# 4.2.37. MRCI¶

The MRCI program generates Multi Reference SDCI or ACPF [57] wavefunctions. ACPF is a modification of the CPF [55] method which allows more than one reference configuration. The program is based on the Direct CI method [58], and with the coupling coefficients generated with the Graphical Unitary Group Approach [59][60][61]. (See program description for GUGA). If requested, MRCI computes matrix elements of those one-electron properties for which it can find integrals in the ONEINT file. It also generates natural orbitals that can be fed into the property program to evaluate certain one electron properties. The natural orbitals are also useful for Iterated Natural Orbital (INO) calculations.

The MRCI code is a modification of an MRCI program written by M. Blomberg and P. E. M. Siegbahn (Institute of Physics, Stockholm University, Sweden), which has later been extensively modified (P.-Å. Malmqvist)

The program can calculate several eigenvectors simultaneously, not necessarily those with lowest eigenvalue. However, in the ACPF case, only one single eigenvector is possible.

Orbital subspaces

The orbital space is divided into the following subspaces: Frozen, Inactive, Active, Secondary, and Deleted orbitals. Within each symmetry type, they follow this order.

**Frozen:**Frozen orbitals are always doubly occupied, i.e., they are not correlated. Orbitals may be frozen already in the integral integral transformation step, program MOTRA, but can also be specified in the input to the MRCI program. The former method is more efficient, and has the effect that the frozen orbitals are effectively removed from the subsequent MRCI calculation.**Inactive:**Inactive orbitals are doubly occupied in all reference configurations, but excitations out of this orbital space are allowed in the final CI wavefunction, i.e., they are correlated but have two electrons in all reference configurations. Restrictions may be applied to excitation from some inactive orbitals, see keyword NoCorr in the GUGA input section.**Active:**Active orbitals are those which may have different occupation in different reference configurations. Restrictions may be applied to occupation of some active orbitals, see keyword OneOcc in the GUGA input section.**Secondary:**This subspace is empty in all reference configurations, but may be populated with up to two electrons in the excited configurations. This subspace is not explicitly specified, but consists of the orbitals which are left over when other spaces are accounted for.**Deleted:**This orbital subspace does not participate in the CI wavefunction at all. Typically the 3s,4p,… components of 3d,4f,…, or orbitals that essentially describe core correlation, are deleted. Similar to freezing, deleting can be done in MOTRA, which is more efficient, but also as input specifications to the MRCI program.

Since ordinarily the frozen and deleted orbitals were handled by MOTRA and the subdivision into inactive and active orbitals were defined in GUGA, the only time one has to specify orbital spaces in the input to MRCI is when additional frozen or deleted orbitals are required without recomputing the transformed integrals.

## 4.2.37.1. Dependencies¶

The program needs the coupling coefficients generated by the program GUGA and transformed one- and two-electron integrals generated by the program MOTRA.

## 4.2.37.2. Files¶

### 4.2.37.2.1. Input files¶

- CIGUGA
- Coupling coefficients from GUGA.
- TRAINT*
- Transformed two-electron integrals from MOTRA.
- TRAONE
- Transformed one-electron integrals from MOTRA.
- ONEINT
- One-electron property integrals from SEWARD.
- MRCIVECT
- Used for input only in restart case.

### 4.2.37.2.2. Output files¶

- CIORBnn
- One or more sets of natural orbitals, one for each CI root, where nn stands for 01, 02, etc.
- MRCIVECT
- CI vector, for later restart.

Note that these file names are the FORTRAN file names used by the program, so they have to be mapped to the actual file names. This is usually done automatically in the Molcas system. However, in the case of several different numbered files CIORBnn only the first will be defined as default, with the FORTRAN file name CIORB used for CIORB01.

## 4.2.37.3. Input¶

This section describes the input to the MRCI program in the Molcas program system, with the program name:

```
&MRCI
```

### 4.2.37.3.1. Keywords¶

- TITLe
- The line following this keyword is treated as title line
- SDCI
- This keyword is used to perform an ordinary Multi-Reference Singles and Doubles CI, MR-SDCI, calculation. This is the default assumption of the program. Note that SDCI and ACPF are mutually exclusive.
- ACPF
- This keyword tells the program to use the Average Coupled Pair Functional, ACPF, when computing the energy and natural orbitals. Note that SDCI and ACPF are mutually exclusive.
- GVALue
- The coefficient g which is used in the ACPF functional. The default value is = 2.0/(Nr of correlated electrons).
- NRROots
- Specifies the number of CI roots (states) to be simultaneously optimized. The default is 1.
- ROOTs
- Specifies which root(s) to converge to. These are defined as the ordinal number of that eigenvector of the reference CI which is used as start approximation. The default is the sequence 1,2,3,… The values are entered on the next line(s). If the number of roots is larger than 1, it must first have been entered using keyword NRROOTS. The keywords ROOTS and SELECT are mutually exclusive.
- SELEct
- Another way of specifying the roots: instead of using ordinal numbers, the roots selected will be those NRROOTS which have largest projections in a selection space which is specified on the next lines, as follows: One line gives NSEL, the number of vectors used to define the selection space. For each selection vector, program reads the number of CSFs (NC), and # NC pairs of CSEL (text strings) and SSEL (coefficients). The text string is composed of the digits 0,1,2,3 and denotes the GUGA case numbers of the active orbitals, defining uniquely a CSF belonging to the reference space. The keywords ROOTS and SELECT are mutually exclusive.
- RESTart
- Restart the calculation from a previous calculation. No additional input is required. The MRCIVECT file is required for restarted calculations.
- THRPrint
- Threshold for printout of the wavefunction. All configurations with a coefficient greater than this threshold are printed. The default is 0.05.
- ECONvergence
- Energy convergence threshold. The result is converged when the energy of all roots has been lowered less than this threshold in the last iteration. The default is 1.0d-8.
- Print level of the program. Default is 5.
- MAXIterations
- Maximum number of iterations. Default 20. The maximum possible value is 49.
- MXVEctors
- Maximum number of trial vector pairs (CI+sigma) kept on disk. Default is MAX(NRROOTS,10). It should never be smaller than NRROOTS. A good value is 3*NRROOTS or more.
- TRANsition
- This keyword is relevant to a multi-root calculation. In addition to properties, also the transition matrix elements of various operators, for each pair of wave functions, will be computed.
- FROZen
- Specify the number of orbitals to be frozen in
**addition**to the orbitals frozen in the integral transformation. Default is 0 in all symmetries. - DELEted
- Specify the number of orbitals to be deleted in
**addition**to the orbitals deleted in the integral transformation. Default is 0 in all symmetries. - REFCi
- Perform only reference CI.
- PRORbitals
- Threshold for printing natural orbitals. Only orbitals with occupation number larger than this threshold appears in the printed output. Default is 1.0d-5.

### 4.2.37.3.2. Input example¶

```
&MRCI
Title
Water molecule. 1S frozen in transformation.
Sdci
```