*3.1.1 [Ca(THEEN)(PIC)]<sup>+</sup> (1)*

The coordination number of Ca(II) ion is eight with distorted cube geometry in the optimized geometry of cationic complex (**1**) (**Figure 1**). THEEN is interacting with Ca(II) ion through all the six potential donor atoms. The seventh and eighth coordination sites of Ca(II) are occupied by picrate anion through phenolic oxygen


#### **Table 3.**

*Comparison of calculated and experimental torsion angles (°) of ligand in the complexes (1–3).*

consistency with each other (**Table 3**). The HOMO-LUMO analysis has indicated that there is maximum distribution of HOMO over the carbon atoms and to a lesser extent on the oxygen of the coordinated picrate. LUMO is mainly distributed or concentrated on all the atoms of coordinated picrate except p-nitro group. Neither HOMO nor LUMO distribution is found either on calcium ion or on any ligand atom. The HOMO-LUMO gap (ΔE) is found to be 0.852 eV (**Figure S1c**).

*Quantum Computational Chemistry: Modeling and Calculation of S-Block Metal Ion Complexes*

*DOI: http://dx.doi.org/10.5772/intechopen.90531*

*(a) Optimized geometric structure of [Ca(THEEN)(PIC)]<sup>+</sup> (1) (b) distorted cube geometry.*

Ca(II) is eight coordinated in monomeric cationic complex with a distorted square-antiprismatic geometry in complex (**2**) as is observed in crystal structure of [Ca(THPEN)(H2O)2] (PIC)2. H2O (**Figure 2**). THPEN is acting as hexadentate ligand towards the metal ion. Two remaining sites around the metal ion are occupied by two water molecules. The observed and calculated positions of calcium and donor atoms are in agreement. All strain energy minimized structures reproduced the observed X-ray structures with almost no deviation in M-L bond length and torsion angle of the ligand (**Table 3**). The maximum tolerance of L-M-L bond angle is 15.8° (**Tables 1** and **Table S1**, **Figure S2a,b**). Complex 2 is displaying the main distribution of HOMO as well as LUMO only on water molecules. There is slight distribution of HOMO and LUMO on hydroxyl oxygen of THPEN ligand also with

Ba(II) is ten-coordinate in its monomeric complex (**3**) (**Figure 3**). The ligand THPEN coordinates through both its nitrogen atoms and all the four hydroxyl oxygen. The two picrate ions are also directly coordinated to Ba2+ ion through the phenolic oxygen and one oxygen of the o-nitro group. Since both the picrates are directly interacting with the cation, the complex is termed as tight ion-paired complex as is found in the crystallographically determined complex. The observed and calculated positions of barium and donor atoms are in agreement. There is negligible deviation found in bond length, bond angle (0.11°) and torsion angle of ligand THPEN for calculated title complex (**3**) and experimental Ba(THPEN)(PIC)2

*2+ (2)*

HOMO-LUMO gap (HLG) of 0.419 eV (**Figure S2c**).

*3.1.2 [Ca(THPEN)(H2O)2]*

**Figure 1.**

*3.1.3 Ba(THPEN)(PIC)2 (3)*

**17**


#### **Table 4.**

*Comparison of experimental and calculated and torsion angles (°) of ligand in the complexes (4–6).*

and one of the o-nitro oxygen. The observed and calculated positions of calcium and donor atoms are in agreement. A comparison of bond lengths and bond angles provided a maximum tolerance of 0.27 Å and 16.33°Å, respectively (**Table 1** and **Table S1**; **Figure S1a,b**) of computed title complex (**1**) and crystallographically determined complex [Ca(THEEN)(PIC)](PIC). The torsion angles of the ligand THEEN in theoretically determined and experimental complex are also in well

*Quantum Computational Chemistry: Modeling and Calculation of S-Block Metal Ion Complexes DOI: http://dx.doi.org/10.5772/intechopen.90531*

**Figure 1.** *(a) Optimized geometric structure of [Ca(THEEN)(PIC)]<sup>+</sup> (1) (b) distorted cube geometry.*

consistency with each other (**Table 3**). The HOMO-LUMO analysis has indicated that there is maximum distribution of HOMO over the carbon atoms and to a lesser extent on the oxygen of the coordinated picrate. LUMO is mainly distributed or concentrated on all the atoms of coordinated picrate except p-nitro group. Neither HOMO nor LUMO distribution is found either on calcium ion or on any ligand atom. The HOMO-LUMO gap (ΔE) is found to be 0.852 eV (**Figure S1c**).

#### *3.1.2 [Ca(THPEN)(H2O)2] 2+ (2)*

Ca(II) is eight coordinated in monomeric cationic complex with a distorted square-antiprismatic geometry in complex (**2**) as is observed in crystal structure of [Ca(THPEN)(H2O)2] (PIC)2. H2O (**Figure 2**). THPEN is acting as hexadentate ligand towards the metal ion. Two remaining sites around the metal ion are occupied by two water molecules. The observed and calculated positions of calcium and donor atoms are in agreement. All strain energy minimized structures reproduced the observed X-ray structures with almost no deviation in M-L bond length and torsion angle of the ligand (**Table 3**). The maximum tolerance of L-M-L bond angle is 15.8° (**Tables 1** and **Table S1**, **Figure S2a,b**). Complex 2 is displaying the main distribution of HOMO as well as LUMO only on water molecules. There is slight distribution of HOMO and LUMO on hydroxyl oxygen of THPEN ligand also with HOMO-LUMO gap (HLG) of 0.419 eV (**Figure S2c**).
