It is notable that all molecules examined here possess a high degree of spatial
symmetry. Issues with optimization to any of the multiple low-lying excited states
may be less severe if less symmetry or no symmetry were present as this lifts many
of the degeneracies that exasperate the problem of multiple stable solutions to the
Hartree-Fock equations (i.e. Löwdin’s symmetry dilemma) [41].
Acknowledgments This material is based on work supported by the National Science Foundation
under grant numbers CHE-1213874 and instrument support was provided via CHE-0741936. RJW
acknowledges support from the National Science Foundation GFRP under grant number
DGE-1144248. Additional computing resources were provided by the Academic Computing
Services at the University of North Texas. Support from the United States Department of Energy
for the Center for Advanced Scientific Computing and Modeling (CASCaM) is acknowledged.
References
1. Stanton RE (1968) J Chem Phys 48:257
2. Gilbert ATB, Besley NA, Gill PMW (2008) J Phys Chem A 112:13164
3. Sears JC, Sherrill CD (2006) J Chem Phys 124:144314
4. Cramer CJ (2004) Essentials of computational chemistry: theories and models, 2nd edn.
Wiley, West Sussex, p 182
5. Jensen F (2007) Introduction to computational chemistry, 2nd edn. Wiley, West Sussex
6. Plakhutin BN, Davidson ER (2009) J Phys Chem A 113:12386
7. Ghanty TK, Davidson ER (2000) Int J Quantum Chem 77:291
8. Lynch BJ, Truhlar DG (2002) Chem Phys Lett 361:251
9. Morokuma K, Iwata S (1972) Chem Phys Lett 16:192
10. Schoendorff G, South C, Wilson AK (2013) J Phys Chem A 117:42
11. Seeger R, Pople JA (1977) J Chem Phys 66:3045
12. Pulay P (1982) J Comp Chem 3:556
13. Schmidt MW, Baldridge KK, Boatz JA, Elbert ST, Gordon MS, Jensen JH, Koseki S,
Matsunaga N, Nguyen KA, Su SJ, Windus TL, Dupuis M, Montgomery JT (1993) J Comput
Chem R1:1347
14. Feller D, Peterson KA, Crawford TD (2006) J Chem Phys 124:054107
15. Piecuch P, Wloch M (2005) J Chem Phys 123:1–224105
16. Wloch M, Gour JR, Piecuch P (2007) J Phys Chem A 111:11359
17. Krylov AI (2001) Chem Phys Lett 338:375
18. Krylov AI, Slipchenko LV, Levchenko SV (2007) ACS Symp Ser 958:89
19. Szalay PG, Müller T, Gidofalvi G, Lischka H, Shepard R (2012) Chem Rev 112:108
20. Anderrson K, Malmqvist P, Roos BO, Sadlej AJ, Wolinski K (1990) J Phys Chem 94:5483
21. Schmidt MW, Gordon MS (1998) Annu Rev Phys Chem 49:233
22. Pulay P (2011) Int J Quantum Chem 111:3273
23. Burke K (2012) J Chem Phys 136:150901
24. Huber KP, Herzberg G Constants of diatomic molecules. In: Linstrom PJ, Mallard WG (eds)
NIST chemistry WebBook, NIST standard reference database, vol 69. National Institute of
Standards and Technology, Gaithersburg, MD, 20899 http://webbook.nist.gov, (Retrieved 6
Sept 2014)
25. Lee TJ, Taylor PR (1989) Int J Quantum Chem 23:199
26. Janssen CL, Nielsen IMB (1998) Chem Phys Lett 290:423
27. Lee TJ (2003) Chem Phys Lett 372:362
28. Jiang W, DeYonker NJ, Determan JJ, Wilson AK (2012) J Phys Chem A 116:870
The Importance of Orbital Analysis
27
symmetry. Issues with optimization to any of the multiple low-lying excited states
may be less severe if less symmetry or no symmetry were present as this lifts many
of the degeneracies that exasperate the problem of multiple stable solutions to the
Hartree-Fock equations (i.e. Löwdin’s symmetry dilemma) [41].
Acknowledgments This material is based on work supported by the National Science Foundation
under grant numbers CHE-1213874 and instrument support was provided via CHE-0741936. RJW
acknowledges support from the National Science Foundation GFRP under grant number
DGE-1144248. Additional computing resources were provided by the Academic Computing
Services at the University of North Texas. Support from the United States Department of Energy
for the Center for Advanced Scientific Computing and Modeling (CASCaM) is acknowledged.
References
1. Stanton RE (1968) J Chem Phys 48:257
2. Gilbert ATB, Besley NA, Gill PMW (2008) J Phys Chem A 112:13164
3. Sears JC, Sherrill CD (2006) J Chem Phys 124:144314
4. Cramer CJ (2004) Essentials of computational chemistry: theories and models, 2nd edn.
Wiley, West Sussex, p 182
5. Jensen F (2007) Introduction to computational chemistry, 2nd edn. Wiley, West Sussex
6. Plakhutin BN, Davidson ER (2009) J Phys Chem A 113:12386
7. Ghanty TK, Davidson ER (2000) Int J Quantum Chem 77:291
8. Lynch BJ, Truhlar DG (2002) Chem Phys Lett 361:251
9. Morokuma K, Iwata S (1972) Chem Phys Lett 16:192
10. Schoendorff G, South C, Wilson AK (2013) J Phys Chem A 117:42
11. Seeger R, Pople JA (1977) J Chem Phys 66:3045
12. Pulay P (1982) J Comp Chem 3:556
13. Schmidt MW, Baldridge KK, Boatz JA, Elbert ST, Gordon MS, Jensen JH, Koseki S,
Matsunaga N, Nguyen KA, Su SJ, Windus TL, Dupuis M, Montgomery JT (1993) J Comput
Chem R1:1347
14. Feller D, Peterson KA, Crawford TD (2006) J Chem Phys 124:054107
15. Piecuch P, Wloch M (2005) J Chem Phys 123:1–224105
16. Wloch M, Gour JR, Piecuch P (2007) J Phys Chem A 111:11359
17. Krylov AI (2001) Chem Phys Lett 338:375
18. Krylov AI, Slipchenko LV, Levchenko SV (2007) ACS Symp Ser 958:89
19. Szalay PG, Müller T, Gidofalvi G, Lischka H, Shepard R (2012) Chem Rev 112:108
20. Anderrson K, Malmqvist P, Roos BO, Sadlej AJ, Wolinski K (1990) J Phys Chem 94:5483
21. Schmidt MW, Gordon MS (1998) Annu Rev Phys Chem 49:233
22. Pulay P (2011) Int J Quantum Chem 111:3273
23. Burke K (2012) J Chem Phys 136:150901
24. Huber KP, Herzberg G Constants of diatomic molecules. In: Linstrom PJ, Mallard WG (eds)
NIST chemistry WebBook, NIST standard reference database, vol 69. National Institute of
Standards and Technology, Gaithersburg, MD, 20899 http://webbook.nist.gov, (Retrieved 6
Sept 2014)
25. Lee TJ, Taylor PR (1989) Int J Quantum Chem 23:199
26. Janssen CL, Nielsen IMB (1998) Chem Phys Lett 290:423
27. Lee TJ (2003) Chem Phys Lett 372:362
28. Jiang W, DeYonker NJ, Determan JJ, Wilson AK (2012) J Phys Chem A 116:870
The Importance of Orbital Analysis
27