Relativistic Quantum Chemistry Valérie Vallet ([email protected]) CNRS, Lille University, France Outline ▸ Why do relativistic effects become significant when the atomic number Z increases? ▸ How to account for relativistic effects in quantum chemistry? ▸ Which role do relativistic effects play in the chemistry across the periodic table ? ✴ Bond lengths, frequencies ✴ Binding energies, reaction barriers ✴ Spectroscopy ✴ Ionization potentials, electron affinities ✴ NMR properties Relativistic Quantum Chemistry | Valérie Vallet @ CNRS Uni. Lille 2 Relevance and nature of relativistic effects Can you spot the difference? Property Ag Au Electronic configuration [Kr] 4d105s1 [Xe] 4f14 5d10 6s1 Crystal structure FCC FCC Color silver golden Why does gold look so… golden? Relativistic Quantum Chemistry | Valérie Vallet @ CNRS Uni. Lille 4 Have a look at relativistic effects in chemistry Chem. Rev. 1988. 88. 563-594 583 Relativistic Effects in Structural Chemistry EKKA PYYKKO Department of chemistry. Uinh'ersity of Helsinki, Et. Hesperiankatu 4, 00100 Helsinki, FWand' Received March 17, 1987 (Revised Manuscript Received July 7, 1987) Contents I. Introduction 563 11. Theory and Methods 565 A. Fundamental Questions 565 B. Properties of Individual Atoms 565 C. Available Quantum Chemical Methods for 567 Molecules 0. Effectson Bond Lengths 571 111. Molecular Geometries 573 A. Bond Lengths 573 B. Bond Angles 577 C. Catalysis and Reaction Pathways 577 D. Solids 578 pekka pwkko was bom in 1941 in Hinnerjoki. Finland. and recehed E. The Inert-Pair Effect 578 his FiLKand.. FiLLic.. and FIl.dr from the Unhrersity of Turku. After IV. Other Properties 580 working at We UnWisof Aafhus, Gatebwg. Helsinki. Jyviisky!A, A. Force Constants 580 Paris XI, and Oulu (1968-1974). he became Associate Professor B. Dlssoclatlon Energies 580 of Quantum Chemistry at Abo Akademi in Turku in 1974. Since C. Splittings 582 1984 he has been Professor of Chemistry at the University of Finestructure Hekinki. Finland. where he holds We "Swedish Chair of Chemistry". D. Ionization Potentials, Electron Affinities, 582 founded in 1908 as a parallel one to Johan Gadolin's former chair, and Photoelectron Spectra established in 1761. His main interests have been NMR meorY and E. Colors 583 relativistic quantum chemistry F. Charge Distributions and Molecular 563 Relativistic Quantum Chemistry | Valérie Vallet @ CNRS Uni. Lille 5 Moments the relativistic mass increase G. Magnetic Resonance Parameters 583 V. Further Possible Examples and Open Problems 585 m = mo/(l - (U/C))1'* (la) VI. Summary: Relativistic Effects in the Periodic 587 Table mo being the rest mass and u the speed of the electron, VII. References 587 the effective Bohr radius, a. = (4rc0)(h2/me2) (W I. Introducflon will decrease for inner electrons with large average The two basic theories of modem physics are the speeds. For a 1s shell at the nonrelativistic limit, this theory of relativity and quantum mechanics. While the average speed is 2 au. Thus the 1s electron of Hg has importance of the latter in chemistry was instantly a u/c of 80/137 = 0.58, implying a radial shrinkage by recognized, it was not until the 19708 that the full 23%. Because the higher s shells have to be orthogonal relevance of relativistic effects in heavy-element chem- against the lower ones, they will suffer a similar con- istry was discovered. traction. Due to interacting relativistic and shell- For very precise calculations, relativistic energy con- structure effects, their contraction can in fact he even tributions are already needed for H2+or H,. They in- larger; for gold, the 6s shell has larger (percental) re- crease, for valence shells, roughly like .??. Depending lativistic effects than the Is shell. on the accuracy achieved in the calculation, they be- For readers not convinced by a qualitative argument, come relevant again around Cu, or perhaps Ag. For the we can consider an exactly solvable problem: the hy- sixth row (around W to Bi), relativistic effects are drogen-like atom with 2 = 80 in Figure 1. As seen, the comparable to the usual shell-structure effects and contractions are comparable for the three firsts shells. provide an explanation for much of the basic freshman Alternatively, to understand the valence electron chemistry of these elements. For the existing actinoids effects in a many-electron atom, one can compare (see relativistic effects are essential. ref 35) the relativistic (Dirac) and nonrelativistic The relativistic effects can be defined as anything (Schrodinger) dynamics for the valence electron in a arising from the finite speed of light, c = 137.035 989 5 given atomic potential, to study the importance of the (61)au4I5, as compared to c = m. The basic theory is direct relativistic effect. The (originally surprising) discussed in section 11. result" was that this is the main effect for the 6s of Au It has become a tradition to introduce the reader to or the 6p* (=6p,/,) of TI. The relativistic change of the qualitative effects of relativity as follows: Due to the atomic potential mattered less than the direct, dy- 0009-2665/88/078&0563$06.50/0 0 1988 American Chemical Society Chem. Rev. 1988. 88. 563-594 583 Relativistic Effects in Structural Chemistry EKKA PYYKKO Department of chemistry. Uinh'ersity of Helsinki, Et. Hesperiankatu 4, 00100 Helsinki, FWand' Received March 17, 1987 (Revised Manuscript Received July 7, 1987) Contents I. Introduction 563 11. Theory and Methods 565 A. Fundamental Questions 565 B. Properties of Individual Atoms 565 C. Available Quantum Chemical Methods for 567 Molecules 0. Effectson Bond Lengths 571 111. Molecular Geometries 573 A. Bond Lengths 573 B. Bond Angles 577 C. Catalysis and Reaction Pathways 577 D. Solids 578 pekka pwkko was bom in 1941 in Hinnerjoki. Finland. and recehed E. The Inert-Pair Effect 578 his FiLKand.. FiLLic.. and FIl.dr from the Unhrersity of Turku. After IV. Other Properties 580 working at We UnWisof Aafhus, Gatebwg. Helsinki. Jyviisky!A, A. Force Constants 580 Paris XI, and Oulu (1968-1974). he became Associate Professor B. Dlssoclatlon Energies 580 of Quantum Chemistry at Abo Akademi in Turku in 1974. Since C. Splittings 582 1984 he has been Professor of Chemistry at the University of Finestructure Hekinki. Finland. where he holds We "Swedish Chair of Chemistry". D. Ionization Potentials, Electron Affinities, 582 founded in 1908 as a parallel one to Johan Gadolin's former chair, and Photoelectron Spectra established in 1761. His main interests have been NMR meorY and E. Colors 583 relativistic quantum chemistry F. Charge Distributions and Molecular 563 Moments the relativistic mass increase G. Magnetic Resonance Parameters 583 V. Further Possible Examples and Open Problems 585 m = mo/(l - (U/C))1'* (la) VI. Summary: Relativistic Effects in the Periodic 587 Table mo being the rest mass and u the speed of the electron, VII. References 587 the effective Bohr radius, a. = (4rc0)(h2/me2) (W RelativisticI. Introducflon effects in chemistry will decrease for inner electrons with large average The two basic theories of modem physics are the speeds. For a 1s shell at the nonrelativistic limit, this theory of relativity and quantum mechanics. While the average speed is 2 au. Thus the 1s electron of Hg has importance of the latter in chemistry was instantly a u/c of 80/137 = 0.58, implying a radial shrinkage by recognized, it was not until the 19708 that the full P. 23%.Pyykkö, Because Chem. Rev. the 1988,higher 88, s shells563 have to be orthogonal relevance of relativistic effects in heavy-element chem- against the lower ones, they will suffer a similar con- istry was discovered. traction. Due to interacting relativistic and shell- For very precise calculations, relativistic energy con- structure effects, their contraction can in fact he even tributions are already needed for H2+or H,. They in- larger; for gold, the 6s shell has larger (percental) re- crease, for valence shells, roughly like .??. Depending lativistic effects than the Is shell. ▸ Relativistic effects ariseon fromthe accuracy the finite achieved speed in the calculation, of light (cthey ≈ be- 137 a.u.)For readers not convinced by a qualitative argument, come relevant again around Cu, or perhaps Ag. For the we can consider an exactly solvable problem: the hy- sixth row (around W to Bi), relativistic effects are drogen-like atom with 2 = 80 in Figure 1. As seen, the ▸ v(1s) ∼ Z a.u. comparable to the usual shell-structure effects and contractions are comparable for the three firsts shells. provide an explanation for much of the basic freshman Alternatively, to understand the valence electron chemistry of these elements. For the existing actinoids effects in a many-electron atom, one can compare (see ▸ The relativistic mass increaserelativistic foreffects electrons are essential. with rest mass m0 andref 35) speed the relativistic v is (Dirac) and nonrelativistic The relativistic effects can be defined as anything (Schrodinger) dynamics for the valence electron in a arising from the finite speed of light, c = 137.035 989 5 given atomic potential, to study the importance of the m0 au4I5,as compared to c = m. The basic theory is direct relativistic effect. The (originally surprising) (61) m = γm0 = discussed in section 11. 2 result" was that this is the main effect for the 6s of Au It has become a tradition to introduceZ the reader to or the 6p* (=6p,/,) of TI. The relativistic change of the qualitative effects of relativity1 as follows:2 Due to the atomic potential mattered less than the direct, dy- r − c 0009-2665/88/078&0563$06.50/0 0 1988 American Chemical Society ▸ The Bohr radius is inversely proportional to electron mass: 2 4⇡"0~ a = 0 m ▸ Relativity will contract orbitals of one-electron atoms, e.g., Au78+ (Z/c = 57%), 18% relativistic contraction of the 1s orbital.