Doubly hybrid methods for PySCF.

SCF must run in RI-JK currently. Correlation part (PT2 part) is definitely density fitting. Runs in disk-based way by default.

from pyscf import gto, dh
mol = gto.Mole(atom="O; H 1 0.94; H 1 0.94 2 104.5", basis="cc-pVDZ", verbose=0).build()
mf = dh.DFDH(mol, xc="XYG3").run()
print(mf.e_tot)

Name dh refers to Doubly Hybrid. DFDH refers to Density Fitting Doubly Hybrid.

from pyscf import gto, dh
from pyscf.geomopt.berny_solver import optimize  # or geometric_solver
mol = gto.Mole(atom="O; H 1 1.0; H 1 1.0 2 104.5", basis="cc-pVDZ", verbose=0).build()
mf = dh.DFDH(mol, xc="XYG3").nuc_grad_method()
mol_eq = optimize(mf)  # optimized molecule object

from pyscf import gto, dh
mol = gto.Mole(atom="O; H 1 0.94; H 1 0.94 2 104.5", basis="cc-pVDZ", verbose=0).build()
mf = dh.DFDH(mol, xc="XYG3").polar_method().run()
print(mf.pol_tot)

Hessian is currently not implemented.

Refer to installation of PySCF Extension modules. Declare PYSCF_EXT_PATH=$PYSCF_EXT_PATH:/path/to/dh should work.

This extension overwhelmingly relies on pyscf-tblis. Also recommands modifing EINSUM_MAX_SIZE (in tblis_einsum.py) to much smaller value for dh extension.

• Supported features: Res/Unrestricted single point energy, gradient, polarizability for XYG3-like and B2PLYP-like doubly functionals
• Supported doubly hybrid functionals (and MP2):
  • MP2
  • Early XYG3 family: XYG3, XYGJ-OS, xDH-PBE0
  • xDH@B3LYP family: revXYG3, revXYGJ-OS, XYG5, XYGJ-OS5, XYG6, XYG7
  • B2P family: B2PLYP, B2GPPLYP, mPW2PLYP
  • PBE related: PBE0-DH, LS1DH-PBE, PBE0-2, PBE-QIDH
  • Self-defined functionals (only supports pure HF or hybrid GGA functionals, if gradient/electric property is required)

Default functional is XYG3 currently.

• Quadrupole;
• Rectify APIs, and more formal logging and timing;
• API document and user document;
• Efficiency benchmarking;
• D3(BJ) dispersion derivative properties.

• Another independent module (maybe called dheng) handling only energy evaluation for more doubly-hybrid functionals, such as D3(BJ) dispersion, Laplace-transformation, long-range corrected PT2, renormalization based methods, random-phase-approximation (RPA) based methods, etc.;
• Hessian and dipole-derivative;
• Frozen core;
• RIJONX, RICOSX and conventional SCF method supports;
• Laplace-transformation method derivatives;
• PBC energy;
• Other derivative properties ...

• For functional energy evaluation, refers to the origin paper of those functionals.

• For first order properties (atom nuclear gradient, dipole moment):

  Neil Qiang Su, Igor Ying Zhang, Xin Xu. J. Comput. Chem. 2013, 34, 1759-1774. doi: 10.1002/jcc.23312

  Analytic Derivatives for the XYG3 Type of Doubly Hybrid Density Functionals: Theory, Implementation, and Assessment

• For second order properties (hessian of xDH obtained from conventional SCF/PT2 in Gaussian 09, where polarizability is also implemented) that relates to this work:

  Yonghao Gu, Zhenyu Zhu, Xin Xu. submitted.

Predecessor of this work is Py_xDH.