## Research: Carter Group Software

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

Download (PROFESS 2.0)

### 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

*J. Chem. Phys.*,

**125**,084102 (2006

**)**.

### Linear Scaling MRSDCI/Reduced Scaling MRACPF

##### Goal:

^{6}), 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}

^{7}The CD-LMRSDCI method scales on O(N

^{3}) with a much smaller prefactor than LMRSDCI. The O(N

^{3}) 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:

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

^{10}

^{ }

^{ }

**References:**

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**120**, 1693 (2004).

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**128**, 224106 (2008).

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*Molecular Physics*,

**108**, 2519 (2010).

*Phys. Chem. Chem. Phys.*,

**14**, 7710 (2012).

*Comput. Phys. Rep.,*

**2**, 95 (1985).

**GAMESS - AIDFT+U (ab initio DFT+U)**

##### Goal:

*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:

*U*and

*J*.

*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.

*Physical Review B*,

**76**, 155123 (2007)

*Journal of Chemical Physics*,

**129**, 014103 (2008)

**Abinit-embed**

##### Goal:

*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:

#### 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).