A variational 2-RDM-driven CASSCF plugin to Psi4

##OVERVIEW

This plugin to Psi4[1] performs variational two-electron reduced-density-matrix (2-RDM)-driven complete active space self consistent field (CASSCF) computations. In principle, because variational 2-RDM (v-2RDM) methods scale only polynomially with system size, v-2RDM-driven CASSCF computations can be performed using active spaces that are larger than can be used within conventional configuration-interaction-driven CASSCF methods. For more information regarding the performance of the method, see Refs. 2-3.

##INSTALLATION

To run the psi4 plugin v2rdm_casscf:

• Download psi4public from github.com: https://github.com/psi4/psi4public, and follow the installation instructions given here: http://www.psicode.org/.

• Modify the setup script by specifying your fortran compiler, options, and libraries

cd v2rdm_casscf

vi setup

• Modify F90, F90_FLAGS, and F90_LIB, as needed.

• Compile the plugin:

./setup

##INPUT OPTIONS

###N-representability conditions

• POSITIVITY (string):

  The positivity conditions enforced in the computation. Allowed values include DQG, DQ, DG, D, DQGT1, DQGT2, and DQGT1T2. The default value is DQG.

• CONSTRAIN_D3 (bool):

  Enforce the additional condition that D3 be possitive and correctly contract to D2? Default false.

• CONSTRAIN_SPIN (bool):

  Do constrain the expectation value of spin squared? Default true.

###Convergence

• E_CONVERGENCE (double):

  The convergence in the primal/dual energy gap. Default 1e-4.

• R_CONVERGENCE (double):

  The convergence in the primal and dual errors. Default 1e-4.

• MAXITER (int):

  The maximum number of outer iterations. Default 10000.

###Active space specification

• FROZEN_DOCC (array):

  An array containing the number of frozen doubly-occupied orbitals per irrep. These orbitals are not included in the active space, nor are they optimized during the v2RDM-CASSCF procedure. This option trumps Psi4's NUM_FROZEN_DOCC and FREEZE_CORE options.

• FROZEN_UOCC (array):

  An array containing the number of frozen unoccupied orbitals per irrep. These orbitals are not included in the active space, nor are they optimized during the v2RDM-CASSCF procedure. This option trumps Psi4's NUM_FROZEN_UOCC option.

• RESTRICTED_DOCC (array):

  An array giving the number of restricted doubly-occupied orbitals per irrep. These orbitals are not included in the active space, but they are optimized by the v2RDM-CASSCF procedure.

• RESTRICTED_UOCC (array):

  An array giving the number of restricted unoccupied orbitals per irrep. These orbitals are not included in the active space, but they are optimized by the v2RDM-CASSCF procedure.

• ACTIVE (array):

  An array giving the number of active orbitals (occupied plus unoccupied) per irrep. This option provides a more intuitive way of specifying the active space than the FROZEN_DOCC/RESTRICTED_DOCC/RESTRICTED_UOCC/FROZEN_UOCC keywords. The simplest specification of the active space would involve this keyword and at the RESTRICTED_DOCC keyword. This option trumps the RESTRICTED_UOCC option, which will be determined from the ACTIVE, RESTRICTED_DOCC, FROZEN_DOCC, and FROZEN_UOCC arrays.

###Restarting jobs

• WRITE_CHECKPOINT_FILE (bool):

  Do save progress in a checkpoint file? Default false.

• CHECKPOINT_FREQUENCY (bool):

  Frequency of checkpoint file generation. The checkpoint file is updated every CHECKPOINT_FREQUENCY iterations. The default frequency will be ORBOPT_FREQUENCY.

• RESTART_FROM_CHECKPOINT_FILE (string):

  File containing previous primal/dual solutions and integrals.

###Integrals and SCF type

• DF_BASIS_SCF (string):

  Auxiliary basis set for SCF density fitting computations. Defaults to a JKFIT basis.

• SCF_TYPE (string):

  What algorithm to use for the initial SCF computation. Default DF.

• CHOLESKY_TOLERANCE (double):

  Tolerance for Cholesky decomposition of the ERI tensor. Default 1e-4.

###Orbital optimization

• ORBOPT_ONE_STEP (int):

  Flag to optimize orbitals using a quasi one-step type approach. Default 1.

• ORBOPT_GRADIENT_CONVERGENCE (double):

  Convergence in the orbital gradient norm. Default 1e-4.

• ORBOPT_ENERGY_CONVERGENCE (double):

  Convergence in the energy for orbital rotations. Default 1e-8.

• ORBOPT_EXACT_DIAGONAL_HESSIAN (int):

  Flag for using exact expresions for diagonal Hessian elements. Default 0.

• ORBOPT_FREQUENCY (int):

  Frequency of orbital optimization. Optimization occurs every ORBOPT_FREQUENCY iterations. Default 200.

• ORBOPT_ACTIVE_ACTIVE_ROTATIONS (bool):

  Do rotate active/active orbital pairs? Default false.

###Additional files

• MOLDEN_WRITE (bool):

  Do write a MOLDEN output file containing the natural orbitals? If yes, the filename will end in .molden, and the prefix is determined by WRITER_FILE_LABEL (if set), or else by the name of the output file plus the name of the current molecule. Default false.

• WRITER_FILE_LABEL (string):

  Base filename for text files written by PSI, such as the MOLDEN output file, the Hessian file, the internal coordinate file, etc. Use the add_str_i function to make this string case sensitive.

• ORBOPT_WRITE (bool):

  Do write a ORBOPT output file? If so, the filename will end in .orbopt, and the prefix is determined by WRITER_FILE_LABEL (if set), or else by the name of the output file plus the name of the current molecule.

##KNOWN ISSUES

• For large jobs, when running with multiple threads, sometimes a thread will hang and the job will stall.
• For large jobs, add "ulimit -s unlimited" to .bashrc to avoid segfault when calling the fortran orbital optimization routines.

##REFERENCES

[1] J. M. Turney, A. C. Simmonett, R. M. Parrish, E. G. Hohenstein, F. A. Evangelista, J. T. Fermann, B. J. Mintz, L. A. Burns, J. J. Wilke, M. L. Abrams, N. J. Russ, M. L. Leininger, C. L. Janssen, E. T. Seidl, W. D. Allen, H. F. Schaefer, R. A. King, E. F. Valeev, C. D. Sherrill, and T. D. Crawford, WIREs: Comp. Molec. Sci. 2, 556 (2012). "Psi4: an open-source ab initio electronic structure program"

[2] J. Fosso-Tande, D. R. Nascimento, and A. E. DePrince III, Mol. Phys. 114, 423-430 (2015). "Accuracy of two-particle N-representability conditions for describing different spin states and the singlet-triplet gap in the linear acene series"

[3] J. Fosso-Tande, T.-S. Nguyen, G. Gidofalvi, and A. E. DePrince III, in preparation.