Abstract
A brief review of relativistic quantum chemistry is given here. Relativistic effects and their importance in chemistry are discussed. An outline of different theoretical aspects is presented. Aspects of variation techniques relevant to relativistic calculations are discussed in detail. These involve the derivation of min-max theorems for Dirac, Dirac-Hartree-Fock and Dirac-Coulomb calculations. The consequence of relativistic Hamiltonians being unbounded are also discussed for other lines of investigation. The upper bounds derived are physically interpreted. Sample Dirac-Hartree-Fock results for the Be atom, calculated using both STO and GTO bases for the nonrelativistic orbitals and the upper components of the relativistic orbitals, are given. The inadequacy of the so-called kinetically balanced basis set is discussed and illustrated with these results. The importance of the variational or dynamical balance and hence the merit of the LCAS-MS scheme is pointed out. The possibility of calculating quantum electrodynamical pair energy from relativistic configuration interaction calculations on a two-electron atom is discussed and exemplified. The present status of relativistic molecular calculations is briefly reviewed. Conclusions on the aspects of variational analysis and molecular calculations are enclosed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aerts P J C and Nieuwpoort W C 1986Int. J. Quantum Chem. Symp. 19 267
Balasubramanian K 1989J. Phys. Chem. 93 6585
Balasubramanian K 1990Chem. Rev. 90 93
Balasubramanian K and Pitzer K S 1987Adv. Chem. Phys. 67 287
Basch H and Topiol S 1979J. Chem. Phys. 71 802
Bersuker I B, Budnikov S S and Leizerov B A 1972Int. J. Quantum Chem. 6 849
Bersuker I B, Budnikov S S and Leizerov B A 1977Int. J. Quantum Chem. 11 543
Blundell S 1992Phys. Rev. A46 3762
Blundell S A, Johnson W R, Lin Z W and Sapirstein J 1989Phys. Rev. A39 3768
Boca R 1987Int. J. Quantum Chem. 31 941
Brown G E and Ravenhall D G 1951Proc. R. Soc. London. A208 552
Caroll D P, Silverstone H J and Metzger P M 1979J. Chem. Phys. 71 4141
Chandra P and Buenker R J 1983J. Chem. Phys. 79 358, 366
Christiansen P A, Balasubramanian K and Pitzer K S 1982J. Chem. Phys. 76 5087
Christiansen P A and Pitzer K S 1980J. Chem. Phys. 73 360
Clementi E and Roetti C 1974Atom. Data Nucl. Data Tables 14 177
Culberson J C, Knappe P, Rösch N and Zerner M C 1987Theor. Chim. Acta 71 21
Das G P and Wahl A C 1978J. Chem. Phys. 69 53
Datta A, Srivastava C M and Datta S N 1993J. Phys. Chem. 97 9996
Datta S and Datta S N 1992Pramana — J. Phys. 38 521
Datta S N 1980Chem. Phys. Lett. 74 568
Datta S N 1984Pramana — J. Phys. 23 L275
Datta S N 1987Pramana — J. Phys. 28 633
Datta S N 1989Lecture notes in chemistry, No. 50 (ed.) D Mukherjee (Berlin: Springer) pp. 393–410
Datta S N 1992Pramana — J. Phys. 38 51
Datta S N and Devaiah G 1988Pramana — J. Phys. 30 387
Datta S N and Ewig C S 1982Chem. Phys. Lett. 85 443
Datta S N, Ewig C S and Van Wazer J R 1978Chem. Phys. Lett. 57 83
Datta S N and Jagannathan S 1984Pramana — J. Phys. 23 467
Desclaux J P 1973Atom. Data Nucl. Data Tables 12 311
Desclaux J P 1975Comput. Phys. Commun. 9 31
Desclaux J P and Pyykkö P 1974Chem. Phys. Lett. 29 534
Dietz K 1986aProceedings of the NATO Advanced Study Institute Giant Resonances in Atoms and Solids, Let Houches
Dietz K 1986bProceedings of the International Conference on Vacuum Ultraviolet Physics, Lund
Dietz K and Hess B A 1989Phys. Scr. 39 682
Dietz K, Lechtenfeld O and Weymans G 1982J. Phys. B15 4301
Drake G W F and Goldman S P 1981Phys. Rev. A23 2093
Ermler W C, Lee Y, Christiansen P A and Pitzer K S 1981Chem. Phys. Lett. 81 70
Esser M 1984Int. J. Quantum Chem. 26 313
Foldy L and Wouthuysen S 1950Phys. Rev. 78 29
Fuentealba P, Stoll H, Szentpaly L V, Schwerdtfeger P and Preuss H 1983J. Phys. B16 L323
Gorceix O and Indelicato P 1988Phys. Rev. A37 1087
Gorceix O, Indelicato P and Desclaux J P 1987J. Phys. B20 639
Grant I P 1986J. Phys. B19 3187
Grant IP, Mackenzie B J, Norrington P H, Meyers D F and Pyper N C 1980Comput. Phys. Commun. 21 207
Gurtler R and Hestenes D 1975J. Math. Phys. 16 573
Hafner P and Schwarz W H E 1978J. Phys. B11 217
Hafner P and Schwarz W H E 1979Chem. Phys. Lett. 65 537
Hay P J, Wadt W, Kahn L R and Bobrowics F W 1978J. Chem. Phys. 69 984
Hess B A 1985Phys. Rev. A32 756
Hess B A and Chandra P 1987Phys. Scr. 36 412
Huang K-N and Johnson W R 1982Phys. Rev. A25 634
Huber K P and Herzberg G 1979Constants of diatomic molecules (New York: Van Nostrand)
Indelicato P, Gorceix O and Desclaux J P 1987J. Phys. B20 651
Ishikawa Y, Baretty R and Sando K M 1985Chem. Phys. Lett. 117 444
Ishikawa Y, Binning R C Jr and Sando K M 1983Chem. Phys. Lett. 101 111
Johnson W R, Idrees M and Sapirstein J 1987Phys. Rev. A35 3218
Johnson W R and Soff G 1985Atom. Data Nucl. Data Tables 33 405
Kin Y K 1967Phys. Rev. 154 17
Krauss M and Stevens W J 1984Ann. Rev. Phys. Chem. 35 357
Krauss M, Stevens W J and Basch H 1985J. Comput. Chem. 6 287
Kutzelnigg W 1984Int. J. Quantum Chem. 25 107
Lee Y S and McLean A D 1982J. Chem. Phys. 76 735
Li L-M, Ren J-Q, Xu G-X and Wang X-Z 1983Int. J. Quantum Chem. 23 1305
Lindroth E 1988Phys. Rev. A37 316
Lindroth E, Presson H, Salomonson S and Matersson A M 1992Phys. Rev. A45 1493
Lohr L L, Hotokka M and Pyykkö P 1980Quantum chemistry program exchange — QCPE12 387
Lohr L L and Pyykkö P 1979Chem. Phys. Lett. 62 333
MacDonald A H and Vosko S H 1979J. Phys. C12 2977
Mackenzie B J, Grant I P and Norrington P H 1980Computer Phys. Commun. 21 233
Mackenzie B J, Grant I P and Norrington P H 1981Computer Phys. Commun. 23 222
Malli G and Oreg J 1975J. Chem. Phys. 63 830
Malli G L and Pyper N C 1986Proc. Roy. Soc. London, Ser. A407 377
Mittleman M H 1981Phys. Rev. A24 1167
Mohanty A, Panigrahy S and Clementi E 1991Modem techniques in computational chemistry: MOTECC-91, ed. E Clementi; (Leiden, ESCOM) Ch. 15
Mohr P J 1985Phys. Rev. A32 1949
Partridge H 1987J. Chem. Phys. 87 6643
Partridge H 1989NASA Technical Memorandum 101044
Pitzer K S 1979Acc. Chem. Rev. 12 271
Pyper N C 1980Mol. Phys. 39 1327
Pyykkö P 1986 Lecture notes in chemistry No. 41 (Berlin, Springer)
Pyykkö P 1988Chem. Rev. 88 563
Pyykkö P and Desclaux J P 1979Acc. Chem. Res. 12 276
Rajagopal A K 1979Adv. Chem. Phys. 41 59
Rajagopal A K and Callaway J 1973Phys. Rev. B7 1912
Roothaan C C J 1960Rev. Mod. Phys. 32 179
Rosicky F and Mark F 1975J. Phys. B8 2581
Ross R B and Ermler W C 1985J. Phys. Chem. 89 5202
Sakaki S, Hagiwara N, Iwasaki N and Ohyoshi A 1977Bull. Chem. Soc. Japan 50 14
Salomonson S and Oster P 1989aPhys. Rev. A40 5548
Salomonson S and Oster P 1989bPhys. Rev. A41 4670
Sapirstein J 1987Physica Scripta 36 801
Schwarz W H E 1987Physica Scripta 36 403
Schwarz W H E, Chu S Y and Mark F 1983Mol. Phys. 50 603
Schwarz W H E and Wechsel-Trakowski E 1982Chem. Phys. Lett. 85 94
Schwerdtfeger P 1987Physica Scripta 36 453
Serber R 1985Phys. Rev. 49
Simons J and Jorgensen P 1976J. Chem. Phys. 64 1413
Soff G and Mohr P J 1988Phys. Rev. A38 5066
Stanton R E and Havriliak S 1984J. Chem. Phys. 81 1910
Sucher J 1980Phys. Rev. A22 348
Sundholm D 1988Chem. Phys. Lett. 149 251
Sundholm D and Pyykkö P 1987Physica Scripta 36 400
Teichteil C T, Pelissier M and Spiegelmann F 1983Chem. Phys. 81 273
Uehling E A 1935Phys. Rev. 48 55
Weiss A W 1961Phys. Rev. 122 826
Wichmann E H and Kroll N M 1956Phys. Rev. 101 843
Wood J, Grant I P and Wilson S 1985J. Phys. B18 3027
Xu G-X and Ren J-Q 1986Int. J. Quantum Chem. 29 1077
Xu G-X and Ren J-Q 1987Lanth. Act. Res. 2 67
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Datta, S.N. Relativistic quantum chemistry and rigorous variational analysis. Proc. Indian Acad. Sci. (Chem. Sci.) 106, 445–466 (1994). https://doi.org/10.1007/BF02840762
Issue Date:
DOI: https://doi.org/10.1007/BF02840762