# *KRMCSCF¶

## 2- and 4-component relativistic KR-MCSCF module¶

The original implementation written by Joern Thyssen, Timo Fleig and Hans Joergen Aagaard Jensen, parallelization and continuous improvement by Stefan Knecht and Hans Joergen Aagaard Jensen. Linear symmetry adaptation by Stefan Knecht and Hans Joergen Aagaard Jensen.

For more details on the theory and actual implementation see [Jensen1996], [Thyssen2004] , [Thyssen2008], [Knecht2009].

## Mandatory keywords under *KRMCSCF¶

### .GAS SHELLS¶

Specification of CI calculation with electron distribution in orbital (GAS) spaces. The first line contains the number of GA spaces to be used (1-7), followed by one line per GAS with a separation by a “/” of the min/max number of electrons in each GAS and the number of orbitals per fermion corep (either one (no inversion symmetry) or two (inversion symmetry: gerade ungerade) entries per line).

The first entry before the “/” gives the minimal number of accumulated (!) electrons after consideration of this GAS, the second the corresponding maximum number, separated by blanks. The minimum and maximum accumulated occupations allow for a very flexible parameterization of the wave function. All determinants fulfilling the occupation constraints will be constructed. The second entry after the “/” gives the number of orbitals per fermion corep. See also the open-shell input in *SCF which is similar to the syntax used here. The design of a GAS scheme is non-trivial and should be motivated by the electronic structure of the system (e.g. inner core, outer core, valence, virtual space). Sometimes it is useful to subdivide the valence space, for scientific reasons, or/and the virtual space, for technical reasons (save core memory). See reference [Fleig2006a], pp. 27 for more details.

Example for a CASSCF run with 10 electrons in 10 orbitals, also known as CAS(10,10):

.GAS SHELLS
1
10 10 /  5  5

if all orbitals (fullMCSCF, feasible only for systems with 2-3 active electrons) should be included, use:

.GAS SHELLS
1
2 2 / all

### .INACTIVE¶

Inactive orbitals per fermion corep. default: all orbitals are active. The example below for a molecule with inversion center marks the lowest 4 gerade and 2 ungerade orbitals as inactive, i.e. they are always kept doubly occupied in all determinants of the CI expansion:

.INACTIVE
4 2

All remaining orbitals above the inactive + active space are considered as secondary orbitals, i.e. they are kept empty in all determinants of the CI expansion. By default all orbital rotations between the inactive-active and active-secondary space are included.

## Optional keywords under *KRMCSCF¶

### .CI PROGRAM¶

specifies the CI module behind KRMCSCF, choices are LUCIAREL and GASCIP. Note: GASCIP does not work with linear symmetry and for large-scale MCSCF (> $$1.0 \times 10^7$$ determinants) only LUCIAREL can be used efficiently. default:

.CI PROGRAM
GASCIP

### .THRESH¶

convergence threshold in the MCSCF gradient given as double precision value. The present default value is quite tight and might be adapted if one is only interested in MCSCF energies, e.g. $$1.d-03$$ . default:

0.5d-05

### .SYMMETRY¶

integer value giving the (boson/fermion) symmetry of the state to optimize on. default:

1


If you run the calculation in linear symmetry you have to specify 2 $$\times \Omega$$ value of the state to optimize on and use LUCIAREL as CI PROGRAM. The doubling stems from the fact that we want to avoid non-integer input, e.g. in case of an odd number of electrons we might have $$\Omega$$ = 1/2, 3/2, 5/2, etc. values and the corresponding input for the $$\Omega$$ = 1/2 would then read as

1


If we have a system with an even number of electrons and inversion symmetry the input for an $$\Omega$$ = 2g state would read as

4g

### .MAX MACRO¶

integer value giving the maximum number of MACRO iterations in the MCSCF optimization. default:

25


### .MAX MICRO¶

integer value giving the maximum number of MICRO iterations in the MCSCF optimization. default:

50


### .FROZEN¶

specifies how many of the inactive orbitals for each fermion corep should be frozen, that is, not change during the KRMCSCF optimization. The frozen orbitals are not included in 2-electron integral transformation, which saves some CPU time. default: include all inactive orbital rotations. example: Freeze the first two inactive orbitals in fermion corep 1 (gerade) and the first inactive orbital in fermion corep 2 (ungerade):

.FROZEN
2 1

### .DELETE¶

delete occupied-secondary e-e rotations (rotations between electronic-electronic spinors) in the gradient and Hessian calculation specified by an orbital string of virtual (secondary) orbitals for each fermion corep. default: include all active-secondary e-e rotations. example: Delete all e-e rotations for secondary orbitals 20,21 and 22 in fermion corep 1 (gerade) and 24,25,26,27 and 28 in fermion corep 2 (ungerade):

.DELETE
20,21,22
24..28

### .SKIPEE¶

skip e-e rotations (rotations between electronic-electronic spinors) in the gradient and Hessian calculation. default: include e-e rotations.

### .WITHEP¶

include e-p rotations (rotations between electronic-positronic spinors) in the gradient and Hessian calculation. default: skip e-p rotations.

### .SKIPEP¶

skip e-p rotations (rotations between electronic-positronic spinors) in the gradient and Hessian calculation. default: skip e-p rotations.

### .MVOFAC¶

generate modified inactive and virtual orbitals based on block-diagonalization of FC + “MVOFAC”*FV. The value does not change the MCSCF wave functions, but the non-active orbitals for post-MCSCF calculations (e.g. *LUCITA or *KRCI) are modified. default: MVOFAC = 1.0 example: Mimic Bauchschlicher’s MVOs for HF-CI for the MCSCF wave function:

.MVOFAC
0.0

### .PRINT¶

raise default print level to the given integer value. Please use with care as you may get millions of output lines if you choose a too high value. default:

.PRINT
0

# *OPTIMI¶

## optional keywords under *OPTIMI¶

NOTE: the following keywords must be placed under the input deck

*OPTIMI

### .NOOCCN¶

compute natural orbital occupation numbers for the final optimized electronic state. default: do not compute natural orbital occupation numbers.

### .ANALYZ¶

analyze the final CI wave function printing the coefficients for each determinant above a given threshold $$10^{-2}$$ . default: do not analyze the final CI wave function.

### .MAX CI¶

maximum number of initial CI iterations. default:

.MAX CI
5

### .MXCIVE¶

maximum size of Davidson subspace. default: 3 times the number of eigenstates (see .CIROOTS) to optimize on. example:

.MXCIVE
3