Evaluation of Coupled Perturbed and Density Functional Methods of Computing the Parity-Violating Energy Difference between Enantiomers

Abstract

We present new coupled-perturbed Hartree-Fock (CPHF) and density functional theory (DFT) computations of the parity-violating energy difference (PVED) between enantiomers for H(2)O(2) and H(2)S(2). Our DFT PVED computations are the first for H(2)S(2) and the first with the new HCTH and OLYP functionals. Like other "second generation" PVED computations, our results are an order of magnitude larger than the original "first generation" uncoupled-perturbed Hartree-Fock computations of Mason and Tranter. We offer an explanation for the dramatically larger size in terms of cancellation of contributions of opposing signs, which also explains the basis set sensitivity of the PVED, and its conformational hypersensitivity (addressed in the following paper). This paper also serves as a review of the different types of "second generation" PVED computations: we set our work in context, comparing our results with those of four other groups, and noting the good agreement between results obtained by very different methods. DFT PVEDs tend to be somewhat inflated compared to the CPHF values, but this is not a problem when only sign and order of magnitude are required. Our results with the new OLYP functional are less inflated than those with other functionals, and OLYP is also more efficient computationally. We therefore conclude that DFT computation offers a promising approach for low-cost extension to larger biosystems, especially polymers. The following two papers extend to terrestrial and extra-terrestrial amino acids respectively, and later work will extend to polymers.

Electroweak Parity-Violating Energy Shifts of Amino Acids: The “Conformation Problem”

“…Similarly if the solution conformation of aqueous L-alanine were known to a high level of accuracy, the structural hypersensitivity of the PVES would then be less of a problem. The reason for the structural hypersensitivity of the PVES was explained in the preceding paper (MacDermott et al 2009a): the calculated PVES is the result of near-cancellation of many large but oppositely signed contributions from different atoms, different MOs, and so on. The result is that very slight changes in the individual contributions (resulting from very slight changes in structure) can lead to large changes, including changes in sign, in the overall sum of many almost cancelling contributions.…”

“…Note that this convention is used in many commonly employed ab initio packages, such as GAUSSIAN (Frisch et al 1988), but unfortunately the CADPAC program (Amos et al 1998), a modified of version of which we use for Tranter's (1985) "preferred conformation in aqueous solution" (φ = 0 • ); other bondlengths, bond angles and torsion angles also as in Tranter (1985) Computational method E pv /10 −20 E h Gly L-Ala L-Ser L-Val L-Asp Table 1 shows our PVES results, using a variety of basis sets and computational methods, for the five amino acids studied by Mason and Tranter in the φ = 0 • conformation. The methods used-Uncoupled-Perturbed Hartree-Fock (UPHF), CoupledPerturbed Hartree-Fock (CPHF), Uncoupled-Perturbed Kohn-Sham (UPKS) and Coupled-Perturbed Kohn-Sham (CPKS)-are described in the preceding paper (MacDermott et al 2009a), where we also explain that a UPKS procedure can be used with non-hybrid functionals such as HCTH (Hamprecht et al 1998), but CPKS must be invoked with hybrid functionals such as B3LYP. Our values are consistently negative, in common with those of Tranter (1984, 1985), with the CPHF and DFT (UPKS and CPKS) values consistently 5-10 times larger than the UPHF values, in agreement with the results of Zanasi and Lazzeretti (1998).…”

“…In the preceding paper (MacDermott et al 2009a), we reviewed the various methods of computing the PVES, distinguishing between the "first generation" uncoupled-perturbed Hartree-Fock (UPHF) computations of Mason, Tranter and MacDermott Tranter 1984, 1985;Tranter et al 1992;MacDermott 1995), and the various "second generation" computations (Lazzeretti and Zanasi 1997;Laerdahl and Schwerdtfeger 1999;Berger and Quack 2000a;Hennum et al 2002) which take account of perturbative coupling and/or electron correlation. We also presented our own "second generation" coupledperturbed Hartree-Fock (CPHF) and density functional theory (DFT) computations of the PVED of H 2 O 2 and H 2 S 2 as test molecules.…”

“…We therefore decided to apply the methods of our preceding paper (MacDermott et al 2009a) to computing the PVES of these new proposed solution conformations, in an attempt to resolve the conflict and determine which hand of amino acids is actually PVED-stabilized in solution. We begin by applying our computational methods to the PVES of amino acids in the Mason and Tranter geometry (Section "CPHF and DFT PVES of Amino Acids in the Mason and Tranter "Solution Conformation"") and demonstrating the variation of the PVES with torsion angle (Section "Conformational Variation within Mason and Tranter Geometry").…”

The Search for Parity Violation in Chiral Molecules

“…Interestingly, a fit to a f ðZÞ ¼ aZ n function gives basically the same Z scaling law of n ¼ 6.17-6.18 for all levels of theory applied, and is therefore above the Z 5 scaling as suggested by Zeldovich [82]. A number of research groups in the past studied PV on the test molecules H 2 O 2 or H 2 S 2 or similar systems such as H 2 SO [151,156,[161][162][163][164][165][166].…”