1.5 How to Quote Usage of Turbomole

Please quote the usage of the program package under consideration of the version number:

A LaTeX template could look like this:
@misc{TURBOMOLE,
title = {{TURBOMOLE V8.0 2025}, a development of {University of Karlsruhe} and
{Forschungszentrum Karlsruhe GmbH}, 1989-2007,
{TURBOMOLE GmbH}, since 2007; available from \\
{\tt https://www.turbomole.org}.}}
In addition, we kindly ask to cite the recent review of the TURBOMOLE project [2]

A LaTeX template for this review could look like this:

@Article{	  Franzke.Holzer.ea:TURBOMOLE.2023,
  author	= {Franzke, Yannick J. and Holzer, Christof and Andersen,
		  Josefine H. and Begu\v{s}i\'c, Tomislav and Bruder, Florian and
		  Coriani, Sonia and Della Sala, Fabio and Fabiano, Eduardo
		  and Fedotov, Daniil A. and F{\"u}rst, Susanne and Gillhuber,
		  Sebastian and Grotjahn, Robin and Kaupp, Martin and Kehry,
		  Max and Krsti\'c, Marjan and Mack, Fabian and Majumdar,
		  Sourav and Nguyen, Brian D. and Parker, Shane M. and Pauly,
		  Fabian and Pausch, Ansgar and Perlt, Eva and Phun, Gabriel
		  S. and Rajabi, Ahmadreza and Rappoport, Dmitrij and Samal,
		  Bibek and Schrader, Tim and Sharma, Manas and Tapavicza,
		  Enrico and Treß, Robert S. and Voora, Vamsee and
		  Wody{\'n}ski, Artur and Yu, Jason M. and Zerulla, Benedikt and
		  Furche, Filipp and H{\"a}ttig, Christof and Sierka, Marek and
		  Tew, David P. and Weigend, Florian},
  title		= {{TURBOMOLE}: {T}oday and {T}omorrow},
  journal	= {J. Chem. Theory Comput.},
  volume	= {19},
  number	= {20},
  pages		= {6859--6890},
  year		= {2023},
  doi		= {10.1021/acs.jctc.3c00347},
  url		= { https://doi.org/10.1021/acs.jctc.3c00347}
}

Scientific publications require proper citation of methods and procedures employed. The output headers of TURBOMOLE modules include the relevant papers. One may also use the following connections between: method [module] number in the subsequent list (For module ricc2 see also Section link).

• Programs and methods

  • general program structure and features: 1.5

  • HF-SCF [dscf, ridft]: 1.5

  • DFT (quadrature) [dscf, ridft, escf, aoforce]: 1.5, 1.5 (m grids), 1.5 (a grids)

  • RI-DFT [ridft, aoforce, escf, riper]: 1.5, 1.5, 1.5 (marij),  1.5 (escf), 1.5 (aoforce)

  • periodic DFT [riper]: 1.5, 1.5, 1.5, 1.5

  • MP2 [mpgrad]: 1.5

  • RI-MP2 [ricc2]: energies and gradients  1.5, 1.5, 1.5, and (static) polarizabilities 1.5

  • PNO-MP2 [pnoccsd]: energies 1.5

  • stability analysis [escf]: 1.5

  • electronic excitations with CIS, RPA, TD-DFT [escf]: 1.5, 1.5, 1.5, 1.5

  • excited state structures and properties with CIS, RPA, TD-DFT [egrad]: 1.5,
    1.5, 1.5

  • RI-CC2 [ricc2]: 

    • singlet 1.5 and triplet excitation energies 1.5

    • transition moments and first-order properties of excited states 1.5 and first-order properties for triplet states 1.5

    • ground state geometry optimizations 1.5

    • excited state geometry optimizations and relaxed properties 1.5

    • parallelization 1.5

    • spin-component scaled (SCS) variants 1.5

    • frequency-dependent and static polarizabilities 1.5

  • RI-ADC(2), RI-CIS(D) and RI-CIS(D\(_\infty\)) [ricc2]:  1.5

  • SOS variants of MP2, CIS(D), CIS(D\(_\infty\)), ADC(2) and CC2 with \({\cal O}({\cal N}^4)\)-scaling 1.5

  • analytical second derivatives (force fields) [aoforce]: 1.5, 1.5

  • RI-JK [ridft]: 1.5

  • NMR chemical shifts and EPR properties [mpshift]: 1.5,  1.5,  1.5,  1.5,  1.5,  1.5 (HF, DFT)  1.5,  1.5 (MP2)

  • parallel DFT [ridft]: 1.5

  • geometry optimization in redundant internal coordinates [relax]: 1.5

  • RI integral evaluation: 1.5

  • explicitly correlated F12 methods for ground state energies [ccsdf12  and  pnoccsd]:
    MP2-F12 1.5, PNO-MP2-F12 1.5, MP3-F12 1.5, MP4(F12*) 1.5, CCSD(F12) 1.5, CCSD(F12*) 1.5, CCSD(F12)(T) 1.5, CCSD(F12*)(T) 1.5

  • Relativistic approaches: 1.5, 1.5, 1.5, 1.5, 1.5 ([dscf, ridft, etc.]),
     1.5, 1.5,([grad, rdgrad, etc.]),  1.5,  1.5,  1.5  1.5 ([mpshift])

  • Local hybrid calculations: 1.5,  1.5 ([ridft]),  1.5,  1.5 ([grad, rdgrad]),  1.5,  1.5,  1.5,  1.5 ([escf]),  1.5 ([egrad]),

  • Seminumerical and pseudospectral methods:  1.5,  1.5 ([ridft, rdgrad]),  1.5 ([escf,  egrad,  aoforce])

• Orbital and auxiliary basis sets

  • basis sets:

    • SV, SV(P), SVP, DZ (1.5), TZV, TZVP, TZVPP (1.5), TZVPP(Rb-Hg) (1.5), QZV, QZVP, QZVPP (1.5)

    • new balanced basis sets (with smaller ECPs, i.e. the def2 basis sets): 1.5

    • all-electron basis sets for Rb to Xe (SVPall, SVPPall, TZVPall, TZVPPall): 1.5

    • references for the correlation consistent basis sets (cc-pVXZ, etc.) can be found e.g. at
      http://tyr0.chem.wsu.edu/~kipeters/Pages/cc_append.html,

      or http://www.grant-hill.group.shef.ac.uk/ccrepo/, or
      http://www.emsl.pnl.gov/forms/basisform.html.
      Note, that most of the correlation consistent basis sets in the basis set exchange library of TURBOMOLE have been downloaded from the latter EMSL web site and therefore users are requested to include in addition to the original scientific reference an appropriate citation (see web site for details) in any publications resulting from the use of these basis sets. See [3] for the current version of the basis set exchange library and [4] for previous versions. The same applies to the polarization consistent (pc, pcseg, pcSseg, pcJ, pcH, pcX), IGLO (IGLO-II, IGLO-III), and Pople (6-31G, N07D-B3LYP, N07D-PBE0, etc.) basis sets.

    • property–optimized augmentations: def2-SVPD, def2-TZVPD, def2-TZVPPD, def2-QZVPD,def2-QZVPPD (1.5).

    • basis sets for Dirac–Fock ECPs, i.e. the dhf basis sets: 1.5.

    • basis sets for relativistic all-electron approaches, i.e. the x2c-XVPall (X=S, TZ, QZ) basis sets: 1.5, 1.5 and their extensions for NMR shielding constants 1.5, 1.5. Also partly available in decontracted form (-unc, for light elements).

    • decontracted basis sets of Dyall and co-workers (dyall-vdz, dyall-vtz, dyall-vqz) for all elements (H–Rn) from
      http://doi.org/10.1080/00268976.2023.2245061.

  • auxiliary basis sets for RI-DFT: 1.5, 1.5, 1.5

  • auxiliary basis sets for RI-MP2: 1.5, 1.5, 1.5 (for Dunning basis sets)

Further references of papers not from the TURBOMOLE group are given in the bibliography.

The following publications describe details of the methodology implemented in TURBOMOLE:

Methods

1. Electronic Structure Calculations on Workstation Computers: The Program System TURBOMOLE. R. Ahlrichs, M. Bär, M. Häser, H. Horn and C. Kölmel; Chem. Phys. Lett., 162, 165 (1989).

2. Improvements on the Direct SCF Method. M. Häser and R. Ahlrichs; J. Comput. Chem., 10, 104 (1989).

3. Semi-direct MP2 Gradient Evaluation on Workstation Computers: The MPGRAD Program. F. Haase and R. Ahlrichs; J. Comp. Chem., 14, 907 (1993).

4. Efficient Molecular Numerical Integration Schemes.
   O. Treutler and R. Ahlrichs; J. Chem. Phys., 102, 346 (1995).

5. Auxiliary Basis Sets to Approximate Coulomb Potentials.

   K. Eichkorn, O. Treutler, H. Öhm, M. Häser and R. Ahlrichs; Chem. Phys. Lett., 242, 652 (1995).

6. Auxiliary basis sets for main row atoms and transition metals and their use to approximate Coulomb potentials. K. Eichkorn, F. Weigend, O. Treutler and R. Ahlrichs; Theor. Chem. Acc., 97, 119 (1997).

7. Error-consistent segmented contracted all-electron relativistic basis sets of double- and triple-zeta quality for NMR shielding constants.
   Y. J. Franzke, R. Treß, T. M. Pazdera and F. Weigend; Phys. Chem. Chem. Phys., 21, 16658–16664 (2019).

8. Stability Analysis for Solutions of the Closed Shell Kohn–Sham Equation. R. Bauernschmitt and R. Ahlrichs; J. Chem. Phys., 104, 9047 (1996).

9. Treatment of Electronic Excitations within the Adiabatic Approximation of Time Dependent Density Functional Theory.
   R. Bauernschmitt and R. Ahlrichs; Chem. Phys. Lett., 256, 454 (1996).

10. Calculation of excitation energies within time-dependent density functional theory using auxiliary basis set expansions. R. Bauernschmitt, M. Häser, O. Treutler and R. Ahlrichs; Chem. Phys. Lett., 264, 573 (1997).

11. RI-MP2: first derivatives and global consistency. F. Weigend and M. Häser; Theor. Chem. Acc., 97, 331 (1997).

12. RI-MP2: Optimized Auxiliary Basis Sets and Demonstration of Efficiency. F. Weigend, M. Häser, H. Patzelt and R. Ahlrichs; Chem. Phys. Lett., 294, 143 (1998).

13. Direct computation of second-order SCF properties of large molecules on workstation computers with an application to large carbon clusters. M. Häser, R. Ahlrichs, H. P. Baron, P. Weis and H. Horn; Theoret. Chim. Acta, 83, 455 (1992).

14. Calculation of Magnetic Shielding Constants with meta-GGA Functionals Employing the Multipole-Accelerated Resolution of the Identity: Implementation and Assessment of Accuarcy and Efficiency. K. Reiter, F. Mack and F. Weigend; J.. Chem. Theory Comput., 14, 191 (2018).

15. Paramagnetic NMR Shielding Tensors and Ring Currents: Efficient Implementation and Application to Heavy Element Compounds. S. Gillhuber, Y. J. Franzke, and F. Weigend; J. Phys. Chem. A 125, 9707 (2021).

16. Paramagnetic NMR Shielding Tensors Based on Scalar Exact Two-Component and Spin–Orbit Perturbation Theory. F. Bruder, Y. J. Franzke, and F. Weigend; J. Phys. Chem. A 126, 5050 (2022).

17. Paramagnetic NMR Shielding Tensors Based on Scalar Exact Two-Component and Spin–Orbit Perturbation Theory. Y. J. Franzke, F. Bruder, S. Gillhuber, C. Holzer, and F. Weigend; J. Phys. Chem. A 128, 670 (2024).

18. Impact of the current density on paramagnetic NMR properties. Y. J. Franzke and C. Holzer; J.. Chem. Phys. 157, 031102 (2022).

19. A direct implementation of the GIAO-MBPT(2) method for calculating NMR chemical shifts. Application to the naphthalenium and anthracenium ions. M. Kollwitz and J. Gauss; Chem. Phys. Lett., 260, 639 (1996).

20. Non-Abelian point group symmetry in direct second-order many-body perturbation theory calculations of NMR chemical shifts. M. Kollwitz, M. Häser and J. Gauss; J. Chem. Phys., 108, 8295 (1998).

21. Parallelization of Density Functional and RI-Coulomb Approximation in Turbomole. M. v. Arnim and R. Ahlrichs; J. Comp. Chem., 19, 1746 (1998).

22. Geometry optimization in generalized natural internal Coordinates.
    M. v. Arnim and R. Ahlrichs; J. Chem. Phys., 111, 9183 (1999).

23. CC2 excitation energy calculations on large molecules using the resolution of the identity approximation. C. Hättig and F. Weigend; J. Chem. Phys., 113, 5154 (2000).

24. Implementation of RI-CC2 for triplet excitation energies with an application to trans-azobenzene. C. Hättig and K. Hald; Phys. Chem. Chem. Phys., 4 2111 (2002).

25. First-order properties for triplet excited states in the approximated Coupled Cluster model CC2 using an explicitly spin coupled basis. C. Hättig, A. Köhn and K. Hald; J. Chem. Phys., 116, 5401 (2002) and Vir. J. Nano. Sci. Tech., 5 (2002).

26. Transition moments and excited-state first-order properties in the coupled-cluster model CC2 using the resolution-of-the-identity approximation.
    C. Hättig and A. Köhn; J. Chem. Phys., 117, 6939 (2002).

27. An efficient implementation of second analytical derivatives for density functional methods. P. Deglmann, F. Furche and R. Ahlrichs; Chem. Phys. Lett., 362, 511 (2002).

28. Efficient characterization of stationary points on potential energy surfaces.
    P. Deglmann and F. Furche; J. Chem. Phys., 117, 9535 (2002).

29. A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency. F. Weigend; Phys. Chem. Chem. Phys., 4, 4285 (2002).

30. An improved method for density functional calculations of the frequency-depen­dent optical rotation.
    S. Grimme, F. Furche and R. Ahlrichs; Chem. Phys. Lett., 361, 321 (2002).

31. Adiabatic time-dependent density functional methods for excited state properties. F. Furche and R. Ahlrichs; J. Chem. Phys. 117, 7433 (2002), J. Chem. Phys., 121, 12772 (2004) (E).

32. Geometry optimizations with the coupled-cluster model CC2 using the re­so­lu­tion-of-the-identity approximation. C. Hättig; J. Chem. Phys., 118, 7751, (2003).

33. Analytic gradients for excited states in the coupled-cluster model CC2 employing the resolution-of-the-identity approximation. A. Köhn and C. Hättig; J. Chem. Phys., 119, 5021, (2003).

34. Fast evaluation of the Coulomb potential for electron densities using multipole accelerated resolution of identity approximation. M. Sierka, A. Hogekamp and R. Ahlrichs; J. Chem. Phys., 118, 9136, (2003).

35. Nuclear second analytical derivative calculations using auxiliary basis set expansion. P. Deglmann, K. May, F. Furche and R. Ahlrichs; Chem. Phys. Lett., 384, 103, (2004).

36. Efficient evaluation of three-center two-electron integrals over Gaussian functions. R. Ahlrichs; Phys. Chem. Chem. Phys., 6, 5119, (2004).

37. Analytical time-dependent density functional derivative methods within the RI-J approximation, an approach to excited states of large molecules. D. Rappoport and F. Furche; J. Chem. Phys., 122, 064105 (2005).

38. Density functional theory for excited states: equilibrium structure and electronic spectra. F. Furche and D. Rappoport; Ch. III of "Computational Photochemistry", Ed. by M. Olivucci, Vol. 16 of "Computational and Theoretical Chemistry", Elsevier, Amsterdam, 2005.

39. Structure optimizations for excited states with correlated second-order methods: CC2, CIS(D\(_{\infty}\)), and ADC(2). C. Hättig; Adv. Quant. Chem., 50, 37-60 (2005).

40. Distributed memory parallel implementation of energies and gradients for second-order Møller-Plesset perturbation theory with the resolution-of-the-identity approximation. C. Hättig, A. Hellweg and A. Köhn; Phys. Chem. Chem. Phys., 8, 1159-1169, (2006).

41. Quintuple-\(\zeta\) quality coupled-cluster correlation energies with triple-\(\zeta\) basis sets. D. P. Tew, W. Klopper, C. Neiss and C. Hättig; Phys. Chem. Chem. Phys., 9 921–1930 (2007).

42. Benchmarking the performance of spin-component scaled CC2 in ground and electronically excited states. A. Hellweg, S. A. Grün and C. Hättig; Phys. Chem. Chem. Phys., 10, 4119-4127 (2008).

43. Scaled opposite-spin CC2 for ground and excited states with fourth order scaling computational costs. N. O. C. Winter and C. Hättig; J. Chem. Phys., 134, 184101 (2011).
    and: Quartic scaling analytical gradients of scaled opposite-spin CC2. N. O. C. Winter and C. Hättig; Chem. Phys., 401 (2012) 217.

44. The MP2-F12 Method in the TURBOMOLE Programm Package. R. A. Bachorz, F. A. Bischoff, A. Glöß, C. Hättig, S. Höfener, W. Klopper and D. P. Tew; J. Comput. Chem., 32, 2492–2513 (2011).

45. Accurate and efficient approximations to explicitly correlated coupled-cluster singles and doubles, CCSD-F12. C. Hättig, D. P. Tew and A, Köhn; J. Chem. Phys., 132, 231102 (2010).

46. Large scale polarizability calculations using the approximate coupled cluster model CC2 and MP2 combined with the resolution-of-the identity approximation. D. H. Friese, N. O. C. Winter, P. Balzerowski, R. Schwan and C. Hättig; J. Chem. Phys., 136, 174106 (2012).

47. A \({\cal O}({\cal N}^3)\)-scaling PNO-MP2 method using a hybrid OSV-PNO approach with an iterative direct generation of OSVs. G. Schmitz, B. Helmich and C. Hättig; Mol. Phys., 111, 2463–2476, (2013).

48. Explicitly correlated PNO-MP2 and PNO-CCSD and its application to the S66 set and large molecular systems. G. Schmitz, C. Hättig and D. P. Tew; Phys. Chem. Chem. Phys., 16, 22167–22178 (2014).

49. Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole methods. R. Łazarski, A. M. Burow and M. Sierka; J. Chem. Theory Comput., 11, 3029–3041 (2015).

50. Low-memory iterative density fitting. L. Grajciar; J. Comput. Chem., 36, 1521–1535 (2015).

51. Linear scaling hierarchical integration scheme for the exchange-correlation term in molecular and periodic systems. A. M. Burow and M. Sierka; J. Chem. Theory Comput., 7, 3097–3104 (2011).

52. Resolution of identity approximation for the Coulomb term in molecular and periodic systems. A. M. Burow, M. Sierka and F. Mohamed; J. Chem. Phys., 131, 214101 (2009).

53. Self-consistent treatment of spin-orbit interactions with efficient Hartree-Fock and density functional methods. M. K. Armbruster, F. Weigend, C. van Wüllen and W. Klopper; Phys. Chem. Chem. Phys., 10, 1748–1756, (2008).

54. Seminumerical exchange and two-component local hybrids. P. Plessow and F. Weigend; J. Comput. Chem., 33, 810–816 (2012).

55. Improved SCF treatment of spin-orbit interactions and gradients. A. Baldes and F. Weigend; Mol. Phys., 111, 2617–2624 (2013).

56. Relativistic all-electron approaches (BSS, DKH, and X2C). Daoling Peng, Nils Middendorf, Florian Weigend, Markus Reiher; J. Chem. Phys., 138, 184105 (2013).

57. Relativistic all-electron approaches including finite nucleus model and SNSO approach, and geometry gradients. Y. J. Franzke, N. Middendorf and F. Weigend; J. Chem. Phys., 148, 104110 (2018).

58. NMR Shielding Tensors and Chemical Shifts in Scalar-Relativistic Local Exact Two-Component Theory. Y. J. Franzke and F. Weigend; J. Chem. Theory Comput., 15, 1028–1043 (2019).

59. Hyperfine Coupling Constants in Local Exact Two-Component Theory. Y. J. Franzke and J. M. Yu; J. Chem. Theory Comput., 18, 323–343 (2022).

60. Quasi-Relativistic Calculation of EPR \(g\) Tensors with Derivatives of the Decoupling Transformation, Gauge-Including Atomic Orbitals, and Magnetic Balance. Y. J. Franzke and J. M. Yu; J. Chem. Theory Comput., 18, 2246–2266 (2022).

61. Exact Two-Component Theory Becoming an Efficient Tool for NMR Shieldings and Shifts with Spin–Orbit Coupling. Y. J. Franzke and C. Holzer; J. Chem. Phys. 159, 184102 (2023).

62. Efficient self-consistent implementation of local hybrid functionals. H. Bahmann and M. Kaupp; J. Chem. Theory Comput., 11, 1540–1548, (2015).

63. Implementation of molecular gradients for local hybrid density functionals using seminumerical integration techniques. S. Klawohn, H. Bahmann and M. Kaupp; J. Chem. Theory Comput., 12, 4254–4262, (2016).

64. Efficient semi-numerical implementation of global and local hybrid functionals for time-dependent density functional theory. T. M. Maier, H. Bahmann and M. Kaupp; J. Chem. Theory Comput., 11, 4226–4237, (2015).

65. Quasirelativistic two-component core excitations and polarisabilities from a damped-response formulation of the Bethe–Salpeter equation. M. Kehry, Y. J. Franzke, C. Holzer and W. Klopper; Mol. Phys., 118, e1755064 (2020).

66. An improved seminumerical Coulomb and exchange algorithm for properties and excited states in modern density functional theory. C. Holzer; J. Chem. Phys., 153, 184115 (2020).

67. Assessing the accuracy of local hybrid density functional approximations for molecular response properties. C. Holzer, Y. J. Franzke, M. Kehry; J. Chem. Theory. Comput., 17, 2928–2947 (2021).

68. Development and implementation of excited-state gradients for local hybrid functionals. R. Grotjahn; F. Furche; M. Kaupp, J. Chem. Theory Comput., 15, 5508–5522, (2019).

69. A local hybrid exchange functional approximation from first principles. C. Holzer, Y. J. Franzke, J. Chem. Phys., 157, 034108 (2022).

Basis sets

The following tables can be used to find the proper citations of the standard orbital and auxiliary basis sets in the TURBOMOLE basis set library. Recommendations for applications and a historical overview are provided in the supporting information of [5]. There, the employed ECPs for heavy elements are listed. ECPs can also be obtained from the website of the Dolg group together with a detailed bibliography, please see http://www.tc.uni-koeln.de/PP/clickpse.en.html.

Orbital basis sets, elements H–Kr  

Note: For H–Kr def-SV(P), def-SVP, ... are identical with the basis sets without def prefix. def2-QZVPP and def2-QZVP are identical with QZVPP and QZVP. One-component dhf and def2 type basis sets are identical for the elements up to Kr.
def2-XVPD/XVPPD denotes the property–optimized augmentations def2-SVPD, def2-TZVPD, def2- TZVPPD, def2-QZVPD, def2-QZVPPD.

Orbital basis sets, elements Rb–Rn  

Auxiliary basis sets for RI-J in HF/DFT (Coulomb fitting)  

Auxiliary basis sets for RI-K in HF/DFT (Exchange fitting)  

Auxiliary basis sets for RI-MP2 and RI-CC, elements H–Ar  

Note: the auxiliary basis sets for the (aug-)cc-pV(X+d)Z basis sets for Al–Ar are identical with the (aug-)cc-pVXZ auxiliary basis sets.

Auxiliary basis sets for RI-MP2 and RI-CC, elements K–Kr  

Auxiliary basis sets for RI-MP2 and RI-CC, elements Rb–Rn  

1. Fully Optimized Contracted Gaussian Basis Sets for Atoms Li to Kr. A. Schäfer, H. Horn and R. Ahlrichs; J. Chem. Phys., 97, 2571 (1992).

2. Fully Optimized Contracted Gaussian Basis Sets of Triple Zeta Valence Quality for Atoms Li to Kr. A. Schäfer, C. Huber and R. Ahlrichs; J. Chem. Phys., 100, 5829 (1994).

3. Auxiliary Basis Sets to Approximate Coulomb Potentials.

   K. Eichkorn, O. Treutler, H. Öhm, M. Häser and R. Ahlrichs; Chem. Phys. Lett., 242, 652 (1995).

4. Auxiliary basis sets for main row atoms and transition metals and their use to approximate Coulomb potentials. K. Eichkorn, F. Weigend, O. Treutler and R. Ahlrichs; Theor. Chem. Acc., 97, 119 (1997).

5. Accurate Coulomb-fitting basis sets for H to Rn. F. Weigend; Phys. Chem. Chem. Phys., 8, 1057 (2006).

6. RI-MP2: Optimized Auxiliary Basis Sets and Demonstration of Efficiency. F. Weigend, M. Häser, H. Patzelt and R. Ahlrichs; Chem. Phys. Lett., 294, 143 (1998).

7. Contracted all-electron Gaussian basis sets for Rb to Xe. R. Ahlrichs and K. May; Phys. Chem. Chem. Phys., 2, 943 (2000).

8. Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations. F. Weigend, A. Köhn and C. Hättig; J. Chem. Phys., 116, 3175 (2002).

9. Gaussian basis sets of quadruple zeta valence quality for atoms H–Kr. F. Weigend, F. Furche and R. Ahlrichs; J. Chem. Phys., 119, 12753 (2003).

10. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design an assessment of accuracy. F. Weigend and R. Ahlrichs; Phys. Chem. Chem. Phys., 7, 3297 (2005).

11. Optimization of auxiliary basis sets for RI-MP2 and RI-CC2 calculation: Core-valence and quintuple-\(\zeta\) basis sets for H to Ar and QZVPP basis sets for Li to Kr. C. Hättig; Phys. Chem. Chem. Phys., 7, 59 (2005).

12. Optimized accurate auxiliary basis sets for RI-MP2 and RI-CC2 calculations for the atoms Rb to Rn. A. Hellweg, C. Hättig, S. Höfener and W. Klopper; Theor. Chem. Acc., 117, 587 (2007).

13. Property–optimized Gaussian basis sets for molecular response calculations. D. Rappoport and F. Furche; J. Chem. Phys., 133, 134105 (2010).

14. Error-Balanced Segmented Contracted Basis Sets of Double-\(\zeta\) to Quadruple-\(\zeta\) Valence Quality for the Lanthanides. R. Gulde, P. Pollak and F. Weigend; J. Chem. Theory Comput., 18, 4062 (2012).

15. A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency. F. Weigend; Phys. Chem. Chem. Phys., 4, 4285 (2002).

16. Hartree–Fock Exchange Fitting Basis Sets for H to Rn. F. Weigend; J. Comput. Chem., 29, 167 (2008).

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18. Segmented Contracted Error-Consistent Basis Sets of Double- and Triple-\(\zeta\) Valence Quality for One- and Two-Component Relativistic All-Electron Calculations. P. Pollak and F. Weigend; J. Chem. Theory Comput., 13, 3696 (2017).

19. Error-consistent segmented contracted all-electron relativistic basis sets of double- and triple-zeta quality for NMR shielding constants.
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20. Segmented contracted error-consistent basis sets of quadruple-\(\zeta\) valence quality for one-and two-component relativistic all-electron calculations.
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22. Development of new auxiliary basis functions of the Karlsruhe segmented contracted basis sets including diffuse basis functions (def2-SVPD, def2-TZVPPD, and def2-QVPPD) for RI-MP2 and RI-CC calculations. A. Hellweg and D. Rappoport; Phys. Chem. Chem. Phys., , 1010 (2015).

23. Optimized auxiliary basis sets for density fitted post-Hartree-Fock calculations of lanthanide containing molecules. J. Chmela and M. E. Harding; Mol. Phys., 116, 1523 (2018).

24. unpublished. Orbital basis sets given in the supporting information of 1.5.