May 312012

I just found a few interesting articles related to density matrices and Green’s functions:

There are interesting parallels between these works and papers published in the quantum chemistry literature.  And why not, let’s add a little debate on TD-DFT:

 May 31, 2012  Articles No Responses »
May 222011

I just found a few interesting papers, one on coupled cluster theory and one on orbital localization. I think they are pretty interesting and worth a read.

External coupled-cluster perturbation theory: Description and application to weakly interaction dimers. Corrections to the random phase approximation
J. Chem. Phys. 134, 184108 (2011)
Local orbitals by minimizing powers of the orbital variance
J. Chem. Phys. 134, 194104 (2011)
 May 22, 2011  Articles No 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 »