# 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. Especially **pre-allocating GA memory** might be required for large calculations as described in memory specifications.
The corresponding publications can be found in bibliography

## Single-state PNO-CASPT2

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

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

## Options

General local correlation options
`IEXT`

, `REXT`

,`THRDIST`

, `FITLMO`

, `LOCFIT_PNO`

, `THRLOC`

can be found in options for PNO or PAO based methods.

### PNO-CASPT2 specific options

`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).

## Multi-state PNO-CASPT2

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.

### Additional options

`H0`

(default: *0*) use CASPT2**D** (*=1*) or CASPT2**D2** (*=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**)

## Bibliography

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)