# GRASP computer exercises¶

The following exercises are to be done in groups of 2-3 students. Each group shall cover different groups/atoms of the periodic table of elements. At the end of the day, all groups should give a short presentation on their findings to the other groups.

In order to run a GRASP calculation you need an input file of arbitrary name, e.g. grasp.inp which will be setup in the following. The run-command inside your cluster run script looks as:

\$ grasp.x < grasp.inp > grasp.out

where the GRASP output is re-directed to the file grasp.out. Make sure that you give a proper name to your output file if you want to take a look at what you did back home.

If not stated otherwise we will always use a Gaussian nuclear model in GRASP.

## Exercises - Day 1¶

### Nuclear models in GRASP¶

GRASP offers four different nuclear models, we will start with calculations on a one-electron system for each of the four nuclear models.

One electron atom
1 1 1
1s 1
ANG 7
-1
MCP 8 9
MCDF
9 0 10
86 222.0
NUC 0
AL
END
• point nucleus:

NUC 0
• finite nucleus (Uniform Sphere):

NUC 1
• finite nucleus (Fermi):

NUC 2
• finite nucleus (Gaussian):

NUC 3

Questions:

1. How does the use of a finite-nucleus model affect the total energy of an atom compared to the point-nucleus model?
2. What is the effect on the spin-orbit splitting?
3. Do differences between finite-nuclear models increase or decrease with increasing nuclear charge Z?

## Exercises - Day 2¶

Note

A database for atomic data can be found here: http://physics.nist.gov/PhysRefData/Handbook/periodictable.htm

### Atomic numerical calculations¶

In order to get started on “real” atoms we calculate the average level structure of the ground state configuration of a coinage-metal (Cu, Ag, Au, Rg), using numeric GRASP.

Cu average calculation
2 7 1
1s
2s
2p
3s
3p
3d 10 9
4s  1 2
ANG 7
-1
-1
MCP 8 9
MCDF
9 0 10
29 63.0
NUC 3
SCF NITIT=10
AL
END

Run all atoms of the coinage-metal series:

Cu: Z = 29,  A =  63
Ag: Z = 47,  A = 107
Au: Z = 79,  A = 197
Rg: Z = 111, A = 283

In order to generate a less biased average set of orbital solutions (degeneracy of the d $$^9$$ s $$^2$$: 10; d $$^{10}$$ s $$^1$$: 2), compare your results with an additional calculation using:

AL 10 2

Note

We explicitly set the maximum number of SCF iterations (“SCF NITIT=10”) in order to allow Cu to converge (default SCF iteration = 6)

Questions:

1. Does the ground state configuration vary down the coinage-metal series?
2. What would you expect as dominant oxidation states for Cu/Au in molecular compounds and why?
3. How does the d-s excitation energy change down the coinage-metal series?

### Spin-orbit mixing within a group¶

• Look at the jj-LS transformation with GRASP to get a feel for spin-orbit mixing down a group, pick the “C” group 14:

Note

the third number “2” in line 2 activates the transformation from jj-coupling to LS-coupling. Note also the “ANG” line to print all configurations (“ANG 7” will suppress the printout).

jj-LS transformation Si atom
1 5 2
1s
2s
2p
3s
3p 2
ANG
-1
MCP 8 9
MCDF
9 0 10
14 28.0
NUC 3
AL
END

Questions:

1. Does the singlet-triplet mixing (state interaction) increase or decrease with increasing Z?
2. How much of the ground state is described by the $$p_{1/2}^{2}$$ configuration with increasing Z?

### Speed of light and the non-relativistic limit¶

• Run an average-of-configuration SCF calculation the gold atom:
Au average calculation
2 14 1
1s
2s
2p
3s
3p
3d
4s
4p
4d
5s
5p
4f
5d 10 9
6s 1  2
ANG 7
-1
-1
MCP 8 9
MCDF
9 0 10
79 197.0
NUC 3
SCF CON=1.0D0
AL
END
• GRASP allows you to vary the speed of light c between Z < c < $$\infty$$:

SCF CON=x.xDx
• perform a non-relativistic calculation using a very large c value, c $$>> 137$$:

SCF CON=1.0D6

Questions:

1. Is it possible to set c < Z?
2. Can you argue from a comparison of the relativistic (“regular” speed-of-light) and non-relativistic calculation why gold is golden? What about Ag?
3. Which spinors are stabilized by relativistic effects and which are destabilized?

### Radial densities for the d-/p block¶

Note

a basic GNUPLOT script (needs to be adapted according to your data file names) for visualizing radial densities is available online: http://wiki.chem.vu.nl/dirac/index.php/GRASP_and_DIRAC_inputs

• Plot radial functions for heavy elements, compare s and d functions (d block) resp. p $$_{1/2}$$ and p $$_{3/2}$$ (p block).
Cu average calculation
2 7 1
1s
2s
2p
3s
3p
3d 10 9
4s  1 2
ANG 7
-1
-1
MCP 8 9
MCDF 28
9 0 10
29 63.0
NUC 3
AL
END

Each group should pick one of their favorite block/group.

calculate the 3d, 4d, 5d, 6d block (coinage metals)
calculate the 3d, 4d, 5d, 6d block (group: "Zn, Cd, Hg, Cn")
calculate the 2p, 3p, 4p, 5p, 6p, 7p block (group 14)
calculate the 2p, 3p, 4p, 5p, 6p, 7p block (group 16)

Questions:

1. How does the radial overlap between s and d resp. p $$_{1/2}$$ and p $$_{3/2}$$ change down a group?
2. Where would you expect the most open-shell character (at the top or bottom of a group)?

### Using a non-relativistic or relativistically optimized basis set for heavy atoms?¶

Note

all basis set inputs are available online: http://wiki.chem.vu.nl/dirac/index.php/GRASP_and_DIRAC_inputs

• run the Thallium atom with a non-relativistic double-$$\zeta$$ basis set:
Thallium atom
1 15 1
1S
2S
2P
3S
3P
3D
4S
4P
4D
4F
5S
5P
5D
6S
6P 1
ANG 1 7
-1
MCP 1 2
MCDF 24
2 0 3 0 14
81 204.0
NUC 3
GAUSS 4
1S  22
2P- 17
2P  17 2P- 1 17
3D- 13
3D  13 3D- 1 13
4F-  8
4F   8 4F- 1  8
1.8623969E+07
3.6867955E+06
9.6378590E+05
2.9791376E+05
1.0338698E+05
3.9115255E+04
1.5831221E+04
6.7653929E+03
3.0236823E+03
1.4021816E+03
6.6607727E+02
3.0047853E+02
1.5516535E+02
7.9776475E+01
3.7180980E+01
1.9582277E+01
8.6490359E+00
4.4732684E+00
1.5727172E+00
7.2742584E-01
1.4401137E-01
5.4696933E-02
8.4903516E+04
2.0108565E+04
6.5288090E+03
2.4952142E+03
1.0578546E+03
4.8183325E+02
2.3099156E+02
1.1460187E+02
5.6345780E+01
2.8858154E+01
1.4257420E+01
7.1249109E+00
3.4904261E+00
1.5777429E+00
6.6465131E-01
1.5479093E-01
4.8201891E-02
4.4351057E+03
1.3418293E+03
5.2396706E+02
2.3190630E+02
1.1060211E+02
5.4985007E+01
2.8038853E+01
1.4122437E+01
7.0047966E+00
3.4026123E+00
1.5589903E+00
6.6349200E-01
2.5380659E-01
4.6883901E+02
1.6331607E+02
6.9830068E+01
3.2496980E+01
1.5735686E+01
7.6001533E+00
3.5619156E+00
1.4998623E+00
ORBOUT 1 - 15
AL
END
• run the Thallium atom with a relativistic double-$$\zeta$$ basis set:
Thallium atom
1 15 1
1S
2S
2P
3S
3P
3D
4S
4P
4D
4F
5S
5P
5D
6S
6P 1
ANG 1 7
-1
MCP 1 2
MCDF 24
2 0 3 0 14
81 204.0
NUC 3
GAUSS 4
1S  24
2P- 20
2P  20 2P- 1 20
3D- 13
3D  13 3D- 1 13
4F-  8
4F   8 4F- 1  8
5.8033828E+07
1.4702562E+07
4.6355575E+06
1.5852740E+06
5.7924626E+05
2.2187944E+05
8.8730780E+04
3.6848078E+04
1.5843298E+04
7.0310514E+03
3.2121888E+03
1.5070783E+03
7.2301062E+02
3.3980515E+02
1.7093901E+02
8.8017323E+01
4.3016225E+01
2.2609863E+01
1.0266569E+01
5.2648225E+00
1.8988944E+00
8.8461372E-01
2.0106574E-01
7.3237091E-02
1.3728265E+07
2.3572128E+06
5.2356678E+05
1.3629076E+05
4.0148089E+04
1.3182021E+04
4.7879862E+03
1.9028441E+03
8.1502288E+02
3.6967602E+02
1.7504377E+02
8.4456267E+01
4.2043229E+01
2.1172075E+01
1.0107599E+01
4.9031493E+00
1.9632888E+00
8.0549699E-01
2.0049629E-01
5.5927884E-02
7.8021591E+03
2.0396979E+03
7.3049097E+02
3.0516736E+02
1.3964975E+02
6.7292643E+01
3.3520599E+01
1.6568385E+01
8.0815299E+00
3.8806549E+00
1.6956350E+00
6.9524060E-01
2.5357650E-01
4.8999559E+02
1.6633197E+02
6.9980085E+01
3.2175090E+01
1.5417577E+01
7.3699578E+00
3.4086613E+00
1.4138469E+00
ORBOUT 1 - 15
AL
END

Questions:

1. How does the spin-orbit splitting from both basis set calculation compare with the experimental reference?
2. Can you recommend to use a non-relativistically optimized basis set in relativistic (four-component) calculation? Why/why not?
3. What are the major qualitative differences between both basis sets?

### Basis set quality¶

Note

all basis set inputs are available online: http://wiki.chem.vu.nl/dirac/index.php/GRASP_and_DIRAC_inputs

Bismuth atom
1 15 1
1S
2S
2P
3S
3P
3D
4S
4P
4D
4F
5S
5P
5D
6S
6P 3
ANG 7
-1
MCP 8 9
MCDF 28
9 0 10
83 209.0
NUC 3
AL
END
• repeat the calculation using Ken Dyall’s
1. double-$$\zeta$$ basis set
Bi atom - DZ basis
1 15 1
1s
2s
2p
3s
3p
3d
4s
4p
4d
4f
5s
5p
5d
6s
6p 3
ANG 1 7
-1
MCP 1 2
MCDF 24
2 0 3 0 14
83 209.0
NUC 3
GAUSS 4
1S  24
2P- 20
2P  20 2P- 1 20
3D- 14
3D  14 3D- 1 14
4F-  8
4F   8 4F- 1  8
5.8022684E+07
1.4819799E+07
4.7223874E+06
1.6321833E+06
6.0232740E+05
2.3262600E+05
9.3657019E+04
3.9098920E+04
1.6878840E+04
7.5127674E+03
3.4393803E+03
1.6158149E+03
7.7585154E+02
3.6612190E+02
1.8440048E+02
9.5065117E+01
4.6466268E+01
2.4477290E+01
1.1190161E+01
5.7978488E+00
2.1587077E+00
1.0422614E+00
2.6590866E-01
1.0073440E-01
1.5267851E+07
2.6863694E+06
6.0456060E+05
1.5848335E+05
4.6785870E+04
1.5325077E+04
5.5345524E+03
2.1842431E+03
9.2942393E+02
4.1932007E+02
1.9785121E+02
9.5696786E+01
4.7435630E+01
2.3929631E+01
1.1351604E+01
5.5346123E+00
2.2410872E+00
9.5317500E-01
2.4829310E-01
7.7915822E-02
1.1456342E+04
2.9347912E+03
1.0364305E+03
4.3032355E+02
1.9654041E+02
9.5235753E+01
4.7867448E+01
2.4364758E+01
1.2223922E+01
6.0607197E+00
2.8412869E+00
1.2973356E+00
5.5200808E-01
2.0223207E-01
5.5102305E+02
1.8692436E+02
7.8801541E+01
3.6351986E+01
1.7527887E+01
8.4583618E+00
3.9675228E+00
1.6865442E+00
AL
END
1. triple-$$\zeta$$ basis set
Bi atom - TZ basis
1 15 1
1s
2s
2p
3s
3p
3d
4s
4p
4d
4f
5s
5p
5d
6s
6p 3
ANG 1 7
-1
MCP 1 2
MCDF 24
2 0 3 0 14
83 209.0
NUC 3
GAUSS 4
1S  30
2P- 25
2P  25 2P- 1 25
3D- 17
3D  17 3D- 1 17
4F- 11
4F  11 4F- 1 11
6.0311989E+07
1.6051490E+07
5.4946022E+06
2.0921783E+06
8.7228608E+05
3.8455448E+05
1.7769146E+05
8.4842022E+04
4.1639260E+04
2.0888520E+04
1.0685288E+04
5.5616491E+03
2.9418744E+03
1.5792819E+03
8.5880021E+02
4.7160384E+02
2.6367206E+02
1.4960897E+02
8.5864339E+01
4.9330236E+01
2.9084112E+01
1.7004392E+01
9.4518823E+00
5.3907940E+00
2.9254412E+00
1.5767178E+00
8.2262394E-01
3.3654907E-01
1.5552971E-01
6.7994583E-02
4.5716312E+07
1.2020013E+07
3.5338508E+06
1.1328857E+06
3.8880908E+05
1.4139323E+05
5.4175877E+04
2.1825254E+04
9.2485101E+03
4.1227683E+03
1.9285313E+03
9.4167499E+02
4.7644513E+02
2.4829591E+02
1.3204380E+02
7.0732928E+01
3.8843957E+01
2.1268489E+01
1.1356211E+01
6.0893913E+00
3.1150062E+00
1.5809224E+00
7.6275107E-01
2.9950363E-01
1.2171302E-01
3.6056471E+04
8.7942690E+03
2.9773896E+03
1.2026340E+03
5.4320948E+02
2.6392698E+02
1.3504708E+02
7.1319062E+01
3.8578165E+01
2.0919821E+01
1.1151610E+01
5.9122803E+00
3.0430319E+00
1.5135542E+00
7.2243078E-01
3.2503953E-01
1.2657989E-01
1.0703029E+03
3.6323880E+02
1.5446734E+02
7.3368355E+01
3.6869724E+01
1.9107106E+01
9.8894189E+00
5.0068176E+00
2.3615820E+00
8.9551709E-01
2.7862580E-01
AL
END
1. quadruple-$$\zeta$$ basis set
Bi atom - QZ basis
1 15 1
1s
2s
2p
3s
3p
3d
4s
4p
4d
4f
5s
5p
5d
6s
6p 3
ANG 1 7
-1
MCP 1 2
MCDF 24
2 0 3 0 14
83 209.0
NUC 3
GAUSS 4
1S  34
2P- 31
2P  31 2P- 1 31
3D- 21
3D  21 3D- 1 21
4F- 14
4F  14 4F- 1 14
6.0327973E+07
1.6059400E+07
5.5002311E+06
2.0965944E+06
8.7614365E+05
3.8775710E+05
1.8029442E+05
8.6844149E+04
4.3076212E+04
2.1842909E+04
1.1293409E+04
5.9507204E+03
3.2014852E+03
1.7641591E+03
1.0016015E+03
5.9564241E+02
3.9672091E+02
2.5845574E+02
1.6068287E+02
9.8444637E+01
6.0146010E+01
3.7934344E+01
2.3912645E+01
1.5276004E+01
9.2087298E+00
5.5574031E+00
3.2023544E+00
1.9180785E+00
1.1731977E+00
7.4463019E-01
4.7115520E-01
2.3902743E-01
1.1886460E-01
5.6025919E-02
7.2548229E+07
2.5127961E+07
8.9943363E+06
3.3978472E+06
1.3406152E+06
5.4867118E+05
2.3165676E+05
1.0069143E+05
4.5050536E+04
2.0784822E+04
9.9000264E+03
4.8664210E+03
2.4655886E+03
1.2855834E+03
6.8790131E+02
3.7620602E+02
2.0950837E+02
1.1794969E+02
6.6689215E+01
3.8460927E+01
2.2109515E+01
1.2482731E+01
7.1083213E+00
4.0003720E+00
2.2284663E+00
1.2125620E+00
6.4365302E-01
3.1488676E-01
1.5158717E-01
7.1607861E-02
3.2913977E-02
1.6463954E+05
3.8667080E+04
1.2458903E+04
4.7981120E+03
2.0858623E+03
9.8974360E+02
5.0061517E+02
2.6520654E+02
1.4561957E+02
8.1829425E+01
4.6861624E+01
2.7006142E+01
1.5460270E+01
8.8034943E+00
4.9821735E+00
2.7644317E+00
1.4934857E+00
8.0288750E-01
4.4714894E-01
2.4637901E-01
1.0017191E-01
2.5971422E+03
8.6492152E+02
3.6744541E+02
1.7603323E+02
9.0982272E+01
4.8997622E+01
2.7207540E+01
1.5262097E+01
8.5485499E+00
4.7315946E+00
2.5336398E+00
1.2638986E+00
4.4762345E-01
1.7508119E-01
AL
END

Questions:

1. Look at the ground and lowest excited states - does a double-$$\zeta$$ basis set suffice to reach a good agreement with the numerical solution?
2. Compare with experiment!
3. R.95 values as a measure for the density at the nucleus: would a quadruple-$$\zeta$$ basis set be large enough to reach agreement with the numerical reference value? What may be missing?

### Using j- or l-optimized basis sets?¶

Note

all basis set inputs are available online: http://wiki.chem.vu.nl/dirac/index.php/GRASP_and_DIRAC_inputs

• use a j-optimized basis set to calculate the spin-orbit spliiting of the ground state of element 113.
element 113 - j-optimized DZ basis
1 19 1
1s
2s
2p
3s
3p
3d
4s
4p
4d
4f
5s
5p
5d
5f
6s
6p
6d
7s 2
7p 1
ANG 7
-1
MCP 8 9
MCDF 11
9 0 0 0 10
113 287.0
NUC 3
SCF NITIT=6 CON=1.0E0
GAUSS 4 CONTROL
CONTROL CNVVEC 6.3 CNVENG 12
1s  26
2p- 26 1s 1 26
2p  22
3d- 22 2p 1 22
3d  15
4f- 15 3d 1 15
4f  10
5.410555451E+07   1.477674220E+07   5.046760516E+06   1.881036246E+06
7.519670234E+05   3.121717712E+05   1.337537787E+05   5.861701238E+04
2.623376918E+04   1.196778403E+04   5.565613895E+03   2.641110608E+03
1.279308333E+03   6.350605841E+02   3.229251397E+02   1.668148069E+02
8.855127743E+01   4.626843234E+01   2.491302232E+01   1.332236224E+01
7.050429402E+00   3.566653213E+00   1.746480412E+00   8.012456416E-01
2.363147173E-01   8.211626183E-02
1.832973111E+06   3.677410004E+05   1.042558311E+05   3.551995083E+04
1.365628428E+04   5.729961829E+03   2.571176326E+03   1.216215930E+03
6.003294614E+02   3.061461712E+02   1.601715602E+02   8.574943752E+01
4.600764505E+01   2.487057706E+01   1.355724873E+01   7.189512031E+00
3.709687491E+00   1.753488637E+00   8.174464605E-01   3.431291818E-01
1.196202297E-01   3.605428667E-02
1.438935404E+04   4.111888007E+03   1.542160218E+03   6.637471705E+02
3.111800230E+02   1.538758849E+02   7.883962728E+01   4.095259646E+01
2.148494432E+01   1.119186568E+01   5.692583697E+00   2.791037755E+00
1.265293623E+00   5.247952224E-01   1.904499576E-01
1.250294088E+03   4.300054627E+02   1.834372720E+02   8.629363698E+01
4.258654175E+01   2.151568823E+01   1.081918963E+01   5.287539266E+00
2.459405736E+00   1.015550465E+00
AL
END
• use an l-optimized double-$$\zeta$$ basis set to calculate the spin-orbit spliiting of the ground state of element 113.
element 113 - l-optimized DZ basis
1 19 1
1s
2s
2p
3s
3p
3d
4s
4p
4d
4f
5s
5p
5d
5f
6s
6p
6d
7s 2
7p 1
ANG 7
-1
MCP 8 9
MCDF 11
9 0 0 0 10
113 287.0
NUC 3
SCF NITIT=6 CON=1.0E0
GAUSS 4 CONTROL FILE
FILE ORBOUT 15
CONTROL CNVVEC 6.2
1s  26
2p- 23 INPUT 23
2p  23 2p- 1 23
3d- 16 INPUT 16
3d  16 3d- 1 16
4f- 10 INPUT 10
4f  10 4f- 1 10
5.265642072E+07   1.398668173E+07   4.744225153E+06   1.773651781E+06
7.211584750E+05   3.072954606E+05   1.361714165E+05   6.186190016E+04
2.870767672E+04   1.354593172E+04   6.493475213E+03   3.160915774E+03
1.566402942E+03   7.828926638E+02   4.032058295E+02   2.129754819E+02
1.130317381E+02   6.157486221E+01   3.081682545E+01   1.745962073E+01
8.406496322E+00   4.569965531E+00   1.838611962E+00   8.939622677E-01
2.577221550E-01   9.512584750E-02
4.229507716E+07   1.141955059E+07   3.385481418E+06   1.077807478E+06
3.626176904E+05   1.278139940E+05   4.700831502E+04   1.803351286E+04
7.236424880E+03   3.047220410E+03   1.346097801E+03   6.212385772E+02
2.974547576E+02   1.444719950E+02   7.281587369E+01   3.559708607E+01
1.847008238E+01   8.782215331E+00   4.364365927E+00   1.807522394E+00
7.635699789E-01   2.235716213E-01   5.494900450E-02
5.139188102E+04   1.215627481E+04   3.972026569E+03   1.553402513E+03
6.804362135E+02   3.219877107E+02   1.600788432E+02   8.229169547E+01
4.263535587E+01   2.234970892E+01   1.166226200E+01   5.953952373E+00
2.940992133E+00   1.282899982E+00   5.318130871E-01   1.946401187E-01
1.424804508E+03   4.735984924E+02   1.985441055E+02   9.228016323E+01
4.523210419E+01   2.271190558E+01   1.138109376E+01   5.546411754E+00
2.573192362E+00   1.061568660E+00
AL
END

Questions:

1. Can you come up with an explanation for the differences in the spin-orbit splitting calculated with an j- and l-optimized basis set?
2. Which calculation yields a value closer to the numerical reference and why?