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| ====== Multireference local correlation methods (PNO-CASPT2) ====== |

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| In this section multireference local correlation methods are described. Many keywords are similar to [[Local correlation methods with pair natural orbitals (PNOs)|PNO-based single-reference methods]] and [[Multireference Rayleigh Schrödinger perturbation theory|RS2 methods]]. Especially **pre-allocating GA memory** might be required for large calculations as described in [[running Molpro on parallel computers#memory specifications|memory specifications]]. |

| The corresponding publications can be found in [[#bibliography]] |

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| ===== Single-state PNO-CASPT2 ===== |

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

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| Many default settings for local approximations are similar to [[Local correlation methods with pair natural orbitals (PNOs)#Default and tight settings|default settings in PNO-LMP2]]. |

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| ===== Options ===== |

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| General local correlation options |

| ''IEXT'', ''REXT'',''THRDIST'', ''FITLMO'', ''LOCFIT_PNO'', ''THRLOC'' |

| can be found in options for [[Local correlation methods with pair natural orbitals (PNOs)#Options|PNO]] or [[PAO-based local correlation treatments#General Options|PAO]] based methods. |

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| ==== PNO-CASPT2 specific options ==== |

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| ''THRPNO_EN'' (default: //0.997//) completeness threshold for PNO construction |

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

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

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

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| ''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 |

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| ''SHIFT'' (default: //0.0//) level shift to reduce the intruder state problem (see [[Multireference Rayleigh Schrödinger perturbation theory#Level shifts|level shifts in RS2]]) |

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| ''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). |

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

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

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

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

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| Using the directive ''STATE'' one can specify the state of interest (see [[Multireference Rayleigh Schrödinger perturbation theory#Excited state calculations|the single-root excited state calculation in RS2]]). |

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| ===== Multi-state PNO-CASPT2 ===== |

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

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| 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. |

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| ==== Additional options ==== |

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| ''H0'' (default: //0//) use CASPT2**D** (//=1//) or CASPT2**D2** (//=2//) approximations (see [[https://doi.org/10.1063/1.5097644|J. Chem. Phys.]] **150**, 214107 (2019)) |

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

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| ===== Bibliography ===== |

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| PNO-CASPT2: |

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| * F. Menezes, D. Kats, and H.-J. Werner, //Local Complete Active Space Second-Order Perturbation Theory Using Pair Natural Orbitals (PNO-CASPT2)// [[https://doi.org/10.1063/1.4963019|J. Chem. Phys.]] **145**, 124115 (2016) |

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| Multi-state PNO-CASPT2: |

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| * D. Kats and H.-J. Werner, //Multi-State Local Complete Active Space Second-Order Perturbation Theory Using Pair Natural Orbitals (PNO-MS-CASPT2)// [[https://doi.org/10.1063/1.5097644|J. Chem. Phys.]] **150**, 214107 (2019) |

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