Multireference local correlation methods (PNO-CASPT2)

In this section multireference local correlation methods are described. Many keywords are similar to PNO-based single-reference methods and RS2 methods. The corresponding publications can be found in bibliography

In order to avoid an expensive canonical integral transformation and the storage of the resulting integrals (which can be huge for large molecules), it is necessary to store the CASSCF wavefunction(s) using the CIREC option, see Saving the CI vectors. The same CIREC option must be given on the PNO_CASPT2 command line. Note that the record number is automatically increased by 100 for each WF directive (i.e. different spatial or spin symmetry) in the CASSCF program (Multi). An example is given below.

examples/h2o_pno_caspt2.inp

 gprint,orbitals,civector
 basis=avtz,h=vtz

 geometry=h2o.xyz

 set,charge=1
 {df-multi;                                                                     ! casscf, state averaged
 wf,spin=1;state,2                                                              ! doublet, 2 states
 wf,spin=3;                                                                     ! quartet
 natorb,cirec=5140.2}                                                           ! save casscf wavefunctions

{pno-caspt2,cirec=5140.2,shift=0.3;state,1,1;wf,spin=1}                         ! first doublet state
{pno-caspt2,cirec=5140.2,shift=0.3;state,1,2;wf,spin=1}                         ! second doublet state
{pno-caspt2,cirec=5240.2,shift=0.3;wf,spin=3}                                   ! quartet state

{pno-caspt2,cirec=5140.2,shift=0.3;state,2;wf,spin=1}                           ! MS-CASPT2 for doublet states

The program can be invoked using PNO-CASPT2, options.

Many default settings for local approximations are similar to default settings in PNO-LMP2.

General local correlation options IEXT, REXT,THRDIST, FITLMO, LOCFIT_PNO, THRLOC can be found in options for PNO or PAO based methods.

THRPNO_EN (default: 0.997) completeness threshold for PNO construction

THRPNO_OCC (default: 1.D-8) occupation number threshold for PNO construction

THRPNOP2_EN/THRPNOP1_EN/THRPNOP0_EN (default: THRPNO_EN) as THRPNO_EN, but only for P2/P1/P0 excitation subspace

THRPNOP2_OCC/THRPNOP1_OCC/THRPNOP0_OCC (default: THRPNO_OCC) as THRPNO_OCC, but only for P2/P1/P0 excitation subspace

FCLOS (default: false) use closed-shell Fock matrix $f^c$ in the right-hand side of the PNO-CASPT2 amplitude equations. Recommended if an averaged Fock matrix is used in the zero-order Hamiltonian

SHIFT (default: 0.0) level shift to reduce the intruder state problem (see level shifts in RS2)

CIREC record for CASSCF CI vectors stored in MULTI. If given, these are used without performing an extra reference CI. The CI vectors have to be saved in multi using the save,cirec directive (see examples below).

USE_SINGLES (default: 0) if set to 1 explicit single excitations are used in the amplitude equations

DIAG_DENF (default: 1) the Gamma matrix is diagonalized in PNO-CASPT2 (makes H0 block-diagonal)

THRDLP threshold for projection of redundant configurations in P1 and P0 subspaces

THRDLS threshold for projection of redundant configurations in the remaining configuration subspaces

Using the directive STATE one can specify the state of interest (see the single-root excited state calculation in RS2).

Note: level shifts have to be given as options. The SHIFT directive refers to denominator shifts, which affect the convergence but not the Hamiltonian and the results.

Multi-state calculations are possible by specifying multiple states on the STATE card.

An effective Hamiltonian \begin{equation} H_{MN}^\textrm{eff}=\frac{1}{2}\left( \langle M|\hat H ~^N\hat T_2|N\rangle + \langle M | ~^M\hat T_2^{\dagger} \hat H | N\rangle\right) + \delta_{MN} \langle M | \hat H | N \rangle. \end{equation} is constructed using state-specific PNO-CASPT2 amplitudes and diagonalized.

H0 (default: 0) use CASPT2D (=1) or CASPT2D2 (=2) approximations (see J. Chem. Phys. 150, 214107 (2019))

COUPCOR (default: 0) use coupling corrections for the above approximations (1: simple Lagrangian correction Dc or D2c; 2: additional relaxation correction Dcr or D2cr)

PNO-CASPT2:

• F. Menezes, D. Kats, and H.-J. Werner, Local Complete Active Space Second-Order Perturbation Theory Using Pair Natural Orbitals (PNO-CASPT2) J. Chem. Phys. 145, 124115 (2016)

Multi-state PNO-CASPT2:

• D. Kats and H.-J. Werner, Multi-State Local Complete Active Space Second-Order Perturbation Theory Using Pair Natural Orbitals (PNO-MS-CASPT2) J. Chem. Phys. 150, 214107 (2019)