ECP calculation¶
In DIRAC12, effective core potential (ECP) is implemented and various corrleation methods are availiable within the two-component or one-component effective Hamiltonian. From the inclusion (exclusion) of spin-orbit potential parameters in input file, molecular spinors (orbitals) are obtained and this is the starting point of several ground and excited state calculation with ECP.
The first example is the SCF calculation of hydrogen iodide.
SOREP calculation¶
The simplest input file (HF.inp) for ECP calculation is
**DIRAC
.WAVE F
**HAMILTONIAN
.ECP
**WAVE FUNCTIONS
.SCF
*END OF DIRAC
together with the molecular input (HI_SOREP.mol)
INTGRL
HI MOLECULE
I:Christiansen RECP, H:Aug-cc-pVTZ
C 2 2 Y Z A
53. 1
I 1.59900000 0.00000000 0.00000000
LARGE 4 1 1 1 1
F 7 4 0
8.9655217 -0.0054740 0.0000000 0.0000000 0.0000000
4.5610628 0.0250170 0.0000000 0.0000000 0.0000000
1.8188811 -0.8900750 0.0000000 0.0000000 0.0000000
1.4925532 1.3195220 0.0000000 0.0000000 0.0000000
0.2875149 0.0000000 1.0000000 0.0000000 0.0000000
0.0824299 0.0000000 0.0000000 1.0000000 0.0000000
0.0237922 0.0000000 0.0000000 0.0000000 1.0000000
F 7 4 0
4.8262036 0.0122770 0.0000000 0.0000000 0.0000000
2.2639587 -0.0457030 0.0000000 0.0000000 0.0000000
1.1561771 0.2251760 0.0000000 0.0000000 0.0000000
0.5506509 -0.2514460 0.0000000 0.0000000 0.0000000
0.2444091 0.0000000 1.0000000 0.0000000 0.0000000
0.0908574 0.0000000 0.0000000 1.0000000 0.0000000
0.0299745 0.0000000 0.0000000 0.0000000 1.0000000
F 3 3 0
0.4320000 1.0000000 0.0000000 0.0000000
0.2200000 0.0000000 1.0000000 0.0000000
0.1000000 0.0000000 0.0000000 1.0000000
F 2 2 0
0.4265000 1.0000000 0.0000000
0.1700000 0.0000000 1.0000000
ECP 46 4 3
4
2 .922500 -1.447005
2 2.569100 -14.188832
2 7.908600 -43.263306
1 25.061100 -27.740856
6
2 1.503600 -124.037542
2 1.874600 235.545458
2 2.682800 -261.475363
2 3.446600 144.184313
1 1.124200 31.003269
0 11.458300 6.512373
6
2 1.245400 -95.368794
2 1.582600 188.963297
2 2.242900 -221.153567
2 2.930100 104.680452
1 .950300 30.809252
0 12.782000 5.414640
6
2 .668500 -50.340552
2 .828000 102.276429
2 1.115700 -133.296812
2 1.419000 75.010821
1 .503000 19.150171
0 4.557600 8.099959
#spin-orbit
6
2 1.245400 5.416752
2 1.582600 3.711418
2 2.242900 -25.208180
2 2.930100 27.780892
1 .950300 -2.699622
0 12.782000 .351446
6
2 .668500 -.406356
2 .828000 2.040806
2 1.115700 -3.283400
2 1.419000 1.842046
1 .503000 -.126998
0 4.557600 .008442
4
2 .922500 -.019085
2 2.569100 .035451
2 7.908600 -.007995
1 25.061100 .096830
1. 1
H 0.00000000 0.00000000 0.00000000
LARGE BASIS aug-cc-pVTZ
FINISH
This is the two-component spin-orbit relativistic effective core potential (SOREP) calulation. (For the detail of input, see How to specify ECP parameters in mol files)
In the final output, the two-component molecular spinors are obtained
* Fermion symmetry E1
* Closed shell, f = 1.0000
-0.91849028398625 ( 2) -0.53547268879208 ( 2) -0.40006484189588 ( 2) -0.37307836548798 ( 2)
* Virtual eigenvalues, f = 0.0000
0.03426904787073 ( 2) 0.05875502261229 ( 2) 0.08417741978544 ( 2) 0.08661765422042 ( 2) 0.08729608075284 ( 2)
0.13645335183505 ( 2) 0.20146339739788 ( 2) 0.20209264550882 ( 2) 0.23363818798538 ( 2) 0.23500980856689 ( 2)
0.26681617711053 ( 2) 0.33365537629186 ( 2) 0.34280937791647 ( 2) 0.34322959805083 ( 2) 0.45833702543722 ( 2)
0.48328741534790 ( 2) 0.50649128877099 ( 2) 0.51736684713002 ( 2) 0.61447310303433 ( 2) 0.61538818610103 ( 2)
0.61831033924315 ( 2) 0.61894855200797 ( 2) 0.63389639932323 ( 2) 0.63480881100894 ( 2) 0.63698525034339 ( 2)
0.67886357619745 ( 2) 0.68325244000339 ( 2) 0.75638614817881 ( 2) 0.75745722311601 ( 2) 0.82161646959771 ( 2)
0.92201376113948 ( 2) 0.98455089264787 ( 2) 0.98468688973278 ( 2) 1.01721143371678 ( 2) 1.01778243972275 ( 2)
1.19559448686781 ( 2) 1.32033135104656 ( 2) 1.32175612476556 ( 2) 1.47246800149637 ( 2) 1.47312441361493 ( 2)
1.48573327678144 ( 2) 1.48673373305796 ( 2) 1.52583503659726 ( 2) 1.66340941889701 ( 2) 1.66434543208265 ( 2)
1.68305757276943 ( 2) 1.99128262601425 ( 2) 1.99405394098767 ( 2) 2.00507423191293 ( 2) 2.00643391158823 ( 2)
2.23720017057984 ( 2) 2.96761200756551 ( 2) 3.86994566085372 ( 2) 3.87002312971009 ( 2) 4.03165192324828 ( 2)
4.03197238122657 ( 2) 4.26133522183310 ( 2) 4.26149442194385 ( 2) 4.35237329819399 ( 2) 4.68664685801378 ( 2)
6.91601218905285 ( 2) 7.39252180916936 ( 2) 7.61998005503501 ( 2) 21.10496588735050 ( 2)
In the final output, the molecular spinors are generated from the inclusion of spin-orbit coupling in SCF step. The orbital degeneracies showing AREP calculation are broken in SOREP. (See AREP calculation below)
Note: Compared to all-electron calculation, only small number of occupied molecular spinors are listed in the above example. Here, only four occupied molecular spinors are shown. Because only eight electrons (7 electrons in iodine and 1 electron in hydorgen) are described. 46 electrons in iodine are omitted and substituted as core potentials.
AREP calculation¶
One-component scalar relativistic effective core potential (AREP) calculation is obtained from the omitting of the SO parameters in SOREP. (HI_AREP.mol)
INTGRL
HI MOLECULE
I:Christiansen RECP, H:Aug-cc-pVTZ
C 2 2 Y Z A
53. 1
I 1.59900000 0.00000000 0.00000000
LARGE 4 1 1 1 1
F 7 4 0
8.9655217 -0.0054740 0.0000000 0.0000000 0.0000000
4.5610628 0.0250170 0.0000000 0.0000000 0.0000000
1.8188811 -0.8900750 0.0000000 0.0000000 0.0000000
1.4925532 1.3195220 0.0000000 0.0000000 0.0000000
0.2875149 0.0000000 1.0000000 0.0000000 0.0000000
0.0824299 0.0000000 0.0000000 1.0000000 0.0000000
0.0237922 0.0000000 0.0000000 0.0000000 1.0000000
F 7 4 0
4.8262036 0.0122770 0.0000000 0.0000000 0.0000000
2.2639587 -0.0457030 0.0000000 0.0000000 0.0000000
1.1561771 0.2251760 0.0000000 0.0000000 0.0000000
0.5506509 -0.2514460 0.0000000 0.0000000 0.0000000
0.2444091 0.0000000 1.0000000 0.0000000 0.0000000
0.0908574 0.0000000 0.0000000 1.0000000 0.0000000
0.0299745 0.0000000 0.0000000 0.0000000 1.0000000
F 3 3 0
0.4320000 1.0000000 0.0000000 0.0000000
0.2200000 0.0000000 1.0000000 0.0000000
0.1000000 0.0000000 0.0000000 1.0000000
F 2 2 0
0.4265000 1.0000000 0.0000000
0.1700000 0.0000000 1.0000000
ECP 46 4 0
4
2 .922500 -1.447005
2 2.569100 -14.188832
2 7.908600 -43.263306
1 25.061100 -27.740856
6
2 1.503600 -124.037542
2 1.874600 235.545458
2 2.682800 -261.475363
2 3.446600 144.184313
1 1.124200 31.003269
0 11.458300 6.512373
6
2 1.245400 -95.368794
2 1.582600 188.963297
2 2.242900 -221.153567
2 2.930100 104.680452
1 .950300 30.809252
0 12.782000 5.414640
6
2 .668500 -50.340552
2 .828000 102.276429
2 1.115700 -133.296812
2 1.419000 75.010821
1 .503000 19.150171
0 4.557600 8.099959
1. 1
H 0.00000000 0.00000000 0.00000000
LARGE BASIS aug-cc-pVTZ
FINISH
After SCF step, the following molecular orbitals are obtained
* Fermion symmetry E1
* Closed shell, f = 1.0000
-0.91858300709907 ( 2) -0.53332424176610 ( 2) -0.38664035068657 ( 4)
* Virtual eigenvalues, f = 0.0000
0.03415914639101 ( 2) 0.05878598572499 ( 2) 0.08511594399606 ( 2) 0.08655831374568 ( 4) 0.13616239596081 ( 2)
0.20167198225135 ( 4) 0.23444552560595 ( 4) 0.26659777181880 ( 2) 0.33379422568499 ( 2) 0.34298998830327 ( 4)
0.46036400731232 ( 2) 0.49614437446042 ( 4) 0.51225813066935 ( 2) 0.61491923213700 ( 4) 0.61871900761802 ( 4)
0.63458123096312 ( 4) 0.63671447698655 ( 2) 0.68126113881102 ( 4) 0.75708271906160 ( 4) 0.82156075161775 ( 2)
0.92185115859998 ( 2) 0.98434317399476 ( 4) 1.01698231678790 ( 4) 1.19528790938055 ( 2) 1.32084962430606 ( 4)
1.47297468375170 ( 4) 1.48649707416567 ( 4) 1.52558291015577 ( 2) 1.66381720482403 ( 4) 1.68291895964979 ( 2)
1.99293721990332 ( 4) 2.00580508554321 ( 4) 2.23700102551750 ( 2) 2.96678284298137 ( 2) 3.86917720594751 ( 4)
4.03098540560673 ( 4) 4.26054689341582 ( 4) 4.35208715121292 ( 2) 4.68579647949884 ( 2) 7.21075466518969 ( 4)
7.50571888682965 ( 2) 21.10478953048176 ( 2)
Compared to molecular spinors from SOREP calculation, spin-orbit coupling neglected in AREP molecular orbitals. As a result, some degenercies in molecular orbitals appear in spin-free (AREP) calculation.
