Effects of Three Body Transformed Hamiltonian

Published Date: 16 Jan 2018

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-VUMRCCSDτ 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-MRCCSD 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 D_2h. 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 ²Π_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 ²Π_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 ²Σ_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 ²Σ_g⁺ is significant. In ²Π_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 ²Σ_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  0.3 or more.

The next test case is Cl₂ molecule, the IPs of which are presented in Table 6.2. The first ²Σ_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 ²Π_u state, the contribution is 0.167 eV(3.851 kcal/mol) for cc-pVDZ basis. In ²Σ_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.

Table 6.1 : Contribution of the diagrams for three-body transformed Hamiltonian of 3h2p-3h2p block of EIP-MRCCSDτ 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-MRCCSDτ matrix (Fig.3.3, Chap. 3) to inner valence main and satellite vertical ionization potentials ( in eV) of F₂ and Cl₂

^cRef.[8]

Table 6.2 continued

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

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[5] EMSL Basis Set Library (www.emsl.pnl.gov/forms/basisform.html).

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