Codes developed in the Carter group are available through github repositories: https://github.com/EACcodes
Princeton orbitalfree electronic structure software (PROFESS): https://github.com/EACcodes/PROFESS
TigerCI: https://github.com/EACcodes/TigerCI under the GPL2.0 license.
VASP density functional embedding theory (DFET): https://github.com/EACcodes/VASPEmbedding under the Mozilla Public License Version 2.0 (access to VASP ver. 5.3.3 is required)
ABINIT DFET: https://github.com/EACcodes/AbinitEmbedding under the GPL3.0 license (access to ABINIT ver. 7 required)
Embedding integral generator: https://github.com/EACcodes/EmbeddingIntegralGenerator under the Mozilla Public License Version 2.0
Density matrix functional embedding theory (DMFET) in NWCHEM: https://github.com/EACcodes/DMFETpublic (requires access to NWCHEM ver. 6.5)
Globally optimized local pseudopotential (goLPS) generation: https://github.com/EACcodes/goLPS under the CC BYND 4.0 license
Bulkderived pseudopotential (BLPS) generator: https://github.com/EACcodes/BLPSGenerator under the GPL3.0 license
Ab Initio DFT+U determination: https://github.com/EACcodes/AIDFTU (currently implemented in GAMESS)
Descriptions of the softwares are provided below.
PROFESS (PRINCETON ORBITALFREE ELECTRONIC STRUCTURE SOFTWARE)
You may download PROFESS 3.0 from the Computer Physics Communications Program Library. Previous versions of PROFESS (1.0 and 2.0) are also available for download.
Goal:
Provide a quasilinear scaling orbitalfree density functional theory (OFDFT) implementation to simulate condensed matter and molecules. The current versions use the electron density as the sole variable. By calculating the total energy and its potential (the functional derivative with respect to the density), the total energy is minimized while conserving the total electron number to find the ground state.
Implementation (in the newest version: PROFESS 3.0): ^{1,2,3}
 Inhousedeveloped FORTRAN package based on plane waves. FFT via the fftw3 library is extensively used to evaluate energies and potentials.
 Parallelization is implemented through domain decomposition using MPI.
 A number of kinetic density energy functionals (KEDFs), including ThomasFermi, vonWeizsäcker (vW), WantTeter (WT),^{4} WangGovindCarter (WGC),^{5,6} CAT,^{7} HuangCarter (HC),^{8} densitydecomposition,^{9} WGCdecomposition,^{10} EnhancedvWWGC,^{11} etc., are implemented.
 Local density approximation (LDA) with Perdew and Zunger as exchange,^{12} Cepeley and Alder as correlation,^{13} and generalized gradient approximation (GGA) with PerdewBurkeErnzerhof (PBE)^{14} exchangecorrelation functionals are available. Spin polarized calculations are supported. Note that the spin polarized PBE functional is implemented through the Libxc library (version 2.0.1).
 The electron density minimization,^{15} using the square root of electron density as the variable, is implemented via modified truncatedNewton, conjugate gradient (CG) or Limited BroydenFletcherGoldfarbShanno (LBFGS) methods^{16} to efficiently find the ground state, while conserving the electron number. The LBFGS method shows better stability and efficiency for spinpolarized and vacuum systems.
 CG and other methods are available to optimize ion positions. Specific ions can be fixed during the optimization as requested.
 Algorithms are also implemented for cell lattice optimization.
 Molecular dynamics methods with three ensembles^{17} are implemented and tested:^{18} the microcanonical NVE (constant number of particles N, constant volume V, and constant energy E), the canonical NVT (constant number of particles N, constant volume V, and constant temperature T) with the NoséHoover thermostat,^{19,20} and the isothermalisobaric NPT (constant number of particles N, constant pressure P, and constant temperature T) with the ParinelloRahman thermostat.^{21}
 An option to set the initial density as a superposition of atomic densities is added.
 Local pseudopotentials (LPSs) must be used. A variety of these LPSs can be found on the Carter group website.
References:
 G. Ho, V. L. Lignères, and E. A. Carter, “Introducing PROFESS: a new program for orbitalfree density functional theory calculations,” Comput. Phys. Commun., 179, 839 (2008). Online Link (doi: 10.1016/j.cpc.2008.07.002)
 L. Hung, C. Huang, I. Shin, G. Ho, V. L. Ligneres, and E. A. Carter, “Introducing PROFESS 2.0: A parallelized, fully linear scaling program for orbitalfree density functional theory calculations,”Comput. Phys. Comm., 181, 2208 (2010). Online Link (doi: 10.1016/j.cpc.2010.09.001)
 M. Chen, J. Xia, C. Huang, J. M. Dieterich, L. Hung, I. Shin, and E. A. Carter, “Introducing PROFESS 3.0: An advanced program for orbitalfree density functional theory molecular dynamics simulations,” Comp. Phys. Comm., 190, 228 (2015). Online Link (doi: 10.1016/j.cpc.2014.12.021)
 L. Wang and M. P. Teter, “Kineticenergy functional of the electron density,” Phys. Rev. B, 45, 13196 (1992). Online Link (doi: 10.1103/PhysRevB.45.13196)
 Y. A. Wang, N. Govind, and E. A. Carter, “OrbitalFree KineticEnergy Density Functionals with a DensityDependent Kernel,” Phys. Rev. B, 60, 16350 (1999). Online Link (doi: 10.1103/PhysRevB.60.16350)
 Y. A. Wang, N. Govind, and E. A. Carter, “Erratum: OrbitalFree KineticEnergy Density Functionals with a DensityDependent Kernel,” Phys. Rev. B, 64, 0899031 (2001). Online Link (doi: 10.1103/PhysRevB.64.089903)
 D. GarcíaAldea and J. E. Alvarellos, “Kineticenergy density functionals with nonlocal terms with the structure of the ThomasFermi functional,” Phys. Rev. A, 76, 052504 (2007). Online Link (doi: 10.1103/PhysRevA.76.052504)
 C. Huang and E. A. Carter, “Nonlocal orbitalfree kinetic energy density functional for semiconductors,” Phys. Rev. B, 81, 045206 (2010). Online Link (doi: 10.1103/PhysRevB.81.045206)
 C. Huang and E. A. Carter, “Toward an Orbitalfree Density Functional Theory of Transition Metals Based on an Electron Density Decomposition,” Phys. Rev. B, 85, 045126 (2012). Online Link (doi: 10.1103/PhysRevB.85.045126)
 J. Xia and E. A. Carter, “DensityDecomposed OrbitalFree Density Functional Theory for Covalently Bonded Molecules and Materials,” Phys. Rev. B, 86, 235109 (2012). Online Link (doi: 10.1103/PhysRevB.86.235109)
 J. P. Perdew and A.Zunger, “Selfinteraction correction to densityfunctional approximations for manyelectron systems,” Phys. Rev. B, 23, 5048 (1981). Online Link (doi: 10.1103/PhysRevB.23.5048)
 I. Shin and E. A. Carter, “Enhanced von Weizsäcker WangGovindCarter Kinetic Energy Density Functional for Semiconductors,”J. Chem. Phys.,140, 18A531 (2014). Online Link (doi: 10.1063/1.4869867)
 M. Ceperley and B. J. Alder, “Ground State of the Electron Gas by a Stochastic Method,” Phys. Rev. Lett., 45, 566 (1980). Online Link (doi: 10.1103/PhysRevLett.45.566)
 J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized Gradient Approximation Made Simple,” Phys. Rev. Lett., 77, 3865 (1996). Online Link (doi: 10.1103/PhysRevLett.77.3865)
 L. Hung, C. Huang, and E. A. Carter, “Preconditioners and Electron Density Optimization in OrbitalFree Density Functional Theory,” Comm. Comp. Phys., 12, 135 (2012). Online Link (doi: 10.4208/cicp.190111.090911a)
 D. C. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Math. Program., 45, 503 (1989). Online Link (doi: 10.1007/BF01589116)
 G. J. Martyna, M. E. Tuckerman, D. J. Tobias, and M. L. Klein, “Explicit reversible integrators for extended systems dynamics,” Mol. Phys., 87, 1117 (1995). Online Link (doi: 10.1080/00268979600100761)
 M. Chen, L. Hung, C. Huang, J. Xia, and E. A. Carter, “The Melting Point of Lithium: An OrbitalFree FirstPrinciples Molecular Dynamics Study,” Mol. Phys., 111, 3448 (2013). Online Link (doi: 10.1080/00268976.2013.828379)
 S. Nose, “A unified formulation of the constant temperature molecular dynamics methods,” J. Chem. Phys., 81, 511 (1984). Online Link (doi: 10.1063/1.447334)
 W. G. Hoover, “Canonical dynamics: Equilibrium phasespace distributions,” Phys. Rev. A, 31, 1695 (1985). Online Link (doi: 10.1103/PhysRevA.31.1695)
 M. Parrinello and A. Rahman, “Crystal Structure and Pair Potentials: A MolecularDynamics Study,” Phys. Rev. Lett. 45, 1196 (1980). Online Link (doi: 10.1103/PhysRevLett.45.1196)
EMBEDDED CORRELATED WAVEFUNCTION THEORY
Goal:
Provide an improved description of electron exchange and correlation in a local region of condensed matter via an embedded cluster method.^{1,2,3} In current applications, we are focusing on molecule/metal surface interactions, such as dissociative adsorption of dioxygen on aluminum,^{4 }or plasmoninduced dissociation of dihydrogen on gold.^{5 }The cluster of atoms close to the molecule is treated with correlated wavefunction methods, while the background atoms are described by periodic density functional theory. A DFTbased embedding potential describes the effect of the background atoms on the cluster. We implement interfaces to read in the embedding potential in both MOLCAS and GAMESS (see Implementation below). The embedding potential may be calculated on the DFT level using our ABINITEMBED program package, with a fully selfconsistent interaction between the DFT and the CW subsystems using our POTENTIALFUNCTIONALEMBEDDING approach,^{6 }or by the CW codes themselves. A new algorithm was also developed to accurately compute the modified oneelectron integrals using allelectron basis sets; and this algorithm has been implemented in both MOLCAS and Gamess.^{7}
Implementation in MOLCAS:

 Construct the embedding potential from orbitalfree 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.
Implementation in GAMESS:

 Construct the embedding potential from orbitalfree DFT OR Read in the embedding potential (as constructed by MOLCASEMBED or ABINITEMBED).
 Calculate the resulting oneelectron integral terms in parallel.
 Include these oneelectron integrals in all subsequent GAMESS calculations.
 Use the embedded wavefunction to find the embedding total energy.
References
 P. Huang and E.A. Carter, “Selfconsistent embedding theory for locally correlated configuration interaction wave functions in condensed matter,” J. Chem. Phys., 125, 084102 (2006). Online PDF(Reproduced from J. Chem. Phys. 125(8), 084102084115, Copyright 2006, American Institute of Physics.)
 S. Sharifzadeh, P. Huang, and E. A. Carter, “AllElectron Embedded Correlated Wavefunction Theory for Condensed Matter Electronic Structure,” Chem. Phys. Lett., 470, 347 (2009). Online Link(doi: 10.1016/j.cplett.2009.01.072)
 C. Huang, M. Pavone, and E. A. Carter, “Quantum mechanical embedding theory based on a unique embedding potential,” J. Chem. Phys., 134, 154110 (2011). Online Link (Reproduced from J. Chem. Phys. 134, 154110, Copyright 2011, American Institute of Physics.)
 F. Libisch, C. Huang, P. Liao, M. Pavone, and E. A. Carter, “Origin of the Energy Barrier to Chemical Reactions of O2 on Al(111): Evidence for Charge Transfer, Not Spin Selection,” Phys. Rev. Lett., 109, 198303 (2012). Online PDF
 S. Mukherjee, F. Libisch, N. Large, O. Neumann, L. V. Brown, J. Cheng, J. B. Lassiter, E. A. Carter, P. Nordlander, and N. J. Halas, “Hot Electrons Do the Impossible: PlasmonInduced Dissociation of H_{2} on Au,” Nano Letters, 13, 240 (2013). Online PDF
 C. Huang and E. A. Carter, “PotentialFunctional Embedding Theory for Molecules and Materials,” J. Chem. Phys., 135, 194104 (2011). Online PDF (Reproduced from J. Chem. Phys. 84, 165122, Copyright 2011, American Institute of Physics.)
 K. Yu, F. Libisch, and E. A. Carter, “Implementation of density functional embedding theory within the projectoraugmentedwave method and applications to semiconductor defect states,” J. Chem. Phys., 143, 102806 (2015). Online Link (doi: 10.1063/1.4922260)
ABINITEMBED
Goal:
Provide a DFT implementation to calculate embedding potentials using planewave 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 highlevel 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). Online Link (Reproduced from J. Chem. Phys. 134, 154110, Copyright 2011, American Institute of Physics.)
F. Libisch, C. Huang, P. Liao, M. Pavone, and E. A. Carter, “Origin of the Energy Barrier to Chemical Reactions of O2 on Al(111): Evidence for Charge Transfer, Not Spin Selection,” Phys. Rev. Lett., 109, 198303 (2012). Online PDF
S. Mukherjee, F. Libisch, N. Large, O. Neumann, L. V. Brown, J. Cheng, J. B. Lassiter, E. A. Carter, P. Nordlander, and N. J. Halas, “Hot Electrons Do the Impossible: PlasmonInduced Dissociation of H_{2} on Au,” Nano Letters, 13, 240 (2013). Online PDF
POTENTIALFUNCTIONAL EMBEDDING
Goal:
Provide a versatile embedding framework to selfconsistently 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 selfconsistently 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 selfconsistency is reached. This allows for a selfconstant 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, “PotentialFunctional Embedding Theory for Molecules and Materials,” J. Chem. Phys., 135, 194104 (2011). Online PDF (Reproduced from J. Chem. Phys. 84, 165122, Copyright 2011, American Institute of Physics.)
OPTIMIZED EFFECTIVE POTENTIALS
Goal:
In conventional formulations of KohnSham density functional theory (KSDFT), the exchangecorrelation functional acts on the total electron density. However, while KSDFT is, in principle, exact, we do not know the correct form of the true exchange correlation functional. Currently used approximations perform poorly for charge transfer processes, highly correlated materials, or dispersion forces. However, much more accurate exchangecorrelation functionals acting on the KS orbitals (instead of the density) can be formulated. While such functionals cannot be incorporated into KSDFT, the HohenbergKohn theorem guarantees that a unique ground state density and a unique effective potential exists. To find this density requires a socalled optimized effective potential formalism. The most direct approach requires calculating of the KS Green’s function, which is both very costly and numerically unstable. Instead, we directly minimize the energy E as a functional of the effective potential V, min E[V]. To do this effectively requires an expression for the gradient dE/dV. We have developed an efficient onedimensional finite difference approach to determine this gradient.^{1 }The resulting formalism is implemented in the abinit software package.
Implementation:

 Solve KS equations for current trial V.
 Calculate shifted trial potential V’ required for gradient.
 Solve KS equations for V’.
 Calculate gradient dE/dV as function of KS orbitals of V and V’.
 Using gradient, do minimization of E[V] to find ground state by, e.g., LBFGS minimization.
 Planewave implementation based on the ABINIT software package.
References
1. C. Huang, and E. A. Carter, “Direct Minimization of the Optimized Effective Problem Based on Efficient Finite Differences,” Phys. Rev. B, 84, 165122 (2011). Online PDF
TIGERCI: REDUCED SCALING MRSDCI/MRACPF
Goal:
A small prefactor, linear scaling MRSDCI/MRACPF algorithm.
Multireference approaches to electron correlation are necessary for studying bondbreaking, diradicals and transition metals. Multireference singles and doubles configuration interaction (MRSDCI) provides a straightforward multireference treatment. However, a conventional MRSDCI code scales as O(N^{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.^{15} 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 twoelectron integrals.^{7} The CDLMRSDCI 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 coupledpaid functional MRACPF) size extensivity corrections.^{9}
Implementation
The CDLMRSDCI 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 CDLMRSDCI calculation.

 MOLCAS produces the one and twoelectron integrals in the SEWARD module.
 The one particle orbitals are produced in the SCF (single reference) or RASSCF (multireference) module.
 The orbitals are localized in the LOCALISATION module.
 TigerCI performs the CDLMRSDCI/CDLMRACPF calculations based on the symmetric group graphical approach (SGGA).^{10}
Coming soon: TIGERCI in GAMESS.
References:
 S. Saebo and P. Pulay, “Fourth‐order Møller–Plessett perturbation theory in the local correlation treatment. I. Method,” J. Chem. Phys., 86, 914 (1987). Online Link
 S. Saebo and P. Pulay, “Local Treatment of Electron Correlation,” Ann. Rev. Phys., 44, 213 (1993). Online Link
 D. Walter and E. A. Carter, “Multireference Weak Pairs Local Configuration Interaction: Efficient Calculations of Bond Breaking,” Chem. Phys. Lett., 346, 177 (2001). Online PDF
 D. Walter, A. Venkatnathan, and E. A. Carter, J. Chem. Phys., “”Local Correlation in the Virtual Space in Multireference Singles and Doubles Configuration Interaction,” 118, 8127 (2003).Online PDF (Reproduction from J. Chem. Phys. 118(18), 81278139, Copyright 2003, American Institute of Physics.)
 A. Venkatnathan, A. B. Szilva, D. Walter, R. J. Gdanitz, and E. A. Carter, “Size Extensive Modification of Local Multireference Configuration Interaction,” J. Chem. Phys., 120, 1693 (2004). Online PDF (Reproduction from J. Chem. Phys. 120(4), 16931704, Copyright 2004, American Institute of Physics.)
 T. S. Chwee, A. B. Szilva, R. Lindh, and E. A. Carter, “Linear Scaling Multireference Singles and Doubles Configuration Interaction,” J. Chem. Phys., 128, 224106 (2008). Online PDF(Reproduced from J. Chem. Phys. 128(2), 224106224114, Copyright 2008, American Institute of Physics.)
 T. S. Chwee and E. A. Carter, “Cholesky decomposition within local multireference singles and doubles configuration interaction,” J. Chem. Phys., 132, 074104 (2010). Online PDF(Reproduced from J. Chem. Phys. 132, 074104, Copyright 2010, American Institute of Physics.)
 T. S. Chwee and E. A. Carter, “Density Fitting of TwoElectron Intergrals in Local Multireference Single and Double Excitation Configuration Interaction Calculations,” Molecular Physics, 108, 2519 (2010). Online PDF
 D. B. Krisiloff and E. A. Carter, “Approximately Size Extensive Local Multireference Singles and Doubles Configuration Interaction,” Phys. Chem. Chem. Phys., 14, 7710 (2012). Online Link
 W. Duch and J. Karwowski, “Symmetric group approach to configuration interaction methods,”Comput. Phys. Rep., 2, 93 (1985). Online Link
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 intraatomic Coulomb and exchange interactions of localized valence electrons are effectively treated at the HartreeFock level of theory. DFT+U theory can correct the selfinteraction 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 HartreeFock calculations on electrostatically embedded clusters.
Implementation in GAMESS:
The method used to evaluate these parameters is based on unrestricted HartreeFock 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 twoelectron 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, “Ab initio Evaluation of Coulomb and Exchange Parameters for DFT+U Calculations,” Phys. Rev. B, 76, 155123 (2007). Online PDF
N. J. Mosey, P. Liao, and E. A. Carter, “Rotationally Invariant ab initio Evaluation of Coulomb and Exchange Parameters for DFT + U Calculations,” J. Chem. Phys., 129, 014103 (2008). Online PDF(Reproduced from J. Chem. Phys. 129(1), 014103014115, Copyright 2008, American Institute of Physics.)