Dynamical mean-field theory from a quantum chemical perspective.

We investigate the dynamical mean-field theory (DMFT) from a quantum chemical perspective. Dynamical mean-field theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local correlation approximation. In addition, quantum chemical techniques can be used to construct new ab initio Hamiltonians and impurity solvers for DMFT. Here, we explore some ways in which these things may be achieved. First, we present an informal overview of dynamical mean-field theory to connect to quantum chemical language. Next, we describe an implementation of dynamical mean-field theory where we start from an ab initio Hartree-Fock Hamiltonian that avoids double counting issues present in many applications of DMFT. We then explore the use of the configuration interaction hierarchy in DMFT as an approximate solver for the impurity problem. We also investigate some numerical issues of convergence within DMFT. Our studies are carried out in the context of the cubic hydrogen model, a simple but challenging test for correlation methods. Finally, we finish with some conclusions for future directions.

[1]  D. Jacob,et al.  Dynamical mean-field theory for molecular electronics: Electronic structure and transport properties , 2010, 1009.0523.

[2]  A. I. Lichtenstein,et al.  Double counting in LDA + DMFT—The example of NiO , 2010, 1004.4569.

[3]  S. Hirata.  Quantum chemistry of macromolecules and solids. , 2009, Physical chemistry chemical physics : PCCP.

[4]  G. Scuseria,et al.  Strong correlations via constrained-pairing mean-field theory. , 2009, The Journal of chemical physics.

[5]  G. Kotliar,et al.  Kondo effect and conductance of nanocontacts with magnetic impurities. , 2009, Physical review letters.

[6]  Jörg Kussmann,et al.  Linear-scaling atomic orbital-based second-order Møller-Plesset perturbation theory by rigorous integral screening criteria. , 2009, The Journal of chemical physics.

[7]  Artur F Izmaylov,et al.  Resolution of the identity atomic orbital Laplace transformed second order Møller-Plesset theory for nonconducting periodic systems. , 2008, Physical chemistry chemical physics : PCCP.

[8]  O. Gunnarsson,et al.  Sum rules and bath parametrization for quantum cluster theories , 2008, 0804.3320.

[9]  Emanuel Gull,et al.  Continuous-time auxiliary-field Monte Carlo for quantum impurity models , 2008, 0802.3222.

[10]  A. Georges,et al.  Solving the dynamical mean-field theory at very low temperatures using the Lanczos exact diagonalization , 2005, cond-mat/0512484.

[11]  R. Scalettar,et al.  Realistic investigations of correlated electron systems with LDA + DMFT , 2006 .

[12]  Emily A Carter,et al.  Self-consistent embedding theory for locally correlated configuration interaction wave functions in condensed matter. , 2006, The Journal of chemical physics.

[13]  Matthias Troyer,et al.  Continuous-time solver for quantum impurity models. , 2005, Physical review letters.

[14]  C. Marianetti,et al.  Electronic structure calculations with dynamical mean-field theory , 2005, cond-mat/0511085.

[15]  K. Held,et al.  Electronic structure calculations using dynamical mean field theory , 2005, cond-mat/0511293.

[16]  R Dovesi,et al.  Local-MP2 electron correlation method for nonconducting crystals. , 2005, The Journal of chemical physics.

[17]  T. Pruschke,et al.  Quantum cluster theories , 2004, cond-mat/0404055.

[18]  R. Friesner,et al.  Ab initio quantum chemical and mixed quantum mechanics/molecular mechanics (QM/MM) methods for studying enzymatic catalysis. , 2005, Annual review of physical chemistry.

[19]  A. Rubtsov,et al.  Continuous-time quantum Monte Carlo method for fermions: Beyond auxiliary field framework , 2004, cond-mat/0411344.

[20]  J. Berakdar.  Correlation spectroscopy of surfaces, thin films, and nanostructures , 2004 .

[21]  Antoine Georges,et al.  Strongly Correlated Electron Materials: Dynamical Mean-Field Theory and Electronic Structure , 2004, cond-mat/0403123.

[22]  Gabriel Kotliar,et al.  Strongly Correlated Materials: Insights From Dynamical Mean-Field Theory , 2004 .

[23]  C. Castellani,et al.  Cluster-dynamical mean-field theory of the density-driven Mott transition in the one-dimensional Hubbard model , 2004, cond-mat/0401060.

[24]  Frederick R. Manby,et al.  Fast linear scaling second-order Møller-Plesset perturbation theory (MP2) using local and density fitting approximations , 2003 .

[25]  A. Savin,et al.  Combining multideterminantal wave functions with density functionals to handle near-degeneracy in atoms and molecules , 2002 .

[26]  G. Kotliar,et al.  Cellular Dynamical Mean Field Approach to Strongly Correlated Systems , 2000, cond-mat/0010328.

[27]  Trygve Helgaker,et al.  Molecular Electronic-Structure Theory: Helgaker/Molecular Electronic-Structure Theory , 2000 .

[28]  Bangalore,et al.  Dynamical cluster approximation: Nonlocal dynamics of correlated electron systems , 1999, cond-mat/9903273.

[29]  M. Ratner.  Molecular electronic-structure theory , 2000 .

[30]  Philippe Y. Ayala,et al.  Linear scaling second-order Moller–Plesset theory in the atomic orbital basis for large molecular systems , 1999 .

[31]  M. Springborg,et al.  On the use of constrained density-functional theory in determining model Hamiltonians. Test calculations for the molecule and a C chain , 1998 .

[32]  H. R. Krishnamurthy,et al.  Nonlocal Dynamical Correlations of Strongly Interacting Electron Systems , 1998, cond-mat/9803295.

[33]  A. Lichtenstein,et al.  First-principles calculations of electronic structure and spectra of strongly correlated systems: the LDA+U method , 1997 .

[34]  G. Kotliar,et al.  Mean Field Theory of the Mott-Anderson Transition , 1996, cond-mat/9611100.

[35]  W. Krauth,et al.  Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions , 1996 .

[36]  Arieh Warshel,et al.  Ab Initio Free Energy Perturbation Calculations of Solvation Free Energy Using the Frozen Density Functional Approach , 1994 .

[37]  Caffarel,et al.  Exact diagonalization approach to correlated fermions in infinite dimensions: Mott transition and superconductivity. , 1994, Physical review letters.

[38]  Zhang,et al.  Mott transition in the d= , 1993, Physical review letters.

[39]  Jarrell,et al.  Hubbard model in infinite dimensions: A quantum Monte Carlo study. , 1992, Physical review letters.

[40]  Georges,et al.  Hubbard model in infinite dimensions. , 1992, Physical review. B, Condensed matter.

[41]  H. Koch,et al.  Analytical calculation of full configuration interaction response properties: Application to Be , 1991 .

[42]  D. Vollhardt,et al.  Correlated Lattice Fermions in High Dimensions , 1989 .

[43]  Jeppe Olsen,et al.  SIRIUS: A General Purpose Direct Second Order MCSCF Program , 1989 .

[44]  Fye,et al.  Monte Carlo method for magnetic impurities in metals. , 1986, Physical review letters.

[45]  Stefan Blügel,et al.  Ground States of Constrained Systems: Application to Cerium Impurities , 1984 .

[46]  A. Fetter,et al.  Quantum Theory of Many-Particle Systems , 1971 .

[47]  Enrico Clementi,et al.  Modern Techniques in Computational Chemistry: MOTECC™ -89 , 1899 .