staroverov; G. E. Scuseria. Climbing the density functional ladder: Nonempirical meta–generalized gradient approximation designed for molecules and solids. Phys. Rev. Lett., 91(14), 146401, (2003).
[71] J. Sun; A. Ruzsinszky; J. P. Perdew. Strongly constrained and appropriately normed semilocal density functional. Phys. Rev. Lett., 115, 036402, (2015).
[72] J. G. Brandenburg; J. E. Bates; J. Sun; J. P. Perdew. Benchmark tests of a strongly constrained semilocal functional with a long-range dispersion correction. Phys. Rev. B, 94, 115144, (2016).
[73] A. D. Becke. A new mixing of Hartree-Fock and local density-functional theories. J. Chem. Phys., 98(2), 1372–1377, (1993).
[74] A. D. Becke. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys., 98(7), 5648–5652, (1993).
[75] J. P. Perdew; M. Ernzerhof; K. Burke. Rationale for mixing exact exchange with density functional approximations. J. Chem. Phys., 105(22), 9982–9985, (1996).
[76] V. N. Staroverov; G. E. Scuseria; J. Tao; J. P. Perdew. Comparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes. J. Chem. Phys., 119(23), 12129–12137, (2003).
[77] S. Grimme. Semiempirical hybrid density functional with perturbative second-order correlation. J. Chem. Phys., 124, 034108, (2006).
[78] A. Görling; M. Levy. Correlation-energy functional and its high-density limit obtained from a coupling-constant perturbation expansion. Phys. Rev. B, 47, 13105, (1993).
[79] A. Görling; M. Levy. Exact Kohn-Sham scheme based on perturbation theory. Phys. Rev. A, 50, 196, (1994).
[80] J. Jaramillo; G. E. Scuseria; M. Ernzerhof. Local hybrid functionals. J. Chem. Phys., 118, 1068–1073, (2003).
[81] H. Bahmann; M. Kaupp. Efficient self-consistent implementation of local hybrid functionals. J. Chem. Theory Comput., 11, 1540–1548, (2015).
[82] S. Klawohn; H. Bahmann; M. Kaupp. Implementation of molecular gradients for local hybrid density functionals using seminumerical integration techniques. J. Chem. Theory Comput., 12, 4254–4262, (2016).
[83] T. M. Maier; H. Bahmann; M. Kaupp. Efficient semi-numerical implementation of global and local hybrid functionals for time-dependent density functional theory. J. Chem. Theory Comput., 11, 4226–4237, (2015).
[84] H. Bahmann; A. Rodenberg; A. V. Arbuznikov; M. Kaupp. A thermochemically competitive local hybrid functional without gradient corrections. J. Chem. Phys., 126, 011103, (2007).
[85] A. V. Arbuznikov; M. Kaupp. Local hybrid exchange-correlation functionals based on the dimensionless density gradient. Chem. Phys. Lett., 440, 160–168, (2007).
[86] A. V. Arbuznikov; M. Kaupp. Importance of the correlation contribution for local hybrid functionals: Range separation and self-interaction corrections. J. Chem. Phys., 136, 014111, (2012).
[87] A. V. Arbuznikov; M. Kaupp. Towards improved local hybrid functionals by calibration of exchange-energy densities. J. Chem. Phys., 141, 204101, (2014).
[88] T. M. Maier; M. Haasler; A. V. Arbuznikov; M. Kaupp. New approaches for the calibration of exchange-energy densities in local hybrid functionals. Phys. Chem. Chem. Phys., 18, 21133–21144, (2016).
[89] K. Theilacker; A. V. Arbuznikov; M. Kaupp. Gauge effects in local hybrid functionals evaluated for weak interactions and the gmtkn30 test set. Mol. Phys., 114, 1118, (2016).
[90] M. K. Armbruster; F. Weigend; C. van Wüllen; W. Klopper. Self-consistent treatment of spin-orbit interactions with efficient hartree-fock and density functional methods. Phys. Chem. Chem. Phys., 10, 1748–1756, (2008).
[91] D. Peng; M. Reiher. Exact decoupling of the relativistic fock operator. Theor. Chem. Acc., 131, 1081, (2012).
[92] D. Peng; M. Reiher. Local relativistic exact decoupling. J. Chem. Phys., 136, 244108, (2012).
[93] D. Peng; N. Middendorf; F. Weigend; M. Reiher. An efficient implementation of two-component relativistic exact-decoupling methods for large molecules. J. Chem. Phys., 138, 184105, (2013).
[94] M. K. Armbruster; W. Klopper; F. Weigend. Basis-set extensions for two-component spin-orbit treatments of heavy elements. Phys. Chem. Chem. Phys., 8, 4862–4865, (2006).
[95] M. Reiher; A. Wolf. Exact decoupling of the Dirac Hamiltonian. I. General theory. J. Chem. Phys., 121, 2037–2047, (2004).
[96] M. Reiher; A. Wolf. Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order. J. Chem. Phys., 121, 10945–10956, (2004).
[97] M. Reiher. Douglas-Kroll-Hess Theory: a relativistic electrons-only theory for chemistry. Theor. Chem. Acc., 116, 241–252, (2006).
[98] J. Hepburn; G. Scoles; R. Penco. A simple but reliable method for the prediction of intermolecular potentials. Chem. Phys. Lett., 36, 451–456, (1975).
[99] R. Ahlrichs; R. Penco; G. Scoles. Intermolecular forces in simple systems. Chem. Phys., 19, 119–130, (1977).
[100] S. Grimme. Accurate Description of van der Waals Complexes by Density Functional Theory Including Empirical Corrections. J. Comput. Chem., 25(12), 1463–1473, (2004).
[101] S. Grimme. Semiempirical GGA-type density functional constructed with a long-range dispersion contribution. J. Comput. Chem., 27(15), 1787–1799, (2006).
[102] S. Grimme; J. Antony; S. Ehrlich; H. Krieg. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys., 132, 154104, (2010).
[103] S. Grimme; S. Ehrlich; L. Goerigk. Effect of the damping function in dispersion corrected density functional theory. J. Comp. Chem., 32, 1456–1465, (2011).
[104] O. A. Vydrov; T. V. Voorhis. Nonlocal van der waals density functional: The simpler the better. J. Chem. Phys., 133, 244103, (2010).
[105] W. Hujo; S. Grimme. Comparison of the performance of dispersion-corrected density functional theory for weak hydrogen bonds. Phys. Chem. Chem. Phys., 13, 13942–13950, (2011).
[106] P. Su; H. Li. Energy decomposition analysis of covalent bonds and intermolecular interactions. J. Chem. Phys., 131, 014102, (2009).
[107] R. Łazarski; A. M. Burow; M. Sierka. Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole methods. J. Chem. Theory Comput., 11, 3029–3041, (2015).
[108] R. Łazarski; A. M. Burow; L. Grajciar; M. Sierka. Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Analytical gradients. Journal of Computational Chemistry, 37(28), 2518–2526, (2016).
[109] A. M. Burow; M. Sierka. Linear scaling hierarchical integration scheme for the exchange-correlation term in molecular and periodic systems. J. Chem. Theory Comput., 7, 3097–3104, (2011).
[110] L. Grajciar. Low-memory iterative density fitting. J. Comp. Chem., 36, 1521–1535, (2015).
[111] A. M. Burow; M. Sierka; F. Mohamed. Resolution of identity approximation for the coulomb term in molecular and periodic systems. J. Chem. Phys., 131, 214101, (2009).
[112] G. Kresse; J. Furthmüller. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mat. Sci., 6, 15–50, (1996).
[113] M. F. Peintinger; D. V. Oliveira; T. Bredow. Consistent gaussian basis sets of triple-zeta valence with polarization quality for solid-state calculations. J. Comp. Chem., 34, 451–459, (2013).
[114] F. Furche; D. Rappoport. Density functional methods for excited states: equilibrium structure and electronic spectra. In M. Olivucci, Ed., Computational Photochemistry, Band 16 von Computational and Theoretical Chemistry, Kapitel III. Elsevier, Amsterdam, 2005.
[115] F. Furche. On the density matrix based approach to time-dependent density functional theory. J. Chem. Phys., 114(14), 5982–5992, (2001).
[116] F. Furche; K. Burke. Time-dependent density functional theory in quantum chemistry. Annual Reports in Computational Chemistry, 1, 19–30, (2005).
[117] D. Rappoport; F. Furche. Excited states and photochemistry. In M. A. L. Marques; C. A. Ullrich; F. Nogueira; A. Rubio; K. Burke; E. K. U. Gross, Eds., Time-Dependent Density Functional Theory, Kapitel 22. Springer, 2005.
[118] J. E. Bates; F. Furche. Harnessing the meta-generalized gradient approximation for time-dependent density functional theory. J. Chem. Phys., 137, 164105, (2012).
[119] S. Grimme; F. Furche; R. Ahlrichs. An improved method for density functional calculations of the frecuency-dependent optical rotation. Chem. Phys. Lett., 361(3–4), 321–328, (2002).
[120] H. Weiss; R. Ahlrichs; M. Häser. A direct algorithm for self-consistent-field linear response theory and application to C60: Excitation energies, oscillator strengths, and frequency-dependent polarizabilities. J. Chem. Phys., 99(2), 1262–1270, (1993).
[121] M. Kühn; F. Weigend. Implementation of Two-component Time-Dependent Density Functional Theory in TURBOMOLE. J. Chem. Theory Comput., 9, 5341–5348, (2013).
[122] M. Kühn; F. Weigend. Two-Component Hybrid Time-Dependent Density Functional Theory within the Tamm-Dancoff Approximation. J. Chem. Phys., 142, 034116, (2015).
[123] D. Rappoport; F. Furche. Lagrangian approach to molecular vibrational raman intensities using time-dependent hybrid density functional theory. J. Chem. Phys., 126(20), 201104, (2007).
[124] F. Furche. Dichtefunktionalmethoden für elektronisch angeregte Moleküle. Theorie–Implementierung–Anwendung. PhD thesis, Universität Karlsruhe, 2002.
[125] E. R. Davidson. The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices. J. Comp. Phys., 17(1), 87–94, (1975).
[126] F. Wang; T. Ziegler. Time-dependent density functional theory based on a noncollinear formulation of the exchange-correlation potential. J. Chem. Phys., 121(24), 12191–12196, (2004).
[127] M. Kühn; F. Weigend. Phosphorescence energies of organic light-emitting diodes from spin-flip Tamm-Dancoff approximation time-dependent density functional theory. Chem. Phys. Chem., 12, 3331–3336, (2011).
[128] M. Kühn; F. Weigend. Phosphorescence lifetimes of organic light-emitting diodes from two-component time-dependent density functional theory. J. Chem. Phys., 141(22), 224302, (2014).
[129] F. Haase; R. Ahlrichs. Semidirect MP2 gradient evaluation on workstation computers: The MPGRAD program. J. Comp. Chem., 14(8), 907–912, (1993).
[130] F. Weigend; M. Häser. RI-MP2: first derivatives and global consistency. Theor. Chem. Acc., 97(1–4), 331–340, (1997).
[131] F. Weigend; M. Häser; H. Patzelt; R. Ahlrichs. RI-MP2: Optimized auxiliary basis sets and demonstration of efficiency. Chem. Phys. Letters, 294(1–3), 143–152, (1998).
[132] F. Weigend; A. Köhn; C. Hättig. Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations. J. Chem. Phys., 116(8), 3175–3183, (2001).
[133] C. L. Janssen; I. M. B. Nielsen. New diagnostics for coupled-cluster and Møller-Plesset perturbation theory. Chem. Phys. Lett., 290(4–6), 423–430, (1998).
[134] I. M. B. Nielsen; C. L. Janssen. Double-substitution-based diagnostics for coupled-cluster and Møller-Plesset perturbation theory. Chem. Phys. Lett., 310(5–6), 568–576, (1999).
[135] F. R. Manby. Density fitting in second-order linear-r12 Møller-Plesset perturbation theory. J. Chem. Phys., 119(9), 4607–4613, (2003).
[136] E. F. Valeev. Improving on the resolution of the identity in linear R12 ab initio theories. Chem. Phys. Lett., 395(4-6), 190–195, (2004).
[137] K. E. Yousaf; K. A. Peterson. Optimized auxiliary basis sets for explicitly correlated methods. J. Chem. Phys., 129(18), 184108, (2008).
[138] K. A. Peterson; T. B. Adler; H.-J. Werner. Systematically convergent basis sets for explicitly correlated wavefunctions: The atoms H, He, B–Ne, and Al–Ar. J. Chem. Phys., 128(8), 084102, (2008).
[139] W. Klopper; C. C. M. Samson. Explicitly correlated second-order Møller-Plesset methods with auxiliary basis sets. J. Chem. Phys., 116(15), 6397–6410, (2002).
[140] W. Klopper; W. Kutzelnigg. Møller-Plesset calculations taking care of the correlation cusp. Chem. Phys. Lett., 134(1), 17–22, (1987).
[141] S. Ten-no. Explicitly correlated second order perturbation theory: Introduction of a rational generator and numerical quadratures. J. Chem. Phys., 121(1), 117–129, (2004).
[142] S. F. Boys. Localized orbitals and localized adjustment functions. In P.-O. Löwdin, Ed., Quantum Theory of Atoms, Molecules and the Solid State, Page 253. Academic Press, New York, 1966.
[143] J. Pipek; P. G. Mezey. A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions. J. Chem. Phys., 90(9), 4916–4926, (1989).
[144] D. P. Tew; W. Klopper. New correlation factors for explicitly correlated electronic wave functions. J. Chem. Phys., 123(7), 074101, (2005).
[145] W. Klopper; B. Ruscic; D. P. Tew; F. A. Bischoff; S. Wolfsegger. Atomization energies from coupled-cluster calculations augmented with explicitly-correlated perturbation theory. Chem. Phys., 356(1–3), 14–24, (2009).
[146] F. A. Bischoff; S. Höfener; A. Glöß; W. Klopper. Explicitly correlated second-order perturbation theory calculations on molecules containing heavy main-group elements. Theor. Chem. Acc., 121(1), 11–19, (2008).
[147] S. Höfener; F. A. Bischoff; A. Glöß; W. Klopper. Slater-type geminals in explicitly-correlated perturbation theory: application to n-alkanols and analysis of errors and basis-set requirements. Phys. Chem. Chem. Phys., 10(23), 3390–3399, (2008).
[148] O. Christiansen; H. Koch; P. Jørgensen. The second-order approximate coupled cluster singles and doubles model CC2. Chem. Phys. Lett., 243(5–6), 409–418, (1995).
[149] W. Klopper; F. R. Manby; S. Ten-no; E. F. Valeev. R12 methods in explicitly correlated molecular electronic structure theory. Int. Rev. Phys. Chem., 25(3), 427–468, (2006).
[150] C. Hättig; A. Köhn. Transition moments and excited state first-order properties in the second-order coupled cluster model CC2 using the resolution of the identity approximation. J. Chem. Phys., 117(15), 6939–6951, (2002).
[151] T. Helgaker; P. Jørgensen; J. Olsen. Molecular Electronic-Structure Theory. Wiley: New York, 2000.
[152] O. Christiansen; P. Jørgensen; C. Hättig. Response functions from Fourier component variational perturbation theory applied to a time-averaged quasienergy. Int. J. Quantum Chem., 68(1), 1–52, (1998).
[153] C. Hättig; P. Jørgensen. Derivation of coupled cluster excited states response functions and multiphoton transition moments between two excited states as derivatives of variational functionals. J. Chem. Phys., 109(21), 9219–9236, (1998).
[154] C. Hättig; O. Christiansen; P. Jørgensen. Multiphoton transition moments and absorption cross section in coupled cluster response theory employing variational transition moment functionals. J. Chem. Phys., 108(20), 8331–8354, (1998).
[155] H. Koch; P. Jørgensen. Coupled cluster response functions. J. Chem. Phys., 93, 3333, (1990).
[156] C. Hättig; O. Christiansen; P. Jørgensen. Coupled cluster response calculations of twophoton transition probability rate constants for helium, neon and argon. J. Chem. Phys., 108, 8355–8359, (1998).
[157] D. H. Friese; C. Hättig; K. Ruud. Calculation of two-photon absorption strengths with the approximate coupled cluster singles and doubles model cc2 using the resolution-of-identity approximation. Phys. Chem. Chem. Phys., 14, 1175–1184, (2012).
[158] B. Helmich-Paris; C. Hättig; C. van Wüllen. Spin-free cc2 implementation of induced transitions between singlet ground and triplet excited states. J. Chem. Theory Comput., 12(4), 1892–1904, (2016).
[159] C. Hättig. Structure optimizations for excited states with correlated second-order methods: CC2, CIS(D∞), and ADC(2). Adv. Quant. Chem., 50, 37–60, (2005).
[160] S. Grimme; E. Ugorodina. Calculation of 0-0 excitation energies of organic molecules by CIS(D) quantum chemical methods. Chem. Phys., 305, 223–230, (2004).
[161] Y. M. Rhee; M. Head-Gordon. Scaled second–order perturbation corrections to configuration interaction singles: Efficient and reliable excitation energy methods. J. Phys. Chem. A, 111, 5314–5326, (2007).
[162] H. Fliegl; C. Hättig; W. Klopper. Coupled–cluster theory with simplified linear-r12 corrections: The CCSD(R12) model. J. Chem. Phys., 122, 084107, (2005).
[163] T. Shiozaki; M. Kamiya; S. Hirata; E. F. Valeev. Explicitly correlated coupled-cluster singles and doubles method based on complete diagrammatic equations. J. Chem. Phys., 129, 071101, (2008).
[164] A. Köhn; G. W. Richings; D. P. Tew. Implementation of the full explicitly correlated coupled-cluster singles and doubles model CCSD-F12 with optimally reduced auxiliary basis dependence. J. Chem. Phys., 129, 201103, (2008).
[165] T. B. Adler; G. Knizia; H.-J. Werner. A simple and efficient ccsd(t)-f12 approximation. J. Chem. Phys., 127, 221106, (2007).
[166] G. Knizia; T. B. Adler; H.-J. Werner. Simplified ccsd(t)-f12 methods: Theory and benchmarks. J. Chem. Phys., 130, 054104, (2009).
[167] M. Torheyden; E. F. Valeev. Variational formulation of perturbative explicitly-correlated coupled-cluster methods. Phys. Chem. Chem. Phys., 10, 3410–3420, (2008).
[168] E. F. Valeev; D. Crawford. Simple coupled-cluster singles and doubles method with perturbative inclusion of triples and explicitly correlated geminals: The ccsd(t) model. J. Chem. Phys., 128, 244113, (2008).
[169] K. D. Vogiatzis; E. C. Barnes; W. Klopper. Interference-corrected explicitly-correlated second-order perturbation theory. Chem. Phys. Lett., 503(1-3), 157–161, (2011).
[170] H. Eshuis; J. Yarkony; F. Furche. Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration. J. Chem. Phys., 132, 234114, (2010).
[171] H. Eshuis; J. E. Bates; F. Furche. Electron correlation methods based on the random phase approximation. Theor. Chem. Acc., 131, 1084, (2012).
[172] A. M. Burow; J. E. Bates; F. Furche; H. Eshuis. Analytical first-order molecular properties and forces within the adiabatic connection random phase approximation. J. Chem. Theory Comput., 0, just accepted, DOI: 10.1021/ct4008553, (0).
[173] M. Kühn. Correlation Energies from the Two-component Random Phase Approximation. J. Chem. Theory Comput., 10, 623–633, (2014).
[174] F. Furche. Molecular tests of the random phase approximation to the exchange-correlation energy functional. Phys. Rev. B, 64, 195120, (2001).
[175] F. Furche. Developing the random phase approximation into a practical post-Kohn–Sham correlation model. J. Chem. Phys., 129, 114105, (2008).
[176] M. J. van Setten; F. Weigend; F. Evers. The gw-method for quantum chemistry applications: Theory and implementation. J. Chem. Theory Comput, 9, 232, (2013).
[177] M. Kühn; F. Weigend. One-Electron Energies from the Two-Component GW Method. J. Chem. Theory Comput., 11, 969–979, (2015).
[178] K. Krause; W. Klopper. Implementation of the bethe-salpeter equation in the turbomole program. J. Comp. Chem., 38, 383–388, (2017).
[179] P. Deglmann; F. Furche; R. Ahlrichs. An efficient implementation of second analytical derivatives for density functional methods. Chem. Phys. Lett., 362(5–6), 511–518, (2002).
[180] P. Deglmann; F. Furche. Efficient characterization of stationary points on potential energy surfaces. J. Chem. Phys., 117(21), 9535–9538, (2002).
[181] M. Bürkle; J. Viljas; T. Hellmuth; E. Scheer; F. Weigend; G. Schön; F. Pauly. Influence of vibrations on electron transport through nanoscale contacts. Phys. Status Solidi B, 250, 2468, (2013).
[182] M. Häser; R. Ahlrichs; H. P. Baron; P. Weis; H. Horn. Direct computation of second-order SCF properties of large molecules on workstation computers with an application to large carbon clusters. Theor. Chim. Acta, 83(5–6), 455–470, (1992).
[183] T. Ziegler; G. Schreckenbach. Calculation of NMR shielding tensors using gauge-including atomic orbitals and modern density functional theory. J. Phys. Chem., 99(2), 606–611, (1995).
[184] A. Klamt; G. Schüürmann. COSMO: A new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient. J. Chem. Soc. Perkin Trans.2, (5), 799–805, (1993).
[185] A. Klamt; C. Moya; J. Palomar. A comprehensive comparison of the iefpcm and ss(v)pe continuum solvation methods with the cosmo approach. J. Chem. Theory Comput., 11(9), 4220–4225, (2015).
[186] A. Klamt; V. Jonas. Treatment of the outlying charge in continuum solvation models. J. Chem. Phys., 105(22), 9972–9981, (1996).
[187] A. Klamt. Calculation of UV/Vis spectra in solution. J. Phys. Chem., 100(9), 3349–3353, (1996).
[188] F. J. Olivares del Valle; J. Tomasi. Electron correlation and solvation effects. I. Basic formulation and preliminary attempt to include the electron correlation in the quantum mechanical polarizable continuum model so as to study solvation phenomena. Chem. Phys., 150(2), 139–150, (1991).
[189] J. G. Ángyán. Rayleigh-Schrödinger perturbation theory for nonlinear Schrödinger equations with linear perturbation. Int. J. Quantum Chem., 47(6), 469–483, (1993).
[190] J. G. Ángyán. Choosing between alternative MP2 algorithms in the self-consistent reaction field theory of solvent effects. Chem. Phys. Lett., 241(1–2), 51–56, (1995).
[191] R. Cammi; B. Mennucci; J. Tomasi. Second-order Møller-Plesset analytical derivatives for the polarizable continuum model using the relaxed density approach. J. Phys. Chem. A, 103(45), 9100–9108, (1999).
[192] G. Scalmani; M. J. Frisch; B. Mennucci; J. Tomasi; R. Cammi; V. Barone. Geometries and properties of excited states in the gas phase and in solution: Theory and application of a time-dependent density functional theory polarizable continuum model. J. Chem. Phys., 124(9), 094107, (2006).
[193] S. Sinnecker; A. Rajendran; A. Klamt; M. Diedenhofen; F. Neese. Calculation of solvent shifts on electronic g-tensors with the Conductor-like Screening Model (COSMO) and its self-consistent generalization to real solvents (Direct COSMO-RS). J. Phys. Chem. A, 110, 2235–2245, (2006).
[194] F. Eckert; A. Klamt. Fast solvent screening via quantum chemistry: COSMO-RS approach. AICHE Journal, 48, 369–385, (2002).
[195] A. Klamt; V. Jonas; T. Bürger; J. C. W. Lohrenz. Refinement and parametrization of COSMO-RS. J. Phys. Chem. A, 102, 5074–5085, (1998).
[196] P. Cortona. Self-consistently determined properties of solids without band-structure calculations. Phys. Rev. B, 44, 8454, (1991).
[197] T. A. Wesolowski; A. Warshel. Frozen density functional approach for ab initio calculations of solvated molecules. J. Phys. Chem., 97, 8050, (1993).
[198] T. A. Wesolowski. In J. Leszczynski, Ed., Chemistry: Reviews of Current Trends, Band 10, Page 1. World Scientific: Singapore, 2006, Singapore, 2006.
[199] T. A. Wesolowski; A. Warshel. Kohn–Sham equations with constrained electron density: an iterative evaluation of the ground-state electron density of interacting molecules. Chem. Phys. Lett., 248, 71, (1996).
[200] S. Laricchia; E. Fabiano; F. Della Sala. Frozen density embedding with hybrid functionals. J. Chem. Phys., 133, 164111, (2010).
[201] S. Laricchia; E. Fabiano; F. Della Sala. Frozen density embedding calculations with the orbital-dependent localized Hartree–Fock Kohn–Sham potential. Chem. Phys. Lett., 518, 114, (2011).
[202] L. A. Constantin; E. Fabiano; S. Laricchia; F. Della Sala. Semiclassical neutral atom as a reference system in density functional theory. Phys. Rev. Lett., 106, 186406, (2011).
[203] S. Laricchia; E. Fabiano; L. A. Constantin; F. Della Sala. Generalized gradient approximations of the noninteracting kinetic energy from the semiclassical atom theory: Rationalization of the accuracy of the frozen density embedding theory for nonbonded interactions. J. Chem. Theory Comput., 7, 2439, (2011).
[204] A. Lembarki; H. Chermette. Obtaining a gradient-corrected kinetic-energy functional from the Perdew-Wang exchange functional. Phys. Rev. A, 50, 5328, (1994).
[205] M. Sierka; A. Burow; J. Döbler; J. Sauer. Point defects in CeO2 and CaF2 investigated using periodic electrostatic embedded cluster method. J. Chem. Phys., 130(17), 174710, (2009).
[206] K. N. Kudin; G. E. Scuseria. A fast multipole method for periodic systems with arbitrary unit cell geometries. Chem. Phys. Lett., 283, 61–68, (1998).
[207] P. Ewald. Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann. Phys., 64, 253–287, (1921).
[208] J. M. Olsen; K. Aidas; J. Kongsted. Excited states in solution through polarizable embedding. J. Chem. Theory Comput, 6, 3721–3734, (2010).
[209] K. Sneskov; T. Schwabe; J. Kongsted; O. Christiansen. Scrutinizing the effects of polarization in QM/MM excited state calculations. J. Chem. Phys., 134, 104108, (2011).
[210] T. Schwabe; K. Sneskov; J. M.Olsen; J. Kongsted; O. Christiansen; C. Hättig. PERI-CC2: A polarizable embedded RI-CC2 method. J. Chem. Theory Comput., 8, 3274–3283, (2012).
[211] K. Krause; W. Klopper. Communication: A simplified coupled-cluster lagrangian for polarizable embedding. J. Chem. Phys., 144, 041101, (2016).
[212] L. Gagliardi; R. Lindh; G. Karlström. Local properties of quantum chemical systems: The LoProp approach. J. Chem. Phys., 121, 4494–5000, (2004).
[213] A. E. Reed; R. B. Weinstock; F. Weinhold. Natural population analysis. J. Chem. Phys., 83(2), 735–746, (1985).
[214] C. Ehrhardt; R. Ahlrichs. Population Analysis Based on Occupation Numbers. II. Relationship between Shared Electron Numbers and Bond Energies and Characterization of Hypervalent Contributions. Theor. Chim. Acta, 68(3), 231–245, (1985).
[215] G. Knizia. Intrinsic atomic orbitals: An unbiased bridge between quantum theory and chemical concepts. J. Chem. Theory Comput., 9, 4834–4843, (2013).
[216] A. V. Luzanov; A. A. Sukhorukov; V. E. Úmanskii. Application of transition density matrix for analysis of excited states. Theor. Exp. Chem., 10, 354, (1976).
[217] R. L. Martin. Natural transition orbitals. J. Chem. Phys., 118, 4775, (2003).
[218] F. Weigend; C. Schrodt. Atom-type assignment in molecule and clusters by pertubation theory— A complement to X-ray structure analysis. Chem. Eur. J., 11(12), 3559–3564, (2005).
[219] F. D. Sala; A. Görling. Efficient localized Hartree-Fock methods as effective exact-exchange Kohn-Sham methods for molecules. J. Chem. Phys., 115(13), 5718–5732, (2001).
[220] A. Görling. Orbital- and state-dependent functionals in density-functional theory. J. Chem. Phys., 123(6), 062203, (2005).
[221] S. Kümmel; L. Kronik. Orbital-dependent density functionals: Theory and applications. Rev. Mod. Phys., 80(1), 3, (2008).
[222] F. Della Sala. Orbital-dependent exact-exchange mmethods in density functional theory. In M. Springborg, Ed., Chemical Modelling: Applications and Theory, Band 7, Pages 115–161. Royal Society of Chemistry, 2010.
[223] A. Heßelmann; A. W. Götz; F. Della Sala; A. Görling. Numerically stable optimized effective potential method with balanced gaussian basis sets. J. Chem. Phys., 127(5), 054102, (2007).
[224] J. B. Krieger; Y. Li; G. J. Iafrate. Construction and application of an accurate local spin-polarized kohn-sham potential with integer discontinuity: Exchange-only theory. Phys. Rev. A, 45, 101, (1992).
[225] O. V. Gritsenko; E. J. Baerends. Orbital structure of the kohn-sham exchange potential and exchange kernel and the field-counteracting potential for molecules in an electric field. Phys. Rev. A, 64, 042506, (2001).
[226] A. F. Izmaylov; V. N. Staroverov; G. E. Scuseria; E. R. Davidson; G. Stoltz; E. Cancès. The effective local potential method: Implementation for molecules and relation to approximate optimized effective potential techniques. J. Chem. Phys., 126(8), 084107, (2007).
[227] F. Della Sala; A. Görling. The asymptotic region of the Kohn-Sham exchange potential in molecules. J. Chem. Phys., 116(13), 5374–5388, (2002).
[228] F. Della Sala; A. Görling. Asymptotic behavior of the Kohn-Sham exchange potential. Phys. Rev. Lett., 89, 033003, (2002).
[229] W. Hieringer; F. Della Sala; A. Görling. Density-functional calculations of NMR shielding constants using the localized Hartree–Fock method. Chem. Phys. Lett., 383(1-2), 115–121, (2004).
[230] E. Fabiano; M. Piacenza; S. D’Agostino; F. Della Sala. Towards an accurate description of the electronic properties of the biphenylthiol/gold interface: The role of exact exchange. J. Chem. Phys., 131(23), 234101, (2009).
[231] F. Della Sala; E. Fabiano. Accurate singlet and triplet excitation energies using the Localized Hartree-Fock Kohn-Sham potential. Chem. Phys., 391(1), 19 – 26, (2011).
[232] O. Treutler; R. Ahlrichs. Efficient molecular numerical integration schemes. J. Chem. Phys., 102(1), 346–354, (1995).
[233] A. D. Becke. A multicenter numerical integration scheme for polyatomic molecules. J. Chem. Phys., 88(4), 2547–2553, (1988).
[234] A. T. B. Gilbert; N. A. Besley; P. M. W. Gill. Self-Consistent Field Calculations of Excited States Using the Maximum Overlap Method (MOM). J. Phys. Chem. A, 112, 13164–13171, (2008).
[235] A. Wolf; M. Reiher; B. Hess. The generalized Douglas-Kroll transformation. J. Chem. Phys., 117, 9215–9226, (2002).
[236] R. Send; F. Furche. First-order nonadiabatic couplings from time-dependent hybrid density functional response theory: Consistent formalism, implementation, and performance. J. Phys. Chem., 132, 044107, (2010).
[237] C. Hättig; D. P. Tew; B. Helmich. Local explicitly correlated second- and third-order møller–plesset perturbation theory with pair natural orbitals. J. Chem. Phys., 146, 204105, (2012).
[238] J. C. Tully. Molecular dynamics with electronic transitions. J. Chem. Phys., 93, 1061, (1990).
[239] E. Tapavicza; I. Tavernelli; U. Rothlisberger. Trajectory surface hopping within linear response time-dependent density-functional theory. Phys. Rev. Lett., 98, 023001, (2007).
[240] E. Tapavicza; A. M. Meyer; F. Furche. Unravelling the details of vitamin D photosynthesis by non-adiabatic molecular dynamics simulations. Phys. Chem. Chem. Phys., 13, 20986, (2011).
[241] B. G. Levine; C. Ko; J. Quenneville; T. J. Martinez. Conical intersections and double excitations in density functional theory. Mol. Phys., 104, 1039, (2006).
[242] E. Tapavicza; I. Tavernelli; U. Rothlisberger; C. Filippi; M. E. Casida. Mixed time-dependent density-functional theory/classical trajectory surface hopping study of oxirane photochemistry. J. Chem. Phys., 129(12), 124108, (2008).