A pair natural orbital based implementation of ADC(2)-x: Perspectives and challenges for response methods for singly and doubly excited states in large molecules

Computational and Theoretical Chemistry

Volumn 1040-1041, Issue , 2014, Pages 35-44

  Helmich, Benjamin ^a   Hättig, Christof ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

ADC(2) x; Coupled cluster; Double excitations; Excited states; Pair natural orbitals

Indexed keywords

EID: 84903908348     PISSN: 2210271X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.comptc.2014.03.004     Document Type: Article

References (62)

1. Stanton J.F., Gauss J. Analytic energy gradients for the equation-of-motion coupled-cluster method: implementation and application to the HCN/HNC system. J. Chem. Phys. 1994, 100:4695-4698.
2. Ishikawa N., Head-Gordon M. Analytical gradient of the CIS(D) perturbative correction to single-excitation configuration-interaction excited-states. Int. J. Quantum Chem. Symp. 1995, 29:421-427.
3. van Caillie C., Amos R. Geometric derivatives of excitation energies using SCF and DFT. Chem. Phys. Lett. 1999, 308:249-255.
4. van Caillie C., Amos R. Geometric derivatives of density functional theory excitation energies using gradient-corrected functionals. Chem. Phys. Lett. 2000, 317:159-164.
5. Furche F., Ahlrichs R. Adiabatic time-dependent density functional methods for excited state properties. J. Chem. Phys. 2002, 117:7433-7447.
6. Köhn A., Hättig C. Analytic gradients for excited states in the coupled-cluster model CC2 employing the resolution-of-the-identity approximation. J. Chem. Phys. 2003, 119:5021-5036.
7. Hettema H., Jensen H.J.A., Jørgensen P., Olsen J. Quadratic response functions for a multiconfigurational self-consistent field wave function. J. Chem. Phys. 1992, 97:1174-1190.
8. Sundholm D., Rizzo A., Jørgensen P. Multiconfiguration self-consistent field quadratic response calculations of the two-photon transition probability rate constants for argon. J. Chem. Phys. 1994, 101:4931-4935.
9. A1Π states of CO. J. Chem. Phys. 1995, 102:4143-4150.
10. Paterson M.J., Christiansen O., Pawłowski F., Jørgensen P., Hättig C., Helgaker T., Sałek P. Benchmarking two-photon absorption with CC3 quadratic response theory, and comparison with density-functional response theory. J. Chem. Phys. 2006, 124:054322.
11. Hättig C., Christiansen O., Jørgensen P. Multiphoton transition moments and absorption cross section in coupled cluster response theory employing variational transition moment functionals. J. Chem. Phys. 1998, 108:8331-8354.
12. Friese D.H., Hättig C., Ruud K. 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. 2012, 14:1175-1184.
13. Christiansen O. First-order nonadiabatic coupling matrix elements using coupled cluster methods. I. Theory. J. Chem. Phys. 1999, 110:711-723.
14. Tajti A., Szalay P.G. Analytic evaluation of the nonadiabatic coupling vector between excited states using equation-of-motion coupled-cluster theory. J. Chem. Phys. 2009, 131:124104.
15. Send R., Furche F. First-order nonadiabatic couplings from time-dependent hybrid density functional response theory: consistent formalism, implementation, and performance. J. Chem. Phys. 2010, 132:044107.
16. Head-Gordon M., Rico R.J., Oumi M., Lee T.J. A doubles correction to electronic excited-states from configuration-interaction in the space of single substitutions. Chem. Phys. Lett. 1994, 219:21-29.
17. Schirmer J. Beyond the random phase approximation: a new approximation scheme for the polarization propagator. Phys. Rev. A 1981, 26:2395-2416.
18. Christiansen O., Koch H., Jørgensen P. The second-order approximate coupled cluster singles and doubles model CC2. Chem. Phys. Lett. 1995, 243:409-418.
19. Hättig C., Weigend F. CC2 excitation energy calculations on large molecules using the resolution of the identity approximation. J. Chem. Phys. 2000, 113:5154-5161.
20. Kats D., Korona T., Schütz M. Local CC2 electronic excitation energies for large molecules with density fitting. J. Chem. Phys. 2006, 125:104106.
21. Kats D., Schütz M. A multistate local coupled cluster CC2 response method based on the Laplace transform. J. Chem. Phys. 2009, 131:124117.
22. Helmich B., Hättig C. Local pair natural orbitals for excited states. J. Chem. Phys. 2011, 135:214106.
23. Helmich B., Hättig C. A pair natural orbital implementation of the coupled cluster model CC2 for excitation energies. J. Chem. Phys. 2013, 139:084114.
24. Head-Gordon M., Oumi M., Maurice D. Quasidegenerate second-order perturbation corrections to single-excitation configuration interaction. Mol. Phys. 1999, 96:593-602.
25. Korona T., Werner H.-J. Local treatment of electron excitations in the EOM-CCSD method. J. Chem. Phys. 2003, 118:3006-3019.
26. Crawford T.D., King R.A. Locally correlated equation-of-motion coupled cluster theory for the excited states of large molecules. Chem. Phys. Lett. 2002, 366:611-622.
27. Meyer W. Ionization energies of water from PNO-CI calculations. Int. J. Quantum Chem. 1971, 5:341-348.
28. Neese F., Wennmohs F., Hansen A. Efficient and accurate local approximations to coupled-electron pair approaches: an attempt to revive the pair natural orbital method. J. Chem. Phys. 2009, 130:114108.
29. Neese F., Hansen A., Liakos D.G. Efficient and accurate approximations to the local coupled cluster singles and doubles method using a truncated pair natural orbital basis. J. Chem. Phys. 2009, 131:064103.
30. Trofimov A.B., Schirmer J. An efficient polarization propagator approach to valence electron-excitation spectra. J. Phys. B 1995, 28:2299-2324.
31. Starcke J.H., Wormit M., Schirmer J., Dreuw A. How much double excitation character do the lowest excited states of linear polyenes have?. Chem. Phys. 2006, 329:39-49.
32. Knippenberg S., Starcke J.H., Wormit M., Dreuw A. The low-lying excited states of neutral polyacenes and their radical cations: a quantum chemical study employing the algebraic diagrammatic construction scheme of second order. Mol. Phys. 2010, 108:2801-2813.
33. Yang J., Kurashige Y., Manby F.R., Chan G.K.L. Tensor factorizations of local second-order Møller-Plesset theory. J. Chem. Phys. 2011, 134:044123.
34. Krause C., Werner H.-J. Comparison of explicitly correlated local coupled-cluster methods with various choices of virtual orbitals. Phys. Chem. Chem. Phys. 2012, 14:7591-7604.
35. Hättig C., Tew D.P., Helmich B. Local explicitly correlated second- and third-order Møller-Plesset perturbation theory with pair natural orbitals. J. Chem. Phys. 2012, 136:204105.
36. Vahtras O., Almlöf J., Feyereisen M. Integral approximations for LCAO-SCF calculations. Chem. Phys. Lett. 1993, 213:514-518.
37. Feyereisen M., Fitzgerald G., Komornicki A. Use of approximate integrals in ab initio theory. An application in MP2 energy calculations. Chem. Phys. Lett. 1993, 208:359-363.
38. Jung Y., Lochan R.C., Dutoi A.D., Head-Gordon M. Scaled opposite-spin second order Møller-Plesset correlation energy: an economical electronic structure method. J. Chem. Phys. 2004, 121:9793-9802.
39. Rhee Y.M., Head-Gordon M. Scaled second-order perturbation corrections to configuration interaction singles: efficient and reliable excitation energy methods. J. Phys. Chem. A 2007, 111:5314-5326.
40. Hellweg A., Grün S., Hättig C. Benchmarking the performance of spin-component scaled CC2 in ground and electronically excited states. Phys. Chem. Chem. Phys. 2008, 10:1159-1169.
41. Almlöf J. Elimination of energy denominators in Møller-Plesset perturbation theory by a Laplace transform approach. Chem. Phys. Lett. 1991, 181:319-320.
42. Häser M., Almlöf J. Laplace transform techniques in Møller-Plesset perturbation theory. J. Chem. Phys. 1992, 96:489-494.
43. Schmitz G., Helmich B., Hättig C. A O(n3) scaling PNO-MP2 method using a hybrid OSV-PNO approach with an iterative direct generation of OSVs. Mol. Phys. 2013, 111:2463-2476.
44. Riplinger C., Neese F. An efficient and near linear scaling pair natural orbital based local coupled cluster method. J. Chem. Phys. 2013, 138:034106.
45. Turbomole Development Version, 2013. For further information see http://www.turbomole.com.
46. Pipek J., Mezey P.G. A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions. J. Chem. Phys. 1989, 90:4916-4926.
47. TURBOMOLE V6.5, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989-2007, TURBOMOLE GmbH, since 2007; available from , 2013. http://www.turbomole.com.
48. Schreiber M., Silva-Junior M.R., Sauer S.P.A., Thiel W. Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3. J. Chem. Phys. 2008, 128:134110.
49. Silva-Junior M.R., Sauer S.P., Schreiber M., Thiel W. Basis set effects on coupled cluster benchmarks of electronically excited states: CC3, CCSDR(3) and CC2. Mol. Phys. 2010, 108:453-465.
50. Schäfer A., Huber C., Ahlrichs R. Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr. J. Chem. Phys. 1994, 100:5829-5835.
51. Weigend F., Häser M., Patzelt H., Ahlrichs R. RI-MP2: Optimized auxiliary basis sets and demonstration of efficiency. Chem. Phys. Lett. 1998, 294:143-152.
52. Häser M., Ahlrichs R. Improvements on the direct SCF method. J. Comp. Chem. 1989, 10:104-111.
53. Starcke J.H., Wormit M., Dreuw A. Nature of the lowest excited states of neutral polyenyl radicals and polyene radical cations. J. Chem. Phys. 2009, 131:144311.
54. Silva-Junior M.R., Schreiber M., Sauer S.P., Thiel W. Benchmarks of electronically excited states: basis set effects on CASPT2 results. J. Chem. Phys. 2010, 133:174318.
55. 2013. See Supplemantary Material at URL.
56. Trofimov A.B., Stelter G., Schirmer J. Electron excitation energies using a consistent third-order propagator approach: comparison with full configuration interaction and coupled cluster results. J. Chem. Phys. 2002, 117:6402-6410.
57. Krauter C.M., Pernpointner M., Dreuw A. Application of the scaled-opposite-spin approximation to algebraic diagrammatic construction schemes of second order. J. Chem. Phys. 2013, 138:044107.
58. ∞), and ADC(2). Adv. Quantum Chem. 2005, 50:37-60.
59. r12 corrections: the CC2-R12 model for excitation energies. J. Chem. Phys. 2006, 124:044112.
60. Trofimov A.B., Stelter G., Schirmer J. A consistent third-order propagator method for electronic excitation. J. Chem. Phys. 1999, 111:9982-9999.
61. Christiansen O., Koch H., Halkier A., Jørgensen P., Helgaker T., Sánchez de Merás A.M. Large-scale calculations of excitation energies in coupled cluster theory: the singlet excited states of benzene. J. Chem. Phys. 1996, 105:6921-6939.
62. Christiansen O., Koch H., Jørgensen P. Perturbative triple excitation corrections to coupled cluster singles and doubles excitation energies. J. Chem. Phys. 1996, 105:1451-1459.