Full scope application of POLPRP to an osmium carbonyl complex¶
In this second section we describe a toolchain how to arrive at physically meaningful spectra suitable for comparison to experiment and publication. This toolchain emerged over the years of application of propagator code and has proven to be useful. Shortly, we will combine the individual small helpers to a combined postprocessing module written in Python3 bringing about a lot of simplification.
The excitation spectrum of the osmium complex exhibits sizeable differences between a scalar relativistic and a four-component treatment. By this we extract the effect of pure spin-orbit coupling on the spectrum.
Therefore two individual calculations once with the .SPINFREE and the .X2Cmmf Hamiltonian are necessary. Since the postprocessing steps are identical for both pathways we do not need to repeat it. The molecule and X2Cmmf input read as
INTGRL H2 Os (CO) 4 complex, C2v symmetry cc-pVTZ basis C 4 A 76. 1 Os 0.00000000 0.00000000 0.00000000 LARGE BASIS dyall.v3z 8. 4 O 2.41214315 0.00000000 -1.98152075 O -2.41214315 0.00000000 -1.98152075 O -0.00000000 -3.03655487 0.59571453 O -0.00000000 3.03655487 0.59571453 LARGE BASIS cc-pVTZ 6. 4 C -0.00000000 -1.93462292 0.31819191 C -0.00000000 1.93462292 0.31819191 C 1.51252482 0.00000000 -1.28284746 C -1.51252482 0.00000000 -1.28284746 LARGE BASIS cc-pVTZ 1. 2 H 1.10331142 0.00000000 1.25671302 H -1.10331142 0.00000000 1.25671302 LARGE BASIS cc-pVTZ FINISH
**DIRAC .WAVE FUNCTION .ANALYZE **GENERAL **HAMILTONIAN .X2Cmmf **INTEGRALS *READIN .UNCONT **WAVE FUNCTION .SCF .POLPRP *SCF .CLOSED SHELL 134 **ANALYZE .MULPOP *MULPOP .VECPOP all .LABDEF 28 C_d 105,106,107,108,116,117,154,155,163,164,165 C_d 166,200,201,207,208,44,45,46,47,57,58,59 C_d 60 C_f 109,110,111,112,113,114,118,119,120,121,156 C_f 157,158,159,167,168,169,170,171,172,202,203 C_f 204,205,209,210,211,212,48,49,50,51,52,53 C_f 61,62,63,64,65,66 C_p 103,104,115,153,161,162,199,206,42,43,55 C_p 56 C_s 102,160,41,54 H_d 123,124,176,177,178,179,214,215,70,71,72 H_d 73 H_p 122,174,175,213,68,69 H_s 173,67 O_d 136,137,138,139,147,148,18,186,187,19,193 O_d 194,20,21,31,32,33,34,83,84,92,93,94,95 O_f 100,101,140,141,142,143,144,145,149,150,151 O_f 152,188,189,190,191,195,196,197,198,22,23 O_f 24,25,26,27,35,36,37,38,39,40,85,86,87,88 O_f 96,97,98,99 O_p 134,135,146,16,17,185,192,29,30,82,90,91 O_s 133,15,28,89 Os_d 126,180,3,4,5,75 Os_f 127,128,129,181,6,7,76,77,78,8 Os_g 10,11,12,13,130,131,132,14,182,183,184,79 Os_g 80,81,9 Os_p 125,2,74 Os_s 1 **MOLTRA .ACTIVE energy -0.80 1.73 0.001 .PRPTRA *PRPTRA .OPERATOR XDIPLEN .OPERATOR YDIPLEN .OPERATOR ZDIPLEN **POLPRP .DOTRMO .PRINT 1 **DAVIDSON .DVROOTS 25 .DVMAXSP 400 .DVMAXIT 12 .DVCONV 1.0E-05 *END OF
As you can see in the .mol file the complex has C2v symmetry and we use basis sets from the library shipped with DIRAC. In the input file a large number of labdef labels are visible. This is necessary later on if we want to analyze the eigenstate composition in terms of atomic orbital contributions. Hereby the grouping occurs according to the angular momentum of the atomic basis functions. A further distinction is not made and would lead to an excess of information in larger systems. In order to generate the LABDEF labels we use the utility
that automatically reads the:
GETLAB: SO-labels ----------------- * Large components: 215 1 L A1 Os s 2 L A1 Os pz 3 L A1 Os dxx 4 L A1 Os dyy 5 L A1 Os dzz 6 L A1 Os fxxz 7 L A1 Os fyyz 8 L A1 Os fzzz 9 L A1 Os g400 10 L A1 Os g220 11 L A1 Os g202 12 L A1 Os g040 . . . . . . . . .
section. A little disadvantage here is that the ordered LABDEF section should be available already for the Mulliken population analysis for a proper labeling of the atomic contributions. So we recommend to run DIRAC with a preliminary input just producing the GETLAB output. Application of labdefmaker produces the file “labdef” that can be included in the production input afterwards. A manual sorting and grouping of labels is out of scope for larger systems. We perform a strict ADC-2 calculation where the satellite block just consists of the diagonal of the orbital energies (see publications). Before we include the transition moments in our analysis we want to get an overview of the final state composition. Hereby the information of a Mulliken analysis, the active orbital list and the ADCSTATE.XX files are required and their information combined. This is done by the two helper programs
spimaker and excmaker
to be excuted in series. spimaker constructs an intermediate list of spinors relating the molecular and atomic basis and excmaker combines this list with the state analysis obtained by the POLPRP calculation. The resulting ‘xstates’ file then serves as the basis for the gnuplot drawing utility that generates a composition analysis of the hole and the particle space:
This graph shows sizeable osmium contributions in the hole and particle space being responsible for SO coupling effects in the excitation spectrum (see below).
In the next step we want to utilize the physical information provided by the transition moments. For this purpose we multiply the pole strength of the impulse peak with the oscillator strength which gives us a modulated spectrum according to the transition probability. This multiplication was done with a simple spreadsheet tool because the number of states is reasonably small. afterwards the new stick spectrum is convoluted with a Lorentzian envelope in order to account for the spectral width. This final step is performed by the
tool. You give the number of peaks, the desired number of graphic points and the spectral width in meV. The resulting graph file can again be plotted by gnuplot and results in the following simulated spectrum:
Upwards we plot the X2Cmmf spectrum, downwards the SPINFREE spectrum which exhibits the pure effect of spin-orbit coupling on the excitation spectrum. Soon an integrated python tool will come combining all the individual tasks from above.