Effects of Three Body Transformed Hamiltonian

Effects of Three Body Transformed Hamiltonian CHAPTER – 6 CONTRIBUTION OF THREE BODY TRANSFORMED HAMILTONIAN () THROUGH FULL CONNECTED TRIPLE EXCITATION COUPLED CLUSTER OPERATORS TO VALENCE IONIZATION POTENTIALS OF F2 AND Cl2 COMPUTED VIA EIP-VUMRCCSDÏ„ SCHEME 6.1 Introduction In this work, the effects of three body transformed Hamiltonian through full connected triples is studied on F2 and Cl2. To see the role of [1] in terms of magnitude, two kinds of computations named scheme–A and scheme–B are done. Scheme – A includes along with the other usual diagrams for EIP-MRCCSDà ¯Ã‚ Ã‚ ´ matrix [1-4]. In scheme–B, the term is totally absent. In this calculations, two chemically interesting and challenging molecules F2, and Cl2 ( because Fluorine atom is most electronegative, and Cl2 contains as many as 34 electrons ) are considered . The basis sets cc-pVDZ and cc-pVTZ (spherical Gaussians) [5] and experimental equilibrium geometry are used in these computations. The basis sets were collected from : http://www.emsl.pnl.gov:2080/forms/basisform.html. Table 6.1 and 6.2 contain all results. 6.2. Results and Discussion Both the molecules are linear and centro-symmetric and hence their point group is D∞h out of which we consider only the largest abelian sub-group D2h. All outer-valence main vertical IPs are presented in Table 6.1. Since independent particle model is valid here, some Koopmans’ configurations appear while going from one basis to another. Naturally, there is same one-to-one correspondence between scheme-A and scheme-B also. For single bonded molecule F2, the contribution of is small. For 2ÃŽ  u state , the differences in the case of cc-pVDZ and cc-pVTZ are 0.026 eV(.600 kcal/mol) and 0.029 eV(0.669 kcal/mol) respectively. For 2ÃŽ  u state of Cl2, the difference (cc-pVDZ) 0.040 eV(0.922 kcal/mol) is significant in view of that we are considering here the correlation dynamics of outer valence electrons. Experimental IPs are presented in the Tables with a view to realizing the reliability of our theoretical results only. Too accurate comparison is not possible here because of the restraint of our starting basis sets. For that, approaching towards basis set saturation as much as possible is necessary. Since scheme-A (as it includes ) gives more accurate IP. From now on or unless otherwise explicitly mentioned, it will be assumed that a theoretical IP value relates to scheme-A only. In the inner valence region, the sizes of the basis sets sometimes influence the IP-profile of the same molecule in higher energy regions considerably. The single bonded F2 molecule is studied first, the IPs of which are presented in Table 6.2. The first 2ÃŽ £g+ satellite of F2 shows that maximum contribution of is by an amount 1.117 eV(25.758 kcal/mol) for cc-pVDZ basis and 0.910 eV(20.985 kcal/mol) for cc-pVTZ basis. The difference (cc-pVTZ) 1.117 eV(25.758 kcal/mol) for 2ÃŽ £g+ is significant. In 2ÃŽ  u state, the maximum contributions are 0.773 eV(17.826 kcal/mol) for cc-pVDZ basis and 0.911 eV(21.001 kcal/mol) for cc-pVTZ basis respectively. In 2ÃŽ £u+ state, the contributions are 0.256 eV(5.903 kcal/mol) for cc-pVDZ basis and 0.267 eV(6.157 kcal/mol) for cc-pVTZ basis. Other satellites do not have the basis-to-basis correspondence. However, scheme-A to scheme-B correspondence is retained, which is based on the dominant configurations with expansion co-efficient à ¯Ã‚ Ã‚ ¾ 0 .3 or more. The next test case is Cl2 molecule, the IPs of which are presented in Table 6.2. The first 2ÃŽ £g+ satellite of Cl2 shows that maximum contribution of is by an amount 0.223 eV(5.142 kcal/mol) for cc-pVDZ basis and 1.305 eV(30.094 kcal/mol) for cc-pVTZ basis, respectively. In 2ÃŽ  u state, the contribution is 0.167 eV(3.851 kcal/mol) for cc-pVDZ basis. In 2ÃŽ £u+ state, the maximum contribution is 1.269 eV(29.263 kcal/mol) for cc-pVDZ basis, no such value for cc-pVTZ basis is found. The IPs onwards are arranged on the basis of dominant configurations. If dominant configurations differ from basis-to-basis substantially, they are put in different rows in the tables. Thus, some IP values which appear in case of cc-pVDZ may not appear at all in case of cc-pVTZ, and vice versa. Similarly, an IP for a basis appearing in scheme-A may be absent in scheme-B, and vice versa. While in the first case it is due to basis-set effect, in the second case it is due to . If for an IP, scheme-A to scheme-B correspondence is observed, only then it is possible to make a comment on the amount by which the IP has been shifted to what extent in scheme-B relative to Scheme-A. In other words, a quantitative picture of the effect of can be made. For quite a few IPs, the contributions of are significant. The values mentioned in parenthesis are relative intensities along with IPs. Molecule States Configurations Basis :cc-pVDZ Basis: cc-pVTZ Expt Scheme-A Scheme-B à ¢Ã¢â€š ¬Ã…’Ãâ€"â‚ ¬DiffÃâ€"â‚ ¬(eV) Scheme-A Scheme-B Ãâ€"â‚ ¬Diffà ¢Ã¢â€š ¬Ã…’à ¢Ã¢â€š ¬Ã…’à ¢Ã¢â€š ¬Ã…’Ãâ€"â‚ ¬ (eV) F2 2ÃŽ  g 1Ï€g -1 15.124 (0.933) 15.136 (0.932) 0.012 15.415 (0.928) 15.429 (0.927) 0.014 15.87a 15.70b 2ÃŽ  u 1Ï€u -1 18.190 (0.873) 18.216 (0.867) 0.026 18.492 (0.874) 18.521 (0.869) 0.029 18.8a 18.4b 2ÃŽ £+g 3ÏÆ'g -1 20.671 (0.956) 20.652 (0.954) 0.019 20.926 (0.948) 20.908 (0.947) 0.018 21.1a Cl2 2ÃŽ  g 2Ï€g -1 11.138 (0.954) 11.136 (0.954) 0.002 11.318 (0.948) 11.315 (0.948) 0.003 11.49b 2ÃŽ  u 2Ï€u -1 14.037 (0.059) 13.997 (0.916) 0.040 14.162 (0.911) 14.160 (0.911) 0.002 14.0b 2ÃŽ £+g 5ÏÆ'g -1 15.687 (0.952) 17.467 (0.018) 17.446 (0.018) 0.021 15.806 (0.942) 15.792 (0.942) 19.698 (0.008) 0.014 15.8b Table 6.1 : Contribution of the diagrams for three-body transformed Hamiltonian of 3h2p-3h2p block of EIP-MRCCSDÏ„ matrix (Fig.3.3, Chap. 3 ) to vertical ionization potentials ( in eV) of outer valence region (relative intensities have been put in the parentheses ) 1 eV = 23 .06035 kcal/mol aRef.[6] bRef.[7] Table 6.2 : Contribution of the diagrams for three-body transformed Hamiltonian of 3h2p-3h2p block of EIP-MRCCSDÏ„ matrix (Fig.3.3, Chap. 3) to inner valence main and satellite vertical ionization potentials ( in eV) of F2 and Cl2 Mol States Basis : cc-pVDZ Basis : cc-pVTZ Expt. Scheme-A Scheme- B à Ã¢â‚¬   Diff à Ã¢â‚¬   Scheme- A Scheme- B I Diff I F2 2ÃŽ £+g 29.680(0.016) 40.785(0.043) 42.672(0.436) 50.701(0.056) 54.836(0.101) 28.863(0.015) 40.835(0.015) 42.653(0.047) 50.600(0.060) 53.719(0.056) 0.817 0.050 0.019 0.101 1.117 41.916(0.659) 42.800(0.157) 42.889(0.048) 50.482(0.190) 41.961(0.617) 42.910(0.149) 42.385(0.059) 50.367(0.032) 0.045 0.910 0.404 0.115 41.75c 2ÃŽ  u 24.524(0.028) 32.416(0.065) 33.151(0.014) 33.671(0.021) 45.999(0.011) 51.633(0.015) 24.461(0.032) 31.643(0.050) 44.431(0.020) 50.239(0.020) 0.063 0.773 25.014(0.026) 32.936(0.039) 24.940(0.029) 32.025(0.052) 0.074 0.911 2ÃŽ  g 41.063(0.021) 42.117(0.013) 47.846(0.022) 40.314(0.067) 0.251 42.491(0.011) 48.659(0.013) 40.691(0.047) 2ÃŽ £+u 29.110(0.015) 29.203(0.040) 32.669(0.017) 37.491(0.675) 28.857(0.012) 32.413(0.017) 37.480(0.743) 0.253 0.256 0.011 29.690(0.030) 29.762(0.038) 33.195(0.022) 29.432(0.039) 32.928(0.023) 37.289(0.667) 0.330 0.267 37.47c cRef.[8] Table 6.2 continued Mol States Basis : cc-pVDZ Basis : cc-pVTZ Expt. Scheme-A Scheme- B à Ã¢â‚¬   Diff à Ã¢â‚¬   Scheme- A Scheme- B I Diff I Cl2 2ÃŽ £+g 22.222(0.027) 25.085(0.013) 28.214(0.650) 29.962(0.020) 37.302(0.038) 22.137(0.026) 25.041(0.012) 28.202(0.635) 29.739(0.029) 37.237(0.038) 0.085 0.044 0.012 0.223 0.065 22.443(0.034) 26.423(0.019) 26.655(0.073) 27.479(0.164) 29.939(0.032) 34.358(0.021) 22.356(0.033) 26.637(0.019) 26.684(0.059) 27.477(0.152) 31.244(0.048) 35.660(0.004) 35.631(0.048) 0.087 0.214 0.029 0.002 1.305 2ÃŽ  u 23.119(0.083) 22.974(0.059) 31.017(0.017) 22.967(0.059) 27.466(0.002) 29.075(0.002) 29.514(0.003) 30.663(0.002) 31.000(0.018) 31.258(0.009) 0.007 0.017 2ÃŽ  g 25.579(0.029) 25.412(0.023) 0.167 22.607(0.002) 25.606(0.015) 31.139(0.002) 33.351(0.014) 33.470(0.012) 34.804(0.010) 25.534(0.011) 26.019(0.006) 31.076(0.002) 33.308(0.008) 33.404(0.011) 34.099(0.003) 34.804(0.003) 34.844(0.011) 36.413(0.007) 37.059(0.002) 37.728(0.002) 38.080(0.002) 38.619(0.001) 48.004(0.001) 48.067(0.001) 0.072 0.063 0.043 0.066 0.040 2ÃŽ £+u 22.258(0.297) 24.399(0.279) 26.268(0.185) 38.132(0.025) 41.469(0.025) 22.222(0.275) 24.339(0.289) 26.220(0.184) 38.082(0.023) 40.200(0.018) 0.036 0.000 0.048 0.050 1.269 22.404(0.424) 24.413(0.111) 26.214(0.071) 31.646(0.033) 34.124(0.021) 36.911(0.042) 37.325(0.013) 22.376(0.341) 24.413(0.274) 31.587(0.032) 34.076(0.022) 34.454(0.029) 36.803(0.045) 38.207(0.027) 0.028 0.000 0.059 0.048 0.108 6.3 Conclusion The present calculations show that for F2 and Cl2, the above-said effect sometimes is considerably high and may even be more than 21 kcal/mol (F2 : cc-pVTZ) and 29 kcal/mol (Cl2 : cc-pVDZ) which are much presumably due to high electronegativity of F and Cl atoms. This suggests that inclusion of is essential in high accuracy EIP-VUMRCC IP calculations. References [1] K. Adhikari, S. Chattopadhyay, R. K. Nath, B. K. De, D. Sinha, Chem. Phys. Lett.  474 (2009) 199. [2] S. Chattopadhyay, A. Mitra, D. Jana, P. Ghosh and D. Sinha, Chem. Phys. Lett. 361  (2002) 298. [3] S. Chattopadhyay, A. Mitra and D. Sinha, J. Chem. Phys. 125 (2006) 244111. [4] K. Adhikari, S. Chattopadhyaya, B. K. De, A. Sharma, R. K. Nath, D. Sinha, J. Comp.  Chem. 34 (2013) 1291. [5] EMSL Basis Set Library (www.emsl.pnl.gov/forms/basisform.html). [6] G. Bieri, A. Schemelzer, L. Ã…sbrink and M. Jonsson, Chem. Phys. 49 (1980) 213. [7] A. B. cornfored, D. C. Frost, C. A. McDowell, J. L. Ragle, and I. A. Stenhouse, J.  Chem. Phys. 54 (1971) 2651. [8] P. Weightman, T. D. Thomas and D. R. Jennison, J. Chem. Phys. 78 (1983) 1652. 1