Sep 062012
 

I can think of a few pretty vigorous historical debates in quantum chemistry, like for example, valence bond theory vs. MO theory and coupled cluster theory vs. quadratic configuration interaction, but I never heard or read of a Green’s function vs. wave function methods debate.  I can recall reading about the utility of Green’s functions in Ostlund and Szabo’s Modern Quantum Chemistry.  My colleague Leif Jacobson brought to my attention a very interesting paper by L. J. Holleboom and J. G. Snijders [J. Chem. Phys. 93, 5826 (1990)], which compares second-order Møller-Plesset theory and Green’s function methods.  This paper is very instructive and is a good introduction to GFs.  The perturbative analysis of the Green’s function presented in the paper is an illuminating way to understand the connection with perturbation theory.  Another interesting result of this paper is that in the minimal basis set the second-order Green’s function energy of the hydrogen molecule is exact in the limit of an infinite internuclear distance.  This is a classical problematic case for MP2 theory, since the energy diverges as we stretch H2.  However, in the case of the Green’s function approach, this result holds only for the minimal basis set.  Using data for the other molecules studied by Holleboom and Snijders, it is difficult to assess which method performs better.  While GF(2) yields more accurate electron-electron repulsion energies, GF(2) total energies appear to be worse than those computed at the MP2 level.

 

 

 September 6, 2012  Article review No Responses »
Sep 272011
 

It has been a month since I moved to New Haven to start a postdoc at Yale. Research is going well, I am going to work on a completely new topic, the scattering of vibrationally excited molecules on metal surfaces. It’s a pretty complicated problem and I think it is going to be fun to work on it. Right now I am working on some experiments done by the Wodtke group. They essentially scatter vibrationally excited NO on a gold surface, Au(111) (see picture). One of the most interesting aspect of these experiments is that the NO can transfer the energy of 5-7 vibrational levels to excite and eject one electron from the surface. This in a bit counter intuitive since one would expect NO to transfer vibrational energy one quantum at a time and excite several electrons (think of the photoelectric effect). I hope to help solve this puzzle.

 September 27, 2011  Research 2 Responses »
Mar 302011
 

I just finished reading a new article by Musial, Perera, and Bartlett on multireference coupled cluster theory. This is an interesting paper that considers a simple but ingenious MRCC approach based on the equation of motion formalism.
For a CAS(2,2) problem, the reference wave function is taken to be a closed shell determinant \Phi^{+2} with the active orbitals either fully occupied or empty.  One then solves for the coupled-cluster wave function for this double anion state to get an intermediate wave function \exp(\hat{T}^{+2})\Phi^{+2}.  The MR ansatz used by Musial et al. is \Psi_\mathrm{easy} = \hat{S} \, \hat{r} \, \exp(\hat{T}^{+2})\Phi^{+2}, where \hat{r} removes a pair of electrons among all the occupied orbitals in \Phi^{+2}

    \[ \hat{r} = \sum_{mn} r_{mn} \hat{a}_m \hat{a}_n, \]

while \hat{S} is an operator that relaxes the wave function via ordinary excitations truncated at a give excitation level n

    \[ \hat{S} = 1 + \hat{S}_1  + \ldots + \hat{S}_n. \]

As the authors claim, the theory is simple, and simple in a multireference many-body approach is good. However, there is one problem with this approach. The energy is very sensitive to the choice of the original orbitals. In my experience, state-specific approaches based on the Jeziorski-Monkhorst ansatz tend to be a bit less sensitive. It would be great if the theory could also determine some optimal set of MOs (Bruckner, NOs, …).

 March 30, 2011  Articles No Responses »
Mar 232011
 

I just read a very nice paper by Hollett and Gill: “The two faces of static correlation” and wanted to write a short post about it.
The article concludes that there are two types of static electron correlation: type A is the correlation energy that can be recovered by UHF. A good example for type A is stretched H2. For infinite separation UHF can recover all the static correlation energy by breaking the spin symmetry of the wave function. Type B correlation is more subtle. Hollett and Gill show that Be-like ions with nuclear charge Z > 4.14 do not display the typical UHF triplet instability that characterize many near-degenerate problems. Nevertheless, these ions still have strong correlation effect that arises from the near-degeneracy of the 2s and 2p orbitals. Hollett and Gill call this type of static correlation Type B.

 March 23, 2011  Articles No Responses »
Mar 172011
 

My article on internally contracted MRCC theory: “An orbital-invariant internally contracted multireference coupled cluster approach” [F. A. Evangelista and J. Gauss, J. Chem. Phys. 134, 114102 (2011)] was finally published in the Journal of Chemical Physics. In this paper I try to depart from the Jeziorski-Monkhorst (JM) ansatz and explore a simple generalization of single-reference coupled cluster theory that uses a multideterminantal reference wave function. This works relates to previous studies of Banerjee and Simons [A. Banerjee and J. Simons, J. Chem. Phys. 76, 4548 (1982)] and many others.
The central result is that the ic-MRCC approach is more accurate than state-specific MRCC approaches based on the Jeziorski-Monkhorst ansatz. Moreover, ic-MRCC is orbital invariant (we test and prove it in the paper), and thus it is formally superior to JM-based methods.
A lot of work still needs to be done in this direction and some of the problematic aspects of the theory are discussed in the paper. The most important one is the elimination of linearly dependent excitations.

 March 17, 2011  Articles 1 Response »