## Nuclear Spin-Rotation Tensor Tutorial

Performing the relativistic nuclear spin-rotation tensor calculations in ReSpect requires the following sequence of steps

SCF(1c) → SCF(4c) → NSR

where the initial SCF(1c) step represents the self-consistent field (SCF) procedure based on a scalar-relativistic, one-component (1c) Hamiltonian and this step is primarily meant to provide a very good guess of initial molecular orbitals for subsequent fully relativistic calculations where both scalar- and spin-orbit corrections are included variationally. In the second SCF(4c) step, the actual relativistic molecular orbitals are determined by means of a relativistic four-component (4c) SCF involving Dirac—Coulomb Hamiltonian. Finally, nuclear spin-rotation tensors are evaluated in the last step (NSR), starting from the relativistic molecular orbitals obtained in the previous SCF(4c).

To perform the SCF(1c) calculation, execute the command

/path/to/ReSpect/respect --scf --inp=1c --scratch=/path/to/scratch/directory


where arguments mandatory to respect mean

• --scf
starts the SCF procedure;

• --inp
specifies a name of the input file;

• --scratch
specifies a path to the scratch directory.

A simple example of the input file 1c.inp for a scalar relativistic one-component DFT/B3LYP calculation of AsH3 with the Douglas–Kroll–Hess Hamiltonian looks like

#scf procedure with 1c scalar DKH2 Hamiltonian
scf:

geometry:
As
H  1  1.5324
H  1  1.5324  2  91.01
H  1  1.5324  2  91.01  3  91.0281

method: ks-dkh2/b3lyp
basis:  dyall-cvdz

charge:        0
multiplicity:  1
nc-model:      point
maxiterations: 30
convergence:   1.0e-5


Note that a comprehensive list of all SCF keywords can be found here.

Having the initial SCF(1c) step finished, let's move on to the next SCF(4c) step. In order to have the 1c molecular orbitals ready for a restart, we execute the linux command first

ln  -sf  1c.50  4c.50

which soft-links the ReSpect checkpoint file 1c.50 generated in the previous SCF(1c) calculation to a new checkpoint file 4c.50. Now, we can perform the second SCF(4c) step

/path/to/ReSpect/respect --restart --scf --inp=4c --scratch=/path/to/scratch/directory

where the additional argument --restart enforces respect to search for the initial molecular orbitals in the checkpoint file 4c.50. An example of the input file 4c.inp is

#4c SCF Dirac-Kohn-Sham DFT calculation of AsH3
#molecule with the Dirac--Coulomb Hamiltonian
scf:

geometry:
As
H  1  1.5324
H  1  1.5324  2  91.01
H  1  1.5324  2  91.01  3  91.0281

method: mdks/b3lyp
basis:  dyall-cvdz

charge:        0
multiplicity:  1
nc-model:      point
maxiterations: 30
convergence:   1.0e-6

#nuclear spin-rotation tensor
nsr:

isotope:
As: 75
H :  1

maxiterations: 30
convergence:   1.0e-5


Here, we replaced the 1c DKH2 Hamiltonian method:ks-dkh2/dft-functional by the 4c Dirac—Coulomb Hamiltonian method:mdks/dft-functional.

Having the SCF(4c) calculation finished successfully, let's perform the final NSR step by running the command

/path/to/ReSpect/respect --nsr --inp=4c --scratch=/path/to/scratch/directory

where the input block nsr: takes control of the setup for the nuclear spin-rotation tensor calculation. A comprehensive list of all spin-rotation keywords can be found here.

As a final note, there are several important and worth-to-remember aspects associated with the input syntax, namely

• the input is case-insensitive
This means that the program does not distinguish between uppercase and lowercase letters.

• the input is insensitive to the number of blank lines and/or comment lines
All comments begin with the number sign (#), can start anywhere on a line and continue until the end of the line.

• the input is compliant with the dictionary syntax of the YAML markup language
This means that each input line is represented either by a single block: statement or by a simple keyword:value pair, such as

• block1:
keyword1: value1
keyword2: value2
...
block2:
keyword3: value3
keyword4: value4
...
block3:
keyword5: value5
keyword6: value6
...


It is essential to remember that all members of one block: are lines beginning at the same indentation level. Whitespace indentation is used to denote the block structure; however, tab characters are never allowed as indentation. The only exception to the YAML-based input syntax is the block geometry: which utilizes a simple xyz format for the molecular geometry specification.

## TIPS & TRICKS

Q: How to scale the speed of light in NSR calculations?

Set the cscale option in the SCF calculation. The scaling value is then automatically transferred to the NSR calculation.

Q: Is it possible to scale spin-orbit interaction in NSR calculations?

No. Currently one can only turn off SO interaction by setting soscale option to zero in the SCF calculation. This setting is then automatically transferred to the NSR calculation.

Q: Is there a way to launch SCF and NSR calculations without the need to explicitly setup the scratch path by "--scratch=/path/to/scratch/directory"?

Yes, the argument "--scratch=/path/to/scratch/directory" can be saved to the file .respectrc in your home directory. If both the file and the command line argument exist, then ReSpect takes the scratch directory setting from the command line.

Q: How to set the number of processors for parallel SCF and NSR calculations?

For OpenMP parallel calculations, the number of processors can be controlled from the command line by the argument --nt=N, where N ideally refers to the total number of physical cores of a machine. Thus, the command line for launching an OpenMP parallel SCF or NSR job reads

/path/to/ReSpect/respect --nt=N --scf --inp=my-input-file
/path/to/ReSpect/respect --nt=N --nsr --inp=my-input-file


Note, however, we have assumed here that the scratch path is setup through the file .respectrc (see the previous discussion).

Q: I want to run a multiple nsr calculations starting from the same four-component molecular orbitals. Is there a way to avoid recalculating the 4c scf job multiple times?

Yes, one can run the nsr calculation with command

/path/to/ReSpect/respect --nsr --inp=nsr-input --start-data=4c

where nsr-input.inp file contains only the nsr: input block

nsr:

isotope:
As: 75
H :  1

maxiterations: 30
convergence:   1.0e-5


The above command will take the initial data from 4c.50 and performs the nsr calculation according to the input in nsr-input.inp. After successful end of the nsr job, the final output data will be stored in the file 4c-nsr-input.out_nsr. This step can be repeated multiple times with different nsr input files but always starting from the same SCF(4c).

March 25, 2020

February, 2019

November 7, 2019