Skip to main content
SpringerLink
Log in

Wave function analysis with Shavitt graph density in the graphically contracted function method

  • Regular Article
  • Published:
Theoretical Chemistry Accounts Aims and scope Submit manuscript

Abstract

The goals of electronic structure theory are to make quantitative predictions of molecular properties and to provide qualitative insight into bonding as well as features of potential energy surfaces. Oftentimes, the two goals are at odds as an accurate treatment requires a complicated wave function that obscures chemical insight. The multifacet graphically contracted function (MFGCF) method offers a new approach that allows both goals to be addressed simultaneously. The recursive product structure of the MFGCF wave function reduces the exponential scaling of the exact wave function and allows the computation of molecular properties with polynomial scaling with respect to system size. Additionally, the graph density concept provides an intuitive tool for visualizing and analyzing the qualitative features of the wave function. In this work, the graph densities for model systems are examined to demonstrate their utility in analyzing the changes in wave function character along potential energy surfaces and near avoided crossings. Finally, we demonstrate that the graph density exposes the structure of the exact wave function for a system of noninteracting molecules as a product of the fragment wave functions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Shavitt I (1977) Int J Quantum Chem S11:131

    Google Scholar 

  2. Shavitt I (1978) Int J Quantum Chem S12:5

    Google Scholar 

  3. Lischka H, Shepard R, Brown FB, Shavitt I (1981) Int J Quantum Chem S15:91

    Google Scholar 

  4. Shavitt I (1981) In: Hinze J (ed) The unitary group for the evaluation of electronic energy matrix elements, lecture notes in chemistry, vol 22. Springer, New York, pp 51–99

  5. Shavitt I (1988) In: Truhlar DG (ed) Mathematical frontiers in computational chemical physics, the IMA volumes in mathematics and its application. Springer, New York, pp 300–349

  6. Paldus J (1974) J Chem Phys 61:5321

    Article  CAS  Google Scholar 

  7. Paldus J, Boyle MJ (1980) Phys Scr 21:295

    Article  CAS  Google Scholar 

  8. Paldus J (1981) In: Hinze J (ed) The unitary group for the evaluation of electronic energy matrix elements, lecture notes in chemistry. Springer, New York, pp 1–50

  9. Paldus J (1988) In: Truhlar DG (ed) Mathematical frontiers in computational chemical physics, the IMA volumes in mathematics and its application. Springer, New York, pp 262–299

  10. Brooks BR, Schaefer HF III (1979) J Chem Phys 70:5092

    Article  CAS  Google Scholar 

  11. Brooks BR, Laidig WD, Saxe P, Handy NC, Schaefer HF III (1980) Phys Scr 21:312

    Article  CAS  Google Scholar 

  12. Aquilante F, Vico LD, Ferré N, Ghigo G, Malmqvist PÅ, Neogrády P, Pedersen TB, Pitonak M, Reiher M, Roos BO, Serrano-Andrés L, Urban M, Veryazov V, Lindh R (2010) J Comput Chem 31:224

    Article  CAS  Google Scholar 

  13. Shepard R, Shavitt I, Pitzer RM, Comeau DC, Pepper M, Lischka H, Szalay PG, Ahlrichs R, Brown FB, Zhao JG (1988) Int J Quantum Chem 22:149

    Article  CAS  Google Scholar 

  14. Lischka H, Shepard R, Pitzer RM, Shavitt I, Dallos M, Müller T, Szalay PG, Seth M, Kedziora GS, Yabushita S, Zhang Z (2001) Phys Chem Chem Phys 3:664

    Article  CAS  Google Scholar 

  15. Shepard R (1994) In: Malli GL (ed) Relativistic and electron correlation effects in molecules and solids, NATO Advanced Science Institutes. Plenum Press, New York, pp 447–460

  16. Davidson ER (1975) J Comput Phys 17:87

    Article  Google Scholar 

  17. Mulliken RS (1955) J Chem Phys 23:1833

    Article  CAS  Google Scholar 

  18. Löwdin PO (1950) J Chem Phys 18:365

    Article  Google Scholar 

  19. Weinhold F (1998) In: Schleyer PVR, Allinger NL, Clark T, Gasteiger J, Kollman PA, Schaefer HF III, Schreiner PR (eds) Encyclopedia of computational chemistry. Wiley, Chichester, pp 1792–1811

  20. Ivanic J, Ruedenberg K (2002) Theor Chem Acc 107:220

    Article  CAS  Google Scholar 

  21. Buenker RJ, Peyerimhoff SD (1974) Theor Chim Acta 35:33

    Article  CAS  Google Scholar 

  22. Abrams ML, Sherrill DC (2002) J Chem Phys 118:1604

    Article  Google Scholar 

  23. Shavitt I, Rosenberg BJ, Palalikit S (1976) Int J Quantum Chem Symp 10:33

    Article  CAS  Google Scholar 

  24. Barr TL, Davidson ER (1970) Phys Rev A 1:644

    Article  CAS  Google Scholar 

  25. Klopper W, Noga J, Koch H, Helgaker T (1997) Theor Chem Acc 97:164

    Article  CAS  Google Scholar 

  26. Sosa C, Geersten J, Trucks GW, Barlett RJ, Franz JA (1989) Chem Phys Lett 159:148

    Article  CAS  Google Scholar 

  27. Taube AG, Bartlett RJ (2005) Collect Czechoslov Chem Commun 70:837

    Article  CAS  Google Scholar 

  28. Landau A, Khistyaev K, Dolgikh S, Krylov AI (2010) J Chem Phys 132:014109

    Article  Google Scholar 

  29. DePrince AE, Sherrill DC (2013) J Chem Theory Comput 9:293

    Article  CAS  Google Scholar 

  30. Shepard R (2005) J Phys Chem A 109:11629

    Article  CAS  Google Scholar 

  31. Shepard R, Minkoff M, Brozell SR (2007) Int J Quantum Chem 107:3203

    Article  CAS  Google Scholar 

  32. Shepard R, Gidofalvi G, Brozell SR (2014) The multifacet graphically contracted function method: I. Formulation and implementation. J Chem Phys (in press)

  33. Shepard R, Gidofalvi G, Brozell SR (2014) The multifacet graphically contracted function method: II. A general procedure for the parameterization of orthogonal matrices and its application to arc factors. J Chem Phys (in press)

  34. Shepard R (2006) J Phys Chem A 110:8880

    Article  CAS  Google Scholar 

  35. Shepard R, Minkoff M (2006) Int J Quantum Chem 106:3190

    Article  CAS  Google Scholar 

  36. Brozell SR, Shepard R, Zhang Z (2007) Int J Quantum Chem 107:3191

    Article  CAS  Google Scholar 

  37. Gidofalvi G, Shepard R (2009) J Comput Chem 30:2414

    Article  CAS  Google Scholar 

  38. Gidofalvi G, Shepard R (2009) Int J Quantum Chem 109:3552

    Article  CAS  Google Scholar 

  39. Brozell SR, Shepard R (2009) J Phys Chem A 113:12741

    Article  CAS  Google Scholar 

  40. Shepard R, Gidofalvi G, Hovland PD (2010) Int J Quantum Chem 110:2938

    Article  CAS  Google Scholar 

  41. Gidofalvi G, Shepard R (2010) Mol Phys 108:2717

    Article  CAS  Google Scholar 

  42. Judd BR (1963) Operator techniques in atomic spectroscopy. McGraw-Hill, New York

    Google Scholar 

  43. White SR (1992) Phys Rev Lett 69:2863

    Article  Google Scholar 

  44. Rissler J, Noack RM, White SR (2006) Chem Phys 323:519

    Article  CAS  Google Scholar 

  45. Legeza Ö, Sólyom J (2003) Phys Rev B 67:195116

    Article  Google Scholar 

  46. Boguslawski K, Tecmer P, Barcza G, Legeza Ö, Reiher M (2013) J Chem Theory Comput 9:2959

    Article  CAS  Google Scholar 

  47. Kurashige Y, Chan GKL, Yanai T (2013) Nat Chem 5:660

    Article  CAS  Google Scholar 

  48. Schollwöck U (2011) Ann Phys 326:96

    Article  Google Scholar 

  49. Sharma S, Chan GKL (2012) J Chem Phys 136:124121

    Article  Google Scholar 

  50. Wouters S, Limacher PA, Neck DV, Ayers PW (2012) J Chem Phys 136:134110

    Article  Google Scholar 

  51. Dunning TH Jr (1989) J Chem Phys 90:1007

    Article  CAS  Google Scholar 

  52. Dunning TH Jr (1994) J Chem Phys 100:2975

    Article  Google Scholar 

  53. Purvis GD III, Shepard R, Brown FB, Bartlett RJ (1983) Int J Quantum Chem 23:835

    Article  CAS  Google Scholar 

  54. Orden AV, Saykally RJ (1998) Chem Rev 98:2313

    Article  Google Scholar 

  55. Hoffmann R (1995) Am Sci 83:309

    Google Scholar 

  56. Abrams ML, Sherrill CD (2004) J Chem Phys 121:9211

    Article  CAS  Google Scholar 

  57. Sherrill CD, Piecuch P (2005) J Chem Phys 122:124104

    Article  Google Scholar 

  58. Booth GH, Cleland D, Thom AJW, Alavi A (2011) J Chem Phys 135:084104

    Article  Google Scholar 

  59. Boschen JS, Theis D, Ruedenberg K, Windus TL (2014) Theor Chem Acc 133:1425

    Article  Google Scholar 

  60. Jankowski K, Meissner L, Wasilewski J (1985) Int J Quantum Chem 28:931

    Article  CAS  Google Scholar 

  61. Jankowski K, Paldus J, Wasilewski J (1991) J Chem Phys 95:3549

    Article  CAS  Google Scholar 

  62. Piecuch P, Adamowicz L (1994) J Chem Phys 100:5792

    Article  CAS  Google Scholar 

  63. Evangelista FA, Allen WD, Schaefer HF III (2006) J Chem Phys 125:154113:1

    Article  Google Scholar 

  64. Pape D, Hanrath M (2012) Chem Phys 401:157

    Article  CAS  Google Scholar 

  65. Huzinaga S (1965) J Chem Phys 42:1293

    Article  Google Scholar 

  66. Kucharski SA, Balková A, Szalay PG, Bartlett RJ (1992) J Chem Phys 97:4289

    Article  CAS  Google Scholar 

Download references

Acknowledgments

This work was supported by the Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, U.S. Department of Energy, under contract DE-AC02-06CH11357. G.G. was supported by an award from the Research Corporation for Science Advancement and a grant to Gonzaga University from the Howard Hughes Medical Institute through the Undergraduate Science Education Program. S.R.B. acknowledges the use of computational facilities at the Ohio Supercomputer Center.

Author information

Authors and Affiliations

  1. Department of Chemistry and Biochemistry, Gonzaga University, 502 E. Boone Ave., Spokane, WA, 99258-0102, USA

    Gergely Gidofalvi

  2. Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, IL, 60439, USA

    Scott R. Brozell & Ron Shepard

Authors
  1. Gergely Gidofalvi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Scott R. Brozell
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ron Shepard
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gergely Gidofalvi.

Additional information

Dedicated to the memory of Professor Isaiah Shavitt and published as part of the special collection of articles celebrating his many contributions.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gidofalvi, G., Brozell, S.R. & Shepard, R. Wave function analysis with Shavitt graph density in the graphically contracted function method. Theor Chem Acc 133, 1512 (2014). https://doi.org/10.1007/s00214-014-1512-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00214-014-1512-7

Keywords

Search

Navigation