Relativistic Effects in Chemistry

We have developed the relativistic theory of molecular science from the first principles offundamental physics, namely from quantum mechanics and from the special theory of relativity. In principle, we are now able to study any molecular system using quantum chemical methods of controllable accuracy. Comparisons with purely mmrelativistic calculations highlight so-called relativistic effects. Prominent macroscopic examples are the yellowish color of elemental gold and the fluidity of mercury at ambient temperature. This final chapter comprises some important examples for which relativity is of paramount importance. 

The importance of relativistic quantum mechanics to molecular science was realized in the 1970s [1007-1011], which came somewhat as a surprise since it was not expected that low-energy molecular physics requires a quantum mechanical description beyond Schrodinger quantum mechanics. 

Relativistic Quantum Chemistry. Markus Reiher and Alexander Wolf 

Since relativistic calculations are not significantly more expensive than nonrelativistic Schrodinger-theory-based calculations (except for a small prefactor at most), the relativistic calculation is always to be preferred as should have become evident especially in the last couple of chapters. Hence, we may be a bit sloppy in discussing qualitative relativistic effects and use the term mostly to emphasize that certain effects (Isuch as spin-orbit coupling), which naturally arise in the relativistic theory, may lead to important differences if they were neglected in the calculation. 

We may discuss relativistic effects at the example of reaction energies. Imagine the decomposition of an ether which, for illustration purposes, we may formally write as 

---

K. Balasubramanian, Relativistic Effects in Chemistry John Wiley Sons, New York (1997). 

Rev..1988, 88, 563. A very detailed paper from the main originator of the studies of relativistic effects in chemistry. There are 428 references ... 

The special theory of relativity (the one germane to chemistry, since gravity is irrelevant to our science) and its chemical consequences are nicely reviewed in Balasubramanian K (1997) Relativistic effects in chemistry, Parts A and B. Wiley, New York... 

K. Balasubramanian, Relativistic Ejfects in Chemistry Theory and Techniques and Relativistic Effects in Chemistry Theory and Techniques Pt. A, John Wiley, Chichester, 1997 ... 

Schwarz, W. H. E. (1991) Fundamentals of relativistic effects in chemistry. In The Concept of the Chemical Bond (ed. Z. B. Maksid), pp. 593-643. Vol. 2 of Theoretical Models of Chemical Bonding. Springer. 

T. Yanai, T. Nakajima, Y. Ishikawa and K. Hirao, in K. Hirao, Y. Ishikawa (Eds.), Recent advances in relativistic effects in chemistry. World Scientific, Singapore, 2004, pp. 221. 

Balasubramanian, K. Relativistic Effects in Chemistry Part A. Theory and Techniques, New York Wiley 1997. 

R. E. yioss. Advanced Molecular Quantum Mechanics, Chapman and Hall, 1973 P. Pyykko, Chem. Rev., 88 (1988), 563 J. Almlof, O. Gropen, Rev. Comp. Chem., 8 (1996), 203 K. Balasubramanian, Relativistic Effects in Chemistry, Wiley, 1997. 

Many examples of relativistic effects in chemistry have been published in a number of papers. Pekka Pyykko has published a complete data base of references in a series of books [8-10] which is also available on-line on the Internet [11]. 

The nature is always relativistic. Non-relativistic objects do not exists. The only way to see the role of relativistic effects in chemistry is through the comparison between relativistic and nonrelativistic theory and results. The values of the relativistic effects for a given quantity X are then usually calculated as a difference between the relativistic and nonrelativistic values of this quantity, i.e. AX = X rel) — X nrel) calculated at the same level of theory. Therefore, from both fundamental and practical points of view there is a necessity for relativistic quantum chemistry theory and applications. While the Hamiltonian of a molecule is exactly known in nonrelativistic quantum mechanics, this is no longer the case for the relativistic formulation. Many relativistic Hamiltonians have been derived over the past decades. It goes beyond the goal of this chapter to review all of the... 

---