Magnetizabilities with London Atomic Orbitals¶
Introduction¶
In this tutorial we will look at the calculation of (static) magnetizabilities with DIRAC. For more details about the method, see [Ilias2013].
The component
The first-order induced magnetic dipole is proportional to the direct product of the position vector
Example: ¶
We shall illustrate these features using the nitrogen trifluoride molecule.
The molecular input file NF3.mol uses the experimental geometry and automatic symmetry detection.
INTGRL
NF3, exp.geom
daug-cc-pVQZ
C 2 A
7. 1
N 0.000000000 0.0000000000 0.0000000000
LARGE BASIS aug-cc-pVDZ
9. 3
F1 0.0000000000 .0000000000 1.3676000000
F2 1.3385030000 0.0000000000 -.2806030000
F3 -.3455290000 1.293136000 -.2806030000
LARGE BASIS aug-cc-pVDZ
FINISH
Generating the HF wave function¶
We first run a Hartree-Fock calculation to generate orbitals and corresponding energies using scf.inp
**DIRAC
.TITLE
NF3
.WAVE F
.ANALYZE
**INTEGRALS
*READIN
.UNCONT
**WAVE FUNCTIONS
.SCF
*SCF
.CLOSED SHELL
34
**ANALYZE
.MULPOP
*END OF
and the command:
pam --inp=scf --mol=NF3 --outcmo
You may notice in the output that DIRAC will center and rotate the molecule.
It detects the full
Magnetizabilities: first attempt¶
We first calculate the magnetizability using the input file cgo.inp
**DIRAC
.TITLE
NF3
.PROPERTIES
**GENERAL
.RKBIMP
**HAMILTONIAN
.URKBAL
**INTEGRALS
*READIN
.UNCONT
**WAVE FUNCTIONS
.SCF
*SCF
.CLOSED SHELL
34
**PROPERTIES
.MAGNET
*NMR
.USECM
*END OF
where the (common) gauge origin has been set to the center of mass using the .USECM keyword.
Notice that we use .RKBIMP (? .RKBIMP ) to convert our molecular coefficients from restricted
to unrestricted kinetic balance (RKB
pam --inp=cgo --mol=NF3 --incmo
and gives the total magnetizability tensor
Bx By Bz
Bx -6.311410457817 -0.000000000000 -0.000004485788
By -0.000000000000 -6.311410738039 -0.000000000000
Bz 0.000000339879 -0.000000000000 -6.753534842323
here reported in atomic units
Magnetizabilities using LAOs¶
We now activate LAOs using the input file lao.inp
**DIRAC
.TITLE
NF3
.PROPERTIES
**GENERAL
.RKBIMP
**HAMILTONIAN
.URKBAL
**INTEGRALS
*READIN
.UNCONT
**WAVE FUNCTIONS
.SCF
*SCF
.CLOSED SHELL
34
**PROPERTIES
.MAGNET
*NMR
.LONDON
*END OF
which gives the total magnetizability tensor
Bx By Bz
Bx -5.215860172448 0.000000000000 -0.000000702830
By 0.000000000000 -5.215856642085 -0.000000000000
Bz 0.000002183587 -0.000000000000 -4.570158593223
which is markedly different from the CGO. The question now is: Which result is ‘best’ ? From microwave spectroscopy (see []) the magnetizability anisotropy, defined as
has been found to be -0.63
Gauge-origin dependence¶
To investigate gauge-origin dependence we do a CGO and LAO calculation with the gauge origin placed at:
**INTEGRALS
.GO ANG ! gauge origin in Angstrom
10.00 0.0 0.0
that is, along the
Bx By Bz
Bx -6.753534785034 -0.000019708625 -0.000000000000
By 0.000016616881 -134.461048086921 -0.000000000000
Bz -0.000000000000 -0.000000000000 -134.460100713107
We see that the parallel component
Bx By Bz
Bx -4.570158198807 -0.000014273103 -0.000000000001
By 0.000001955079 -5.215956665783 0.000000000000
Bz -0.000000000001 0.000000000000 -5.215972281121
where the numerical differences with respect to the original calculation is below the convergence threshold of the linear response calculation. We can therefore see that the use of LAOs removes the gauge dependence in the finite basis approximation.
Basis-set convergence¶
The basis set convergence is illustrated by the following table, taken from [Ilias2013], showing CGO(LAO)
magnetizabilities (in
Basis |
||||
DZ |
-14.83 (-4.27) |
-9.78 (-4.87) |
-11.47 (-4.67) |
+5.04 (-0.60) |
TZ |
-7.88 (-4.36) |
-6.52 (-4.96) |
-6.97 (-4.76) |
+1.37 (-0.60) |
QZ |
-5.65 (-4.43) |
-5.54 (-5.04) |
-5.58 (-4.83) |
+0.11 (-0.61) |
aug-DZ |
-6.75 (-4.57) |
-6.31 (-5.22) |
-6.46 (-5.00) |
+0.44 (-0.65) |
aug-TZ |
-5.01 (-4.64) |
-5.42 (-5.24) |
-5.28 (-5.04) |
-0.41 (-0.60) |
aug-QZ |
-4.70 (-4.64) |
-5.26 (-5.24) |
-5.08 (-5.04) |
-0.56 (-0.60) |
d-aug-DZ |
-6.37 (-4.57) |
-6.18 (-5.22) |
-6.24 (-5.00) |
+0.19 (-0.65) |
d-aug-TZ |
-5.01 (-4.69) |
-5.45 (-5.27) |
-5.31 (-5.08) |
-0.44 (-0.58) |
d-aug-QZ |
-4.76 (-4.68) |
-5.31 (-5.28) |
-5.13 (-5.08) |
-0.55 (-0.60) |
The basis set convergence is seen to be dramatically different, again clearly in favour of LAOs.