Case study: NMR shielding of UF3Cl3
In this tutorial we shall go through the calculation of NMR shieldings of the UF3Cl3 molecule using the scheme of simple magnetic balance (SMB) in conjunction with London orbitals [Olejniczak2012].
Preparing for the atomic start
To ensure a smooth convergence of the SCF calculation we employ an atomic start whereby an initial molecular density matrix is generated as the direct sum of atomic ones. We therefore have to perform a separate SCF calculation of each atomic type. At the moment the approach is somewhat cumbersome, but will be automatized in future versions of DIRAC. Each atom is calculated in maximal symmetry (linear symmery) and the coefficients then exported to C1 symmetry using the keyword .ACMOUT.
Uranium atom
We calculate the U+3 cation in the [Rn] 5f3 configuration.
The input file UIII.inp reads
**DIRAC
.WAVE FUNCTION
.ANALYZE
**GENERAL
.ACMOUT
**HAMILTONIAN
.DFTAUTO
PBE0
**INTEGRALS
*READIN
.UNCONTRACT
**WAVE FUNCTIONS
.SCF
*SCF
.CLOSED SHELL
42 44
.OPEN SHELL
1
3/0,14
**ANALYZE
.MULPOP
*MULPOP
.VECPOP
1..oo
1..oo
*END OF
and the corresponding molecular input file U.mol is
DIRAC
C 1 A
92. 1
U 0.0000000000 0.0000000000 0.0000000000
LARGE BASIS PNNLbas_h
FINISH
The minimal pam command is:
pam --inp=UIII.inp --mol=U.mol --get=DFACMO
We save the C1 coefficients and make a symbolic link for the atomic start:
mv DFACMO ac.UIII
ln -s ac.UIII DFUXXX
Fluorine atom
We calculate the fluorine atom in the [He] 2s2 2p5 ground
state configuration using fractional occupation.
The input file F.inp reads
**DIRAC
.WAVE FUNCTION
.ANALYZE
**GENERAL
.ACMOUT
**HAMILTONIAN
.DFTAUTO
PBE0
**INTEGRALS
*READIN
.UNCONTRACT
**WAVE FUNCTIONS
.SCF
*SCF
.CLOSED SHELL
4 0
.OPEN SHELL
1
5/0,6
**ANALYZE
.MULPOP
*MULPOP
.VECPOP
1..oo
1..oo
*END OF
and the corresponding molecular input file F.mol is
DIRAC
C 1 A
9. 1
F 0.0000000000 0.0000000000 0.0000000000
LARGE BASIS IGLO-IIIunc
FINISH
The minimal pam command is:
pam --inp=F.inp --mol=F.mol --get=DFACMO
We save the C1 coefficients and make a symbolic link for the atomic start:
mv DFACMO ac.F
ln -s ac.F DFFXXX
Chlorine atom
We calculate the chlorine atom in the [Ne] 3s2 3p5 ground
state configuration using fractional occupation.
The input file Cl.inp reads
**DIRAC
.WAVE FUNCTION
.ANALYZE
**GENERAL
.ACMOUT
**HAMILTONIAN
.DFTAUTO
PBE0
**INTEGRALS
*READIN
.UNCONTRACT
**WAVE FUNCTIONS
.SCF
*SCF
.CLOSED SHELL
6 6
.OPEN SHELL
1
5/0,6
**ANALYZE
.MULPOP
*MULPOP
.VECPOP
1..oo
1..oo
*END OF
and the corresponding molecular input file Cl.mol is
DIRAC
C 1 A
17. 1
Cl 0.0000000000 0.0000000000 0.0000000000
LARGE BASIS IGLO-IIIunc
FINISH
The minimal pam command is:
pam --inp=Cl.inp --mol=Cl.mol --get=DFACMO
We save the C1 coefficients and make a symbolic link for the atomic start:
mv DFACMO ac.Cl
ln -s ac.Cl DFCLXX
Initial SCF calculation
Atomic Hartree–Fock start
In this case the atomic start at the PBE0 level did not converge. It is then
recommend to proceed via a Hartree–Fock calculation where the HOMO-LUMO gap is
larger. The HF menu file SCFatom.inp reads
**DIRAC
.WAVE FUNC
**INTEGRALS
*READIN
.UNCONT
**HAMILTONIAN
.DFTAUTO
PBE0
**WAVE FUN
.SCF
*SCF
.CLOSED SHELL
170
.ATOMST
DFUXXX 2
1..43
1.00
44..50
0.214
DFCLXX 2
1..6
1.00
7..9
0.833
DFFXXX 2
1,2
1.00
3..5
0.83
**END OF
For the atomic start it can be noted that orbitals 1 through 43 of the uranium atom are fully occupied whereas the 5f orbitals (44 through 50) are given an fractional occupation of 3/14.
The corresponding molecular file UF3Cl3.mol reads
DIRAC
C 3 A
92. 1
U 0.0000000000 0.0000000000 0.0000000000
LARGE BASIS PNNLbas_h
17. 3
Cl1 0.000000 2.485723 0.152014
Cl2 0.000000 -2.485723 0.152014
Cl3 0.000000 0.000000 -2.343092
LARGE BASIS IGLO-IIIunc
9. 3
F1 2.001913 0.000000 0.142067
F2 0.000000 0.000000 2.143315
F3 -2.001913 0.000000 0.142067
LARGE BASIS IGLO-IIIunc
FINISH
The minimal pam command is:
pam --mol=UF3Cl3.mol --inp=SCFatom.inp --outcmo --copy="DFUXXX DFCLXX DFFXXX"
(I also added –mw=120 as well as –mpi=24)
Initial PBE0 run with restricted kinetic balance
Having good start vectors I next ran the PBE0 SCF calculation using the input SCF.inp:
**DIRAC
.WAVE FUNC
**INTEGRALS
*READIN
.UNCONT
**HAMILTONIAN
.DFTAUTO
PBE0
**GRID
.ATSIZE
.ULTRAFINE
**WAVE FUN
.SCF
*SCF
.CLOSED SHELL
170
.MAXITR
20
.OVLSEL
.NODYNSEL
.LSHIFT
0.2
**END OF
I am running with a level shift of 0.2 hartree as well as static overlap selection to ensure convergence. I also use the keyword .ATSIZE to determine the partitioning of the molecular volume into atomic ones. The minimal pam command reads:
pam --inp=SCF.inp --mol=UF3Cl3.mol --incmo --outcmo
This calculations converges smoothly in 20 iterations to:
TOTAL ENERGY
------------
Electronic energy : -31794.704487527993
Other contributions to the total energy
Nuclear repulsion energy : 2038.659981883082
SS Coulombic correction : 0.007588768574
Sum of all contributions to the energy
Total energy : -29756.036916876335
Property calculation using London orbitals and simple magnetic balance
Starting from the RKB coefficients we proceed to the actual calculation of NMR
parameters using simple magnetic balance and London orbitals. The input file
NMR.inp reads
**DIRAC
.PROPERTIES
**GENERAL
.RKBIMP
**INTEGRALS
*READIN
.UNCONT
**HAMILTONIAN
.URKBAL
.DFTAUTO
PBE0
**GRID
.ATSIZE
.ULTRAFINE
**WAVE FUN
.SCF
*SCF
.CLOSED SHELL
170
**PROPERTIES
.PRINT
2
.SHIELDING
*NMR
.LONDON
**END OF
This calculations gives:
@ isotropic shielding
@ ----------------------------
@atom total dia para skew span anis asym
@----------------------------------------------------------------------------
@U -5418.3074 288.0612 -5706.3685 -0.1585 13571.5391 9641.0019 1.2231
@Cl1 1 -1023.9194 67.4482 -1091.3676 0.8381 2875.6960 2759.3185 0.1265
@Cl1 2 -1023.9194 67.4482 -1091.3676 0.8381 2875.6960 2759.3185 0.1265
@Cl3 -885.2205 85.8218 -971.0423 0.7133 2705.2946 2511.3830 0.2316
@F1 1 -690.9071 103.1746 -794.0817 0.8742 1380.6609 1337.2555 0.0974
@F1 2 -690.9071 103.1746 -794.0817 0.8742 1380.6609 1337.2555 0.0974
@F2 -787.3430 84.2708 -871.6137 0.7175 1704.0367 1583.6803 0.2280
@----------------------------------------------------------------------------