Abstract
The extent of relativistic effects on the Fukui function, which describes local reactivity trends within conceptual density functional theory (DFT), and frontier orbital densities has been analysed on the basis of three benchmark molecules containing the heavy elements: Au, Pb, and Bi. Various approximate relativistic approaches have been tested and compared with the four-component fully relativistic reference. Scalar relativistic effects, as described by the scalar zeroth-order regular approximation methodology and effective core potential calculations, already provide a large part of the relativistic corrections. Inclusion of spin–orbit coupling effects improves the results, especially for the heavy p-block compounds. We thus expect that future conceptual DFT-based reactivity studies on heavy-element molecules can rely on one of the approximate relativistic methodologies.
Similar content being viewed by others
References
Parr RG, Yang W (1989) Density functional theory of atoms and molecules. Oxford University Press, New York
Chermette H (1999) J Comp Chem 20:129–154
Geerlings P, De Proft F, Langenaeker W (2003) Chem Rev 103:1793–1873
Ayers PW, Anderson JSM, Bartolotti LJ (2005) Int J Quantum Chem 101:520–534
Chattaraj PK, Sarkar U, Roy DR (2006) Chem Rev 106:2065–2091
Geerlings P, De Proft F (2008) Phys Chem Chem Phys 10:3028–3042
Hinze J, Jaffé HH (1962) J Am Chem Soc 84:540–546
Hinze J, Jaffé HH (1963) Can J Chem 41:1315–1328
Hinze J, Jaffé HH (1963) J Phys Chem 67:1501–1506
Hinze J, Whitehead MA, Jaffé HH (1963) J Am Chem Soc 85:148–154
Bergmann D, Hinze J (1987) Struct Bonding 66:145–190
Bergmann D, Hinze J (1996) Angew Chem Int Ed 35:781–781
Pearson RG (1963) J Am Chem Soc 85:3533–3539
Pearson RG (1966) Science 151:172–177
Pearson RG (1997) Chemical hardness. Wiley, New-York
Fukui K, Yonezawa T, Shingu H (1952) J Chem Phys 20:722–725
Fukui K (1982) Science 218:747–754
Parr RG, Donnelly RA, Levy M, Palke WE (1978) J Chem Phys 68:3801–3807
Ayers PW, Levy M (2000) Theor Chem Acc 103:353–360
Parr RG, Pearson RG (1983) J Am Chem Soc 105:7512–7516
Parr RG, Yang WT (1984) J Am Chem Soc 106:4049–4050
Elschenbroich C (2006) Organometallics. Wiley, Weinheim
Giju KT, De Proft F, Geerlings P (2005) J Phys Chem A 109:2925–2936
Perdew JP, Parr RG, Levy M, Balduz JL (1982) Phys Rev Lett 49:1691–1694
Kohn W, Sham LJ (1965) Phys Rev A 140:1133–1138
Rajagopal AK, Callaway J (1973) Phys Rev B 7:1912–1919
Saue T, Helgaker T (2002) J Comput Chem 23:814–823
Engel E, Dreizler RM (1996) Top Curr Chem 181:1–80
Reiher M, Hinze J (2003) In: Hess BA (ed) Relativistic effects in heavy-element chemistry and physics. Wiley, Weinheim
Reiher M, Wolf A (2009) Relativistic quantum chemistry. Wiley, Weinheim
Foldy LL, Wouthuysen SA (1950) Phys Rev 78:29–36
Douglas M, Kroll NM (1974) Ann Phys 82:89–155
Hess BA (1986) Phys Rev A 33:3742–3748
Reiher M (2006) Theor Chem Acc 116:241–252
Chang C, Pelissier M, Durand P (1986) Phys Scr 34:394–404
van Lenthe E, Baerends EJ, Snijders JG (1993) J Chem Phys 99:4597–4610
van Lenthe E, Baerends EJ, Snijders JG (1994) J Chem Phys 101:9783–9792
Dolg M (2000) In: Grotendorst J (ed) Modern methods and algorithms of quantum chemistry. John von Neumann Institute for Computing, Jülich
Dolg M (2002) In: Schwerdtfeger P (ed) Relativistic quantum chemistry—part 1 fundamentals. Elsevier, Amsterdam
Michalak A, De Proft F, Geerlings P, Nalewajski RF (1999) J Phys Chem A 103:762–771
Ayers PW, De Proft F, Borgoo A, Geerlings P (2007) J Chem Phys 126:224107
Sablon N, De Proft F, Geerlings P (2009) J Chem Theory Comput 5:1245–1253
Flores-Moreno R, Melin J, Ortiz JV, Merino G (2008) J Chem Phys 129:224105
Ayers PW, Melin J (2007) Theor Chem Acc 117:371–381
Eickerling G, Mastalerz R, Herz V, Scherer W, Himmel HJ, Reiher M (2007) J Chem Theory Comput 3:2182–2197
Becke AD (1988) Phys Rev A 38:3098–3100
Perdew JP (1986) Phys Rev B 33:8822–8824
ADF2006.01, SCM, Theoretical chemistry. Vrije Universiteit, Amsterdam, The Netherlands
Jensen HJ, Saue T, Visscher L with contributions from Bakken V, Eliav E, Enevoldsen T, Fleig T, Fossgaard O, Helgaker T, Laerdahl J, Larsen CV, Norman P, Olsen J, Pernpointner M, Pedersen JK, Ruud K, Salek P, van Stralen JNP, Thyssen J, Visser O, Winther T (2004) Dirac, a relativistic ab initio electronic structure program, Release DIRAC04.0
Dyall KG (2004) Theor Chem Acc 112:403–409
Dyall KG (2002) Theor Chem Acc 108:335–340
Dunning TH (1989) J Chem Phys 90:1007–1023
Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA Jr, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene M, Li X, Kno JE, Hratchian HP, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA (2005) Gaussian 03, Revision D.01. Gaussian, Inc, Wallingford
Metz B, Stoll H, Dolg M (2000) J Chem Phys 113:2563–2569
Figgen D, Rauhut G, Dolg M, Stoll H (2005) Chem Phys 311:227–244
Tozer DJ, De Proft F (2007) J Chem Phys 127:7
Sablon N, De Proft F, Geerlings P, Tozer DJ (2007) Phys Chem Chem Phys 9:5880–5884
Tozer DJ, De Proft F (2005) J Phys Chem A 109:8923–8929
Kohout M, Savin A, Preuss H (1991) J Chem Phys 95:1928–1942
Hebben N, Himmel HJ, Eickerling G, Herrmann C, Reiher M, Herz V, Presnitz M, Scherer W (2007) Chem Eur J 13:10078–10087
Eickerling G, Reiher M (2008) J Chem Theory Comput 4:286–296
Purvis GD III (1991) Comput Aided Mol Des 5:55–80
Acknowledgments
N.S. acknowledges the Research Foundation, Flanders (FWO) for a position as research assistant and a research stay at M. Reiher’s group at the ETH Zurich. F.D.P. and P.G. thank the Vrije Universiteit Brussel (VUB) and FWO for continuous support to their research group. R.M. and M.R. gratefully acknowledge financial support by the Swiss National Science Foundation SNF (project 200020-121870).
Note added in Proof
After having revised this paper we got aware of a recent paper that investigates relativistic effects on the Fukui function of gold clusters: De HS, Krishnamurty S, Pal S (2009) J Phys Chem C 113:7101–7106.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Dedicated to the memory of Professor Jürgen Hinze and published as part of the Hinze Memorial Issue.
N. Sablon: Aspirant of the Research Foundation-Flanders (aspirant van het Fonds Wetenschappelijk Onderzoek-Vlaanderen).
N. Sablon, F. De Proft, and P. Geerlings are members of the QCMM Ghent-Brussels Alliance Group.
Rights and permissions
About this article
Cite this article
Sablon, N., Mastalerz, R., De Proft, F. et al. Relativistic effects on the Fukui function. Theor Chem Acc 127, 195–202 (2010). https://doi.org/10.1007/s00214-009-0722-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00214-009-0722-x