Gulzari L. Malli
Professor Emeritus

M.Sc., McMaster University, 1960
M.S., Ph.D., 1964, University of Chicago

Tel: (778) 782-4880
Fax: (778) 782-3765



Revitalistic and electron correlation effects for molecules of superheavy elements.pdf



Current Research Program :
Relativistic Quantum Chemistry of Heavy and Superheavy Elements:
Rutherfordium through up to primordial superheavy element ekaplutonium
E126 (with Z=126).

Our main research interests lie in the general area of ab initio relativistic quantum chemistry of the heavy and superheavy elements with 75 < Z > 126, viz; to develop theoretical and computational methodology for ab initio all-electron calculation of the relativistic as well as electron correlation effects for molecules, clusters and solids involving heavy and superheavy elements (SHE), with Z =75-126, where Z is the nuclear charge. Our major contributions to this area of research are summarized below:

  1. Three decades ago we developed the “Relativistic Self-consistent Field Theory for Closed-Shell Molecules" : G.Malli and J.Oreg, J.Chem.Phys.63, 830 (1975). A computer code was developed based upon our formalism and the first Dirac-Fock SCF calculations using the basis set of Slater-type-orbitals (STO’s) were reported on the diatomics Li 2 and Be 2, see G.L.Malli and J.Oreg, Chem.Phys.Letters, However, these were preliminary calculations with a minimum of basis set and for the medium and heavy atom molecules very extensive calculations involving extended basis set would be mandatory. As is well-known in nonrelativisic quantum chemistry, the STO’s are unsuitable for molecular calculations in general on polyatomics as first pointed out by Boys who proposed the use of Gaussian type orbitals (GTO’s) for quantum mechanical calculations on polyatomics.
  2. In 1979 we introduced the Gaussian spinor basis set for relativistic Dirac-Fock SCF calculations on atoms and (molecules): G.L.Malli, Chem.Phys.Letters, 68, 529(1979) where we reported the DF SCF calculations for Xe using our G-spinor basis set.
  3. The first all-electron fully relativistic calculation on the heavy diatomic AuH was reported by Malli and Pyper [G.L.Malli and N.C.Pyper, Proc.Roy.Soc. A407, 377(1986)] using the numerical DF atomic spinors of Au and H as the basis set. We showed for the first time that due to relativity
      1. there was significant 5d-6s hybridization in the gold atom,
      2. the predicted dissociation energy was doubled, and
      3. there was a bond contraction of 0.45 bohr.
  4. We performed the first limited Relativistic Configuration Interaction (RCI) calculation for AuH and we reported the effects of relativity and electron correlation on bond length, vibrational frequency, dissociation energy (and dipole moment). Later we reported such results for the diatomic hydrides of the sixth row elements. A 50% reduction of the dipole moment was predicted by relativity for AuH: A.F.Ramos, N.C.Pyper and G.L.Malli, Phys.Rev. A 38, 2729(1989).No such calculations had been reported for any heavy atom molecule. We extended our relativistic DF SCF theory to a general class of open shell molecular systems [G.L.Malli, Chem.Phys.Lett.73, 510(1980)] and its application to AuH+ was reported [Y.Ishikawa, G.L.Malli and N.C.Pyper, Chem.Phys.Lett.194, 481(1992)].
  5. We have developed the Universal Gaussian Basis set [G.L.Malli et al, Phys.Rev. A 47,143 (1993), ibid Chem.Phys.Lett, 201, 37 (1993);ibid J.Chem.Phys. 101,6829 (1994); ibid, J.Chem.Phys.109,8759(1998)] for the first ab initio all-electron Dirac-Fock (DF) relativistic self-consistent field (RSCF) calculations for a large number of diatomics and polyatomics involving heavy and superheavy elements(SHE).
  6. We have performed the first Dirac- scattered wave (DSW) SCF calculations on gold clusters with 3 to 13 gold atoms in various geometries including the first Icosahedral (I h*) and cuboctahedron geometries for 13 gold atoms and we discussed the relative stabilities for the 13 gold -atom geometrical configurations:
  7. Recently we have investigated both the effects of relativity and electron correlation using our fully relativistic Dirac-Fock, relativistic Moller-Plesset second order perturbation theory (MP2 ), coupled-cluster single and doubles (RCCSD) and RCCSD(T) calculations which treat the triple excitations as perturbation.for a large number of molecules involving heavy actinides and SHE elements up to the primordial SHE E126 ekaplutonium.
  8. Currently we are using the relativistic coupled-cluster methodology for atoms and molecules of heavy and SHE. These calculations are performed using our universal Gaussian basis set (UGBS) for atoms of the heaviest elements (Z=104-126) assuming a Gaussian nuclear model using the MOLFDIR code.
  9. All-electron fully relativistic 4-component DF SCF calculations have been performed for over 200 molecules of the transactinides and their lighter homologs which include the following: tetrachlorides of Zr, Hf and Rf (Z=104); pentachlorides of Nb, Ta and Ha (Z=105); hexachlorides of Mo, W and Sg (Z=106); oxychlorides TaOCl 3 HaOCl 3 , SgOCl 4 , SgO 2Cl 2 ; hexafluorides and hexachlorides of E110 ( Z=110); tetra,penta,and hexachlorides and the corresponding-bromides of Rf, Ha, Sg , Ns( Z=107) and E111 ( Z=111), hexafluoride and hexachloride of E126 ( ekaplutonium).
  10. We have also investigated the stability and atomization (binding) energy of the various actinide and superheavy element carbonyls M(CO)n and isocarbonyls M(OC)n (n=1-6, M=Th, U,Pu, Rf,Sg,E110, E112, E118,E122,E124,E126),etc.

Our gargantuan calculations which required thousands of CPU hrs and huge disk space were performed on Cray C90 and IBM RS 6000 Seaborg supercomputers at National Energy Research Scientific Computing Center (NERSC ), supported by the Office of Science of the U.S. Department of Energy and at the Cray supercomputer centre at Chippewa Falls through the generosity of Cray Inc, Canada.

Our recent research in the chemistry and physics of the heavy and superheavy elements was featured in the Chemical & Engineering News (C & EN): Heavy Elements, March 23,1998 issue, see pp 54-55. More recently, our research in Transactinde Chemistry was highlighted in Chemical & Engineering News (C & EN ) December 16, 2002 issue,p.11, devoted to Chemistry Highlights 2002 under “ HEAVY WEIGHTS YIELD TO COMPUTATION”.


Selected Publications (1995-2005)

103. Malli, G.L., J. Styszynki, and A.B.F. DaSilva (1995). Ab Initio Calculation of Relativistic and Electron Correlation Effects in Polyatomics using the universal Gaussian Basis set : XeF 2 . Int. J. Quantum. Chem., 55, 213-225

104. Styszynski, J. and Malli, G.L. (1995). Electron Correlation and Relativistic Effects in Xenon Tetrafluoride, Int. J. Quantum. Chem., 55, 227-235.

105. Malli, G.L. and Styszynki J. (1996) Ab initio all-electron Dirac-Fock-Breit calculations for UF 6, J. Chem. Phys. 104:, 1012-1017.

106 Styszynski, J. Xiaoping, C., Malli, G.L. and L. Visscher (1997). Relativistic All-Electron Dirac-Fock-Breit Calculations on Xenon Fluorides (XeF n, n=1,2,4,6), J. Computational Chem., 18 , 601-608.

107 Malli, G.L. (1997) .Ab Initio Relativistic Quantum Chemistry of Superheavy Transactinide Elements:Rutherfordium through Eka-Astatine , Proceedings of The Robert A.Welch Foundation XXXXI Conference on Chemical Research ‘ The Transactinide Elements ‘, 197-228 , Houston, Texas, U.S.A.

108 Malli, G.L. and J.Styszynski (1998) Ab Initio all-electron fully Relativistic Dirac-Fock-Breit Calculations for Molecules of the Transactinide Superheavy Elements: Rutherfordium Tetrachloride , J.Chem.Phys, 109, 4448-4455.

109. Malli, G.L and Y. Ishikawa (1998) The Generator Coordinate Dirac-Fock Method for Open-Shell Atomic Systems , J.Chem.Phys., 109 , 8759-8763

110 . Malli, G.L. (2001) Relativistic Quantum Chemistry of Superheavy Transactinide Elements. New Trends in Quantum Systems in Chemistry and Physics, Volume 1, 243-255.  

111 Malli, G.L. (2001) Relativistic all-electron Dirac-Fock calculations on RnF 6 and its ions. Journal of Molecular Structure (Theochem), 537,: 71-77.

112. Malli, G.L. (2002) Prediction of the existence of radon carbonyl: RnCO. Int. J Quantum Chem, 90, 611-615.

113. Malli, G.L. (2002) Ab initio all-electron fully relativistic Dirac-Fock self-consistent field calculations for molecules of superheavy elements: Seaborgium hexabromide. J. Chem. Phys, 116, 5476.

114. Malli, G.L. (2002) ( Communication) Dramatic relativistic effects in atomization energy and volatility of the superheavy Hassium tetroxide and OsO 4, J. Chem. Phys, 117, 10441-10443.

115. Malli, G.L. (2003). Ab initio all-electron fully relativistic Dirac-Fock Self-consistent field calculations for UCl 6. Mol. Phys., 101, 287-294.

116. Malli, G.L., Siegert, M and.Turner, D.P (2004) Relativistic and Electron Correlation Effects for Molecules of Heavy Elements: An initio Fully Relativistic Coupled-Cluster Calculations for PbH 4 , Int. J. Quantum Chem.99, 940-949

117. Malli,G.L. (2004) Relativistic Quantum Chemistry of Heavy and Superheavy Elements: Fully Relativistic Coupled-Cluster Calculations for Molecules of Heavy and Transactinide Superheavy Elements. Fundamental World of Quantum Chemistry, Vol. III, 323-363, E.J.Brandas and E.S.Kryachko (eds), Kluwer Academic Publishers.

118. Arratia-Perez, R., Hernandez-Acvedo, L, and Malli, G.L., Calculated optical and magnetic properties of hexafluorouranate(V) anion:UF 6 –, J.Chem.Phys.121,7743-7747 (2004).

119. Malli, G.L., (2005). (Communication), Electronic structure and prediction of atomization energy of naked homoleptic uranium hexacarbonyl U(CO) 6 , J.Chem.Phys. (accepted Nov 21, 2005,in press)

120. Malli, G.L.,(2005). (Communication), Dissociation energy of ekaplutonium fluoride E126F: The first diatomic with molecular spinors consisting of g atomic spinors, J.Chem.Phys. (J.Chem.Phys. (accepted Nov 30, 2005 in press)



  • Fraga, S. and G.L. Malli (1968). Many-electron Systems, Properties and Interactions, W.B. Saunders, Philadelphia, U.S.A., pp. 196.
  • Malli, G.L. (Ed.) (1983). Relativistic Effects in Atoms, Molecules and Solids, Plenum Press, pp. 554, New York, U.S.A. Proceedings of the NATO ASI directed and organized by Professor G.L. Malli, and held at U.B.C., August 10-21, 1981.
  • Malli, G.L. (Ed.) (1994). Relativistic and Electron Correlation Effects in Molecules and Solids, Plenum Press, pp. 486, New York, U.S.A., Proceedings of the NATO ASI directed and organized by Professor G.L. Malli, and held at U.B.C., August 10-21, 1992.

 last updated : Dec. 2, 2005