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Research: Carter Group Software

PROFESS (PRinceton Orbital-Free Electronic Structure Software): An orbital-free density functional theory program for condensed matter computations.

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MOLCAS-embed

Goal:

Provide an improved description of electron exchange and correlation in a local region of condensed matter via an embedded cluster method. Currently, we are focusing on molecule/metal surface interactions. The cluster of atoms close to the molecule is treated with multi-reference singles and doubles CI, while the background atoms are described by density functional theory. A DFT-based embedding potential describes the effect of the background atoms on the cluster.

Implementation in MOLCAS:


·         Construct the embedding potential from orbital-free DFT. 
·         SEWARD module: read in embedding potential and apply as an external potential to the cluster. 
·         RASSCF module: optimize the cluster molecular orbitals in the presence of the embedding potential. 
·         GUGA/MOTRA/MRCI  modules: get an embedded MRSDCI wavefunction
·         Use the embedded wavefunction to find the embedding total energy.
 
References
P. Huang and E.A. Carter, J. Chem. Phys., 125,084102 (2006).

Linear Scaling MRSDCI/Reduced Scaling MRACPF

Goal:
A Small Prefactor, Linear Scaling MRSDCI alogorithm:
 
Multireference approaches to electron correlation are necessary for studying bond-breaking, diradicals and transition metals. Multireference singles and doubles configuration interaction (MRSDCI) provides a straightforward multireference treatment. However, a conventional MRSDCI code scales as O(N6), which severely limits the size of molecule that can be investigated. Applying local truncation schemes can lead to a massive reduction in computational cost.1-5 By employing local truncation schemes together with integral screening, a O(N) local MRSDCI (LMRSDCI) is possible.6
 
Further reduction in computational cost can be achieved by Cholesky decomposing (CD) the two-electron integrals.7 The CD-LMRSDCI method scales on O(N3) with a much smaller prefactor than LMRSDCI. The O(N3) scaling can be reduced to O(N) using an atomic centered CD approach.8 Both of these methods have been expanded to include both a posteriori (Davidson type corrections) and a priori (multireference average coupled-paid functional MRACPF) size extensivity corrections.9

Implementation:

The CD-LMRSDCI algorithm has been implemented in the TigerCI (formerly BrewinCI) code, a plugin to the MOLCAS quantum chemistry package. MOLCAS is used to produce the integrals and orbitals and TigerCI performs the CD-LMRSDCI calculation.

(A)  MOLCAS produces the one- and two-electron integrals in the SEWARD mudule

(B)   The one particle orbitals are produced in the SCF (single reference) or RASSCF (multireference) module
 
(C)  The orbitals are localized in the LOCALISATION module
 
(D)  TigerCI performs the CD-LMRSDCI/CD-LMRACPF calculations based on the symmetric group graphical approach (SGGA).10


References:
 
1.       S. Saebo and P. Pulay, J. Chem. Phys., 86, 914 (1987).
2.       S. Saebo and P. Pulay, Ann. Rev. Phys., 44, 213 (1993). 
3.       D. Walter and E. A. Carter, Chem. Phys. Lett., 346, 177 (2001).
4.       D. Walter, A. Venkatnathan and E. A. Carter, J. Chem. Phys., 118, 8127 (2003).
5.       A. Venkatnathan, A. B. Szilva, D. Walter, R. J. Gdanitz and E. A. Carter, J. Chem. Phys., 120, 1693 (2004).
6.       T. S. Chwee, A. B. Szilva, R. Lindh, and E. A. Carter, J. Chem. Phys., 128, 224106 (2008).
7.       T. S. Chwee and E. A. Carter, J. Chem. Phys., 132, 074104 (2010).
8.       T. S. Chwee and E. A. Carter, Molecular Physics, 108, 2519 (2010).
9.       D. B. Krisiloff and E. A. Carter, Phys. Chem. Chem. Phys., 14, 7710 (2012).
10.     W. Duch and J. Karwowski, Comput. Phys. Rep., 2, 95 (1985).
GAMESS - AIDFT+U (ab initio DFT+U)
Goal:  
Evaluate ab initio the Coulomb and exchange parameters for DFT+U calculations. DFT+U theory is based on DFT, but the intra-atomic Coulomb and exchange interactions of localized valence electrons are effectively treated at the Hartree-Fock level of theory. DFT+U theory can correct the self-interaction errors in DFT, given the average Coulomb (U) and exchange (J) interactions of these localized valence electrons as input. To obtain these two parameters, previously researchers either empirically fitted them or performed constrained DFT calculations. We recently proposed instead to evaluate the U and J using unrestricted Hartree-Fock calculations on electrostatically embedded clusters.
 

Implementation in GAMESS:

The method used to evaluate these parameters is based on unrestricted Hartree-Fock calculations. A few subroutines were modified to get GAMESS to calculate U and J.
The modifications to each subroutine are:
gamess.src : check input files and variables;
prppop.src : get Mulliken populations for calculating U and J;
int2a.src : calculate the onsite two-electron integrals in the basis of the atomic orbitals;
rhfuhf.src : extensive modifications to calculate U and J;
scflib.src : calculate the Coulomb and exchange integrals through building the Fock matrix with direct SCF methods.
 
 
 
References:
N. J. Mosey and E. A. Carter, Physical Review B, 76, 155123 (2007)
N. J. Mosey, P. Liao, and E. A. Carter, Journal of Chemical Physics, 129, 014103 (2008)
Abinit-embed
Goal:  
Provide a DFT implementation to calculate embedding potentials using plane-wave basis sets. A correct treatment of the interaction of, e.g., gas molecules with metal surfaces requires both accurate treatment of exchange and correlation at the adsorption site as well as a correct description of the extended metal surface. To this end, a system of interest is partitioned into a cluster and a surrounding environment. An embedding potential V is used to mediate their interaction: we calculate such a global embedding potential by iteratively improving V based on the residual difference of the summed subsystem densities to a given reference density (obtained by standard DFT calculations on the entire system). The converged potential can then be used in subsequent high-level calculations of the cluster (see below). 

Implementation in Abinit:

  • Two parallel codes calculate electronic ground state densities of cluster and environment as a function of a global embedding potential (use V=0 as a starting guess).
  • The densities are added, compared to the reference density, and an improved embedding potential is calculated.
  • This procedure is iterated until convergence is reached.

References:

C. Huang, M. Pavone, and E. A. Carter, "Quantum mechanical embedding theory based on a unique embedding potential," J. Chem. Phys., 134, 154110 (2011).

Potential-functional embedding
Goal:  
Provide a versatile embedding framework to self-consistently combine different levels of theory in one calculation. We aim for the description of an arbitrarily partitioned complicated system, where each subsystem might be treated by a different level of theory. Their interaction is mediated by a self-consistently determined global embedding potential. To this end, our code calls the appropriate subsystem codes (see embedding software described above) to generate ground state densities of the embedded subsystems. These densities are gathered by the controlling code and used to improve the global embedding potential until self-consistency is reached. This allows for a self-constant interaction between the cluster (treated with correlated wavefunction techniques) and the surrounding environment (treated with, e.g., DFT). 

Implementation:

  • For the current embedding potential, call independent codes for each subsystem to calculate the corresponding ground state density (use V=0 as a starting guess)
  • Calculate the total density, and the corresponding potentials (to obtain a good kinetic potential for the total density, perform an OEP calculation)
  • Obtain the gradient of the total energy with respect to the embedding potential V and use it to improve V
  • Iterate the above sequence until convergence is reached

References:

C. Huang and E. A. Carter, "Potential-Functional Embedding Theory for Molecules and Materials," J. Chem. Phys., 135, 194104 (2011).