C-PCM study on the electronic and optical properties of Fe(CO) 4 B 12 N 12 complexes

Abstract

We explored solvent effect on the stability, dipole moment, polarizability and first hyperpolarizability of Fe(CO)₄B₁₂N₁₂ complexes at MPW1PW91/6-311G(d,p) level of theory. These complexes were considered in the low spin states. The self-consistent reaction field theory (SCRF) based on conductor-like polarizable continuum model (PCM) was employed to illustration of the solvent influences. The relations between the parameters with solvent polarity functions (McRae and Suppan functions) were given. Also, relations of the wavenumbers values of the stretching of carbonyl ligands with the Kirkwood–Bauer–Magat equation (KBM) were provided.

Keywords

solvent effect first hyperpolarizabilit solvent polarity functions Kirkwood–Bauer–Magat equation (KBM)

1 Introduction

Isolobality of Fe(CO)₄ organometallic fragment with CH₃⁺ organic fragment leads to preparation of the various compounds and structure and bonding of these compounds have been illustrated [1 –3]. Fe(CO)₄ fragment interacted with various ligands [4 –8]. Many researches have been reported about the metal–π ligand complexes in organometallic chemistry [9].

The BN nano-cages and carbon bucky balls are iso-structural. the chemical vapor deposition (CVD) technique is useful for preparation of these molecules [10]. These molecules are used in therapeutic owing to the biocompatibility [11]. These compounds are challenger for carbon based fullerenes in the subsequent group electronics. B₁₂N₁₂ nano-cluster has been synthesized by laser desorption time-off light mass spectrometry [12, 13]. Serval quantum mechanical (QM) calculations of interactions between B₁₂N₁₂ nano-cage and different molecules have been published [14 –19].

Solvents plays remarkable role in chemistry and alter the molecular activities by the interactions of solute and solvent molecules [20 –22]. Various computational investigations have been are useful to illustration the solvent effect in the electronic structure [23, 24]. Various researches have reported about of solvent influence on the spectroscopic, electronic and structural properties of organometallic and inorganic compounds [25 –46].

In this research, we illustrated the solvent polarity influence on the electronic and optical properties of Fe(CO)₄B₁₂N₁₂ complexes at mPW1PW91/6-311G(d,p) level of theory.

2 Computational methods

The Gaussian 09 software package [47] was employed for our calculations in this study. The standard 6-311G (d, p) basis set is considered for all elements [48, 49]. All calculations were done by the parameter hybrid functional with adapted Perdew-Wang exchange and correlation (mPW1PW91) [50]. This functional provides better results than B3LYP [51 –54]. The optimized structures correspond to the local minima on the potential energy surfaces are confirmed by vibrational analysis.

The first order hyperpolarizabilities values of optimized geometries were calculated at the identical level of theory for optimization. Total static first hyperpolarizability β was calculated from the following equations:

$β_{tot} = \sqrt{β_{x}^{2} + β_{y}^{2} + β_{z}^{2}}$

upon computing the individual static components:

$β_{i} = β_{iii} + \frac{1}{3} \sum_{i \neq j} (β_{ijj} + β_{jij} + β_{jji})$

In the basis of the Kleinman symmetry [55]:

$β_{xyy} = β_{yxy} = β_{yyx}; β_{yyz} = β_{yzy} = β_{zyy}, \dots$

Therefore:

$β_{tot} = \sqrt{{(β_{xxx} + β_{xyy} + β_{xzz})}^{2} + {(β_{yyy} + β_{yzz} + β_{yxx})}^{2} + {(β_{zzz} zxx + β_{zyy})}^{2}}$

Solvent effects were studied with self-consistent reaction field (SCRF) method, using the conductor-like polarizable continuum model (CPCM) [56, 57].

3 Results and discussion

3.1 Energetic aspects

Figure 1 shows the two modes interaction of Fe(CO)₄ and B₁₂N₁₂ nano-cage. Table 1 reports the energy, relative energy and solvation energy values of these complexes at the mPW1PW91/6-311G(d,p) level of theory. These complexes are considered in the low spin states. Selected solvents in this study are acetone, ethanol, methanol, acetonitrile (MeCN), dimethylsulfoxide (DMSO) and water. Energy values reveal that I-structure is more stable than II-structure in gas and solution phases. Also, energy values show that more stability of these complexes in solution phase than gas phase. This stability enhances in more polar solvents. So, the stabilization of reacting molecule enhances with electrostatic interaction with solvent.

Fig. 1

(a) Front view and (b) 3-D structures of two modes coordination of Fe(CO)₄ fragment to B₁₂N₁₂nano-cage.

Table 1

Energy (E, a.u), relative energy (ΔE, kcal/mol) and solvation energy (ΔE_solv, kcal/mol) of two isomers of Fe(CO)₄B₁₂N₁₂ complexes. ɛis dielectric constant of solvents

Phase	ɛ	E(I)	E(II)	ΔE	ΔE_sol(I)	ΔE_sol(II)
Gas	–	–2673.23	–2673.24	3.80	–	–
Acetone	20.49	–2673.24	–2673.25	4.15	–5.37	–5.71
Ethanol	24.30	–2673.24	–2673.25	4.15	–5.42	–5.77
Methanol	32.63	–2673.24	–2673.25	4.16	–5.48	–5.83
MeCN	35.69	–2673.24	–2673.25	4.16	–5.50	–5.85
DMSO	46.83	–2673.24	–2673.25	4.16	–5.54	–5.90
Water	78.54	–2673.24	–2673.25	4.16	–5.60	–5.96

On the other hand, larger ΔE values are observed in solution phase than gas phase. There is larger ΔE values with increasing of solvent polarity. ΔE values and dielectric constant of solvents are fitted in a quadratic equation:

$Δ E = - 7 \times 1 0^{- 6} ɛ^{2} + 0.00 1 ɛ + 4.1285; R^{2} = 0.9878$

The solvation energies values are given in Table 1. There are smaller ΔE_sol values with increasing of dielectric constant of solvents. Also, solvation is more significance for II-structure than I-structure. ΔE_sol values and dielectric constant of solvents are fitted in a quadratic equation:

$Δ E_{sol} (I - structure) = 9 \times 1 0^{- 5} ɛ^{2} - 0.0 127 ɛ - 5.1567; R^{2} = 0.9872$ $Δ E_{sol} (II - structure) = 1 \times 1 0^{- 4} ɛ^{2} - 0.0 137 ɛ - 5.4822; R^{2} = 0.9872$

3.2 Dipole moment

Dipole moment values of the complexes are computed in gas and various solvents (Table 2). It can be observed larger polarity II-structure than I-structure. Computed dipole moment values are larger in solution phase than gas phase. These values enhance with increasing of dielectric constant values.

Table 2
Dipole moment (μ, Debye) and isotropic polarizability (α_iso,a.u) values of two isomers of Fe(CO)₄B₁₂N₁₂ complexes

Phase μ (I) μ(II) α_iso(I) α_iso(II)

Gas 1.52 1.92 234.81 234.51

Acetone 3.07 3.60 328.68 328.01

Ethanol 3.09 3.62 329.87 329.20

Methanol 3.12 3.65 331.23 330.55

MeCN 3.13 3.66 331.61 330.92

DMSO 3.15 3.68 332.56 331.87

Water 3.17 3.70 333.80 333.10

Phase	μ (I)	μ(II)	α_iso(I)	α_iso(II)
Gas	1.52	1.92	234.81	234.51
Acetone	3.07	3.60	328.68	328.01
Ethanol	3.09	3.62	329.87	329.20
Methanol	3.12	3.65	331.23	330.55
MeCN	3.13	3.66	331.61	330.92
DMSO	3.15	3.68	332.56	331.87
Water	3.17	3.70	333.80	333.10

Dipole moment values and dielectric constant of solvent are fitted in a quadratic equation:

$μ (II) = - 4 \times 1 0^{- 5} ɛ^{2} + 0.00 58 ɛ + 3.5032; R^{2} = 0.9877$ $μ (I) = - 4 \times 1 0^{- 5} ɛ^{2} + 0.00 55 ɛ + 2.9785; R^{2} = 0.9880$

Then, we consider the McRae function (F_McRae(ɛ)) [58] and Suppan function (F_Suppan(ɛ)) [59]. These functions have the equations of:

$F_{McRae} (ɛ) = \frac{2 (ɛ - 1)}{ɛ + 2}$ $F_{Suppan} (ɛ) = \frac{2 (ɛ - 1)}{2 ɛ + 2}$

The relationship between μ and these solvent polarity functions are:

$\begin{matrix} μ (II) = 0.5404 F_{McRae} (ɛ) + 2.6636; R^{2} = 0.999 \\ μ (I) = 0.5173 F_{McRae} (ɛ) + 2.1746; R^{2} = 0.999 \\ μ (II) = 1.5292 F_{Suppan} (ɛ) + 2.2128; R^{2} = 0.9993 \\ μ (I) = 1.4639 F_{Suppan} (ɛ) + 1.7431; R^{2} = 0.9993 \end{matrix}$

As a result, there are good correlations between the dipole moment with McRae and Suppan functions in the studied systems.

3.3 Polarizability

Isotropic polarizability values of the studied complexes are calculated in gas and various solvents (Table 2). The calculated values show higher isotropic polarizability II-structure than I-structure. There are larger isotropic polarizability values in solution phase than gas phase.

Isotropic polarizability values and dielectric constant of solvent and dielectric constant of solvents are fitted in a quadratic equation:

$\begin{matrix} α_{iso} (II) = - 0.00 2 ɛ^{2} + 0.2799 ɛ + 323.37; & R^{2} = 0.9875 \\ α_{iso} (I) = - 0.00 2 ɛ^{2} + 0.2813 ɛ + 324.02; & R^{2} = 0.9877 \end{matrix}$

The linear correlations between α_iso and the solvent polarity functions (F_McRae(ɛ) and F_Suppan(ɛ)) are:

$\begin{matrix} α_{iso} (II) = 26.221 F_{McRae} (ɛ) + 282.65; & R^{2} = 0.9989 \\ α_{iso} (I) = 26.341 F_{McRae} (ɛ) + 283.11; & R^{2} = 0.999 \\ α_{iso} (II) = 74.203 F_{Suppan} (ɛ) + 260.77; & R^{2} = 0.9992 \\ α_{iso} (I) = 74.541 F_{Suppan} (& epsiv;) + 261.14; & R^{2} = 0.9993 \end{matrix}$

It can be seen, there are good correlations between the isotropic polarizability values with McRae and Suppan functions in the studied systems.

3.4 Hyperpolarizability

The β_tot, β_x, β_y, β_z values of the two isomers of Fe(CO)₄(B₁₂N₁₂) complex in different solvents are given in Table 3. The β_total values of I and II isomers are 1.27×10^–30 and 1.07×10^–30 esu, respectively, in gas phase.

Table 3
Total first hyperpolarizability and its components (esu) values of two isomers of Fe(CO)₄B₁₂N₁₂ complexes

Gas Acetone Ethanol Methanol MeCN DMSO Water

I-isomer

β_XXX 201.48 440.64 444.63 449.16 450.43 453.65 457.85

β_XXY –8.95 –18.00 –18.14 –18.29 –18.33 –18.44 –18.58

β_XYY 32.01 64.98 65.54 66.18 66.36 66.81 67.41

β_YYY 16.55 15.03 14.91 14.76 14.71 14.61 14.46

β_XXZ –25.11 –42.52 –42.56 –42.84 –42.84 –42.85 –42.85

β_XYZ 18.49 48.89 49.40 49.95 50.11 50.52 51.07

β_YYZ –12.78 –35.41 –35.73 –35.90 –36.00 –36.25 –36.59

β_XZZ –115.78 –358.94 –363.11 –368.10 –369.42 –372.78 –377.18

β_YZZ –4.45 –18.82 –19.11 –20.13 –20.22 –20.46 –20.76

β_ZZZ –50.71 –163.06 –165.00 –165.73 –166.35 –167.91 –169.95

β_total 1.27×10^–30 2.44×10^–30 2.46×10^–30 2.47×10^–30 2.48×10^–30 2.49×10^–30 2.51×10^–30

10³⁰ β_total 1.27 2.44 2.46 2.47 2.48 2.49 2.51

II-isomer

β_XXX –4.1 17.45 17.16 16.82 16.46 16.72 16.12

β_XXY 0.03 –4.08 –4.10 –4.13 –4.15 –4.13 –4.18

β_XYY 46.71 –99.11 –100.04 –101.10 –102.14 –101.39 –103.12

β_YYY –0.09 –0.03 –0.03 –0.03 –0.03 –0.03 –0.03

β_XXZ –24.23 –72.79 –73.76 –74.87 –75.97 –75.18 –77.01

β_XYZ –0.08 2.05 2.07 2.09 2.11 2.09 2.13

β_YYZ 0.48 2.70 2.65 2.59 2.52 2.57 2.46

β_XZZ –138.82 398.63 402.90 407.74 412.52 409.09 416.99

β_YZZ 0.51 0.33 0.32 0.31 0.30 0.31 0.29

β_ZZZ 101.25 266.54 269.16 272.11 275.02 272.93 277.73

β_total 1.07×10^–30 3.22×10^–30 3.25×10^–30 3.28×10^–30 3.32×10^–30 3.29×10^–30 3.35×10^–30

10³⁰ β_total 1.07 3.22 3.25 3.28 3.32 3.29 3.35

	Gas	Acetone	Ethanol	Methanol	MeCN	DMSO	Water
I-isomer
β_XXX	201.48	440.64	444.63	449.16	450.43	453.65	457.85
β_XXY	–8.95	–18.00	–18.14	–18.29	–18.33	–18.44	–18.58
β_XYY	32.01	64.98	65.54	66.18	66.36	66.81	67.41
β_YYY	16.55	15.03	14.91	14.76	14.71	14.61	14.46
β_XXZ	–25.11	–42.52	–42.56	–42.84	–42.84	–42.85	–42.85
β_XYZ	18.49	48.89	49.40	49.95	50.11	50.52	51.07
β_YYZ	–12.78	–35.41	–35.73	–35.90	–36.00	–36.25	–36.59
β_XZZ	–115.78	–358.94	–363.11	–368.10	–369.42	–372.78	–377.18
β_YZZ	–4.45	–18.82	–19.11	–20.13	–20.22	–20.46	–20.76
β_ZZZ	–50.71	–163.06	–165.00	–165.73	–166.35	–167.91	–169.95
β_total	1.27×10^–30	2.44×10^–30	2.46×10^–30	2.47×10^–30	2.48×10^–30	2.49×10^–30	2.51×10^–30
10³⁰ β_total	1.27	2.44	2.46	2.47	2.48	2.49	2.51
II-isomer
β_XXX	–4.1	17.45	17.16	16.82	16.46	16.72	16.12
β_XXY	0.03	–4.08	–4.10	–4.13	–4.15	–4.13	–4.18
β_XYY	46.71	–99.11	–100.04	–101.10	–102.14	–101.39	–103.12
β_YYY	–0.09	–0.03	–0.03	–0.03	–0.03	–0.03	–0.03
β_XXZ	–24.23	–72.79	–73.76	–74.87	–75.97	–75.18	–77.01
β_XYZ	–0.08	2.05	2.07	2.09	2.11	2.09	2.13
β_YYZ	0.48	2.70	2.65	2.59	2.52	2.57	2.46
β_XZZ	–138.82	398.63	402.90	407.74	412.52	409.09	416.99
β_YZZ	0.51	0.33	0.32	0.31	0.30	0.31	0.29
β_ZZZ	101.25	266.54	269.16	272.11	275.02	272.93	277.73
β_total	1.07×10^–30	3.22×10^–30	3.25×10^–30	3.28×10^–30	3.32×10^–30	3.29×10^–30	3.35×10^–30
10³⁰ β_total	1.07	3.22	3.25	3.28	3.32	3.29	3.35

These values show larger activities NLO in solution phase than gas phase. Therefore, solvent polarity reveals a significant role on the first hyperpolarizabilities in dipolar molecules. On the other hand, β_total values of I-isomer are larger than II- isomer both gas and solution phases. Solvent induced increasing in hyperpolarizability values can be provided with a ratio enhancement factor:

$ζ = \frac{β_{tot}^{solvent}}{β_{tot}^{gas}}$

An empirical linear relationship between β_tot and Onsager function is useful to exploration the solvent effect on first hyperpolarizability [60]:

$\begin{matrix} 10^{30} \cdot β_{tot} (I) = 2.551 \frac{ɛ - 1}{2 ɛ + 1} + 1.26; R^{2} = 0.9801 \\ 10^{30} \cdot β_{tot} (II) = 4.51 \frac{ɛ - 1}{2 ɛ + 1} + 1.13; R^{2} = 0.8958 \end{matrix}$

There is good relationship between β _tot and the Onsager function for I-structure. This equation is typical for a dipolar reaction field interaction in the solvation process [60 –63]. Thus, the electronic reorganization in solution for molecule reveals an important impact on the provided first hyperpolarizabilities.

The linear correlations between β_tot and the solvent polarity functions (F_McRae(ɛ) and F_Suppan(ɛ)) are:

$\begin{matrix} 1 0^{30} β_{tot} (I) = 0.3462 F_{McRae} (ɛ) + 1.8455; R^{2} = 0.9805 \\ 1 0^{30} β_{tot} (II) = 0.6122 F_{McRae} (ɛ) + 2.1667; R^{2} = 0.8908 \\ 1 0^{30} β_{tot} (I) = 0.9788 F_{Suppan} (ɛ) + 1.5576; R^{2} = 0.979 \\ 1 0^{30} β_{tot} (II) = 1.7336 F_{Suppan} (ɛ) + 1.6549; R^{2} = 0.8922 \end{matrix}$

There are good relations between the first hyperpolarizabilities values with McRae and Suppan functions in the I-structure.

3.5 Vibrational spectrum analysis

The vibrational modes of carbonyl groups in the Fe(CO)₄B₁₂N₁₂ complexes are presented in Fig. 2. The computed wavenumbers of these vibrations are listed in Table 4. The wavenumbers of these vibrations are smaller in solution phase rather than gas phase. These values reduce in more polar solvents.

Fig. 2

Vibration modes of carbonyl ligands in Fe(CO)₄ fragment to B₁₂N₁₂nano-cage.

Table 4

Wavenumbers of the stretching of carbonyl ligands (cm^–1) of two isomers of Fe(CO)₄B₁₂N₁₂ complexes

	I				II
Phase	ν₉₀	ν₉₁	ν₉₂	ν₉₃	ν₉₀	ν₉₁	ν₉₂	ν₉₃
Gas	2120.36	2146.08	2155.34	2215.45	2129.08	2151.21	2154.56	2214.08
Acetone	2086.24	2130.10	2131.90	2211.04	2099.75	2123.44	2136.46	2208.98
Ethanol	2085.88	2129.95	2131.63	2211.00	2099.45	2123.09	2136.31	2208.94
Methanol	2085.47	2129.79	2131.39	2210.97	2099.12	2122.70	2136.14	2208.90
MeCN	2085.36	2129.74	2131.31	2210.96	2099.02	2122.60	2136.09	2208.89
DMSO	2085.08	2129.61	2131.13	2210.94	2098.79	2122.32	2135.98	2208.86
Water	2084.72	2129.44	2130.91	2210.91	2098.48	2121.97	2135.82	2208.82

Also, it can be found the larger ν₉₀ and ν₉₁ values for II-isomer than I-isomer. In contrast, the smaller ν₉₂ and ν₉₃ values for II-isomer than I-isomer.

The theoretical study of the solvent-induced ν(CO) shifts is considered by Kirkwood–Bauer–Magat equation (KBM) [64]:

$\frac{ν {(CO)}_{gas} - ν {(CO)}_{solution}}{ν {(CO)}_{gas}} = \frac{Δ ν (CO)}{Δ ν {(CO)}_{gas}} = \frac{C (ɛ - 1)}{(2 ɛ + 1)}$

In this equation, ν(CO)_gas and ν(CO)_solution are the wavenumber of stretching of carbonyl ligands in the gas phase and solution phase, respectively, ɛ is the dielectric constant of the solvent, and C is a constant depending on the dimensions and electrical properties of the solute dipole.

There are good correlations between solvent-induced stretching vibrational frequency shifts of υ(CO) with (ɛ –1)/(2ɛ+1) of the KBM equation:

I-isomer:

$\begin{matrix} \frac{Δ ν {(CO)}_{91}}{ν {(CO)}_{gas, 91}} = 0.0271 \frac{(ɛ - 1)}{(2 ɛ + 1)} + 0.0035; R^{2} = 0.9992 \\ \frac{Δ ν {(CO)}_{92}}{ν {(CO)}_{gas, 92}} = 0.0114 \frac{(ɛ - 1)}{(2 ɛ + 1)} + 0.0021; R^{2} = 0.9984 \\ \frac{Δ ν {(CO)}_{93}}{ν {(CO)}_{gas, 91}} = 0.0171 \frac{(ɛ - 1)}{(2 ɛ + 1)} + 0.0029; R^{2} = 0.9962 \\ \frac{Δ ν {(CO)}_{94}}{ν {(CO)}_{gas, 94}} = 0.0210 \frac{(ɛ - 1)}{(2 ɛ + 1)} + 0.0010; R^{2} = 0.9938 \end{matrix}$

II-isomer:

$\begin{matrix} \frac{Δ ν {(CO)}_{91}}{ν {(CO)}_{gas, 91}} = 0.0225 \frac{(ɛ - 1)}{(2 ɛ + 1)} + 0.0033; R^{2} = 0.9993 \\ \frac{Δ ν {(CO)}_{92}}{ν {(CO)}_{gas, 92}} = 0.0256 \frac{(ɛ - 1)}{(2 ɛ + 1)} + 0.0010; R^{2} = 0.9993 \\ \frac{Δ ν {(CO)}_{93}}{ν {(CO)}_{gas, 91}} = 0.0112 \frac{(ɛ - 1)}{(2 ɛ + 1)} + 0.0032; R^{2} = 0.9992 \\ \frac{Δ ν {(CO)}_{94}}{ν {(CO)}_{gas, 94}} = 0.0270 \frac{(ɛ - 1)}{(2 ɛ + 1)} + 0.0011; R^{2} = 0.9991 \end{matrix}$

So, nonspecific interactions, steric impacts, and hydrogen bonding have negligible effects in carbonyl group shift in numerous solvents [65].

4 Conclusion

In our research, the influence of solvent polarity on structure, electronic and optical properties Fe(CO)₄B₁₂N₁₂ complexes was investigated at mPW1PW91/6-311G(d,p) level. Computed solvation energy values indicated enhanced stability of the Fe(CO)₄B₁₂N₁₂ complexes in polar solvents. Good relations were provided between dipole moment and isotropic polarizability with McRae and Suppan functions. There were good correlations between the first hyperpolarizabilities values with McRae and Suppan functions in the I-structure. Wavenumbers of the stretching of carbonyl ligands were smaller in solution phase rather than gas phase. These values decreased in more polar solvents.

References

Cunden

L.S.

and Linck

R.G.

, Fe(CO)4 and Related Compounds as Isolobal Fragments, Inorg Chem 50 (2011), 4428–4436.

Chen

, Hartmann

and Frenking

, Ligand Site Preference in Iron Tetracarbonyl Complexes Fe(CO)4L (L = CO, CS, N2, NO+, CN–, NC–, η2-C2H4, η2-C2H2, CCH2, CH2, CF2, NH3, NF3, PH3, PF3, η2-H2), Z Anorg Allg Chem 627 (2001), 985–998.

Orbital Interactions in Chemistry. Editor, John Wiley and Sons, New York, 1985.

Macdonald

C.L.B.

and Cowley

A.H.

, A Theoretical Study of Free and Fe(CO)4-Complexed Borylenes (Boranediyls) and Heavier Congeners: The Nature of the Iron– Group 13 Element Bonding, J Am Chem Soc 121 (1999), 12113–12126.

Cymbaluk

T.H.

and Ernst

R.D.

, Crystallization and solid-state structural characterization of (2,2’-bipyridyl)zinc tetracarbonyliron, (bpy)ZnFe(CO)4, Inorg Chem 19 (1980), 2375–2381.

, Li

X.-W.

, Crittendon

R.C.

, Campana

C.F.

and Robinson

G.H.

, Experimental confirmation of an iron-gallium multiple bond: Synthesis, structure, and bonding of a ferrogallyne, Organometallics 16 (1997), 4511–4513.

Cowley

A.H.

, Lomeli

and Voigt

, Synthesis and characterization of a terminal borylene (Boranediyl) complex, J Am Chem Soc 120 (1998), 6401–6402.

Jutzi

, Neumann

, Reumann

and Stammler

H.-G.

, Pentamethylcyclopentadienylgallium (Cp*Ga): Alternative synthesis and application as a terminal and bridging ligand in the chemistry of chromium, iron, cobalt, and nickel, Organometallics 17 (1998), 1305–1314.

Spessard

, Miessler

, Organometallic chemistry Editor, Oxford University Press, New York, 2009.

10.

Kim

K.K.

, Hsu

, Jia

, Kim

S.M.

, Shi

, Hofmann

, Nezich

, Rodriguez-Nieva

J.F.

, Dresselhaus

and Palacios

, Synthesis and Characterization of Hexagonal Boron Nitride Film as a Dielectric Layer for Graphene Devices, Nano Letters 12 (2012), 161–166.

11.

Ciofani

, Genchi

G.G.

, Liakos

, Athanassiou

, Dinucci

, Chiellini

and Mattoli

, A simple approach to covalent functionalization of boron nitride nanotubes, J Colloid Int Sci 374 (2012), 308–314.

12.

Oku

, Nishiwaki

and Narita

, Formation and atomic structure of B12N12 nanocage clusters studied by mass spectrometry and cluster calculation, Sci Technol Adv Mater 5 (2004), 635–638.

13.

Oku

, Narita

and Nishiwaki

, Synthesis, atomic structures, and electronic states of boron nitride nanocage clusters and nanotubes, Mater Manuf Process 19 (2004), 1215–1239.

14.

Baei

M.T.

, Taghartapeh

M.R.

, Lemeski

E.T.

and Soltani

, A computational study of adenine, uracil, and cytosine adsorption upon AlN and BN nano-cages, Physica B 444 (2014), 6–13.

15.

Rad

A.S.

and Ayub

, Adsorption of pyrrole on Al12N12, Al12P12, B12N12, and B12P12 fullerene-like nano-cages; a first principles study, Vacuum 131 (2016), 135–141.

16.

Soltani

, Baei

M.T.

, Lemeski

E.T.

and Shahini

, Sensitivity of BN nano-cages to caffeine and nicotine molecules, Superlattices and Microstructures 76 (2014), 315–325.

17.

Vessally

, Esrafili

M.D.

, Nurazar

, Nematollahi

and Bekhradnia

, A DFT study on electronic and optical properties of aspirin-functionalized B12N12 fullerene-like nanocluster, Structural Chemistry 28 (2017), 735–748.

18.

Onsori

and Alipour

, A computational study on the cisplatin drug interaction with boron nitride nanocluster, J Mol Graph Model 79 (2018), 223–229.

19.

Soltani

, Sousaraei

, Javan

M.B.

, Eskandaric

, Balakheylid

, New J Chem 40 (2016), 7018.

20.

Selvarengan

and Kolandaivel

, Studies of solvent effects on conformers of glycine molecule, J Mol Struct: THEOCHEM 617 (2002), 99–106.

21.

Allin

S.B.

, Leslie

T.M.

and Lumpkin

R.S.

, Solvent effects in molecular hyperpolarizability calculations, Chem Mater 8 (1996), 428–432.

22.

Aquino

A.J.A.

, Tunega

, Haberhauer

, Gerzabek

M.H.

and Lischka

, Ab initio molecular dynamics study of adsorption sites on the (001) surfaces of 1:1 dioctahedral clay minerals, J Phys Chem A 106 (2002), 11515–11525.

23.

Tomasi

, Mennucci

and Cammi

, Quantum mechanical continuum solvation models, Chem Rev 105 (2005), 2999–3094.

24.

Springborg

, Specialist Periodical Reports: Chemical Modelling, Applications and Theory Editor, Royal Society of Chemistry, Cambridge, UK, 2008, Vol. 5.

25.

Taha

, Adly

O.M.I.

and Shebl

, Reactivity and molecular modeling of new solvatochromic mixed-ligand copper(II) chelates of 2-acetylbutyrolactone and dinitrogen bases, Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 140 (2015), 74–84.

26.

Skyner

R.E.

, McDonagh

J.L.

, Groom

C.R.

, Mourika

T.v.

and Mitchell

J.B.O.

, A review of methods for the calculation of solution free energies and the modelling of systems in solution, Phys Chem Chem Phys 17 (2015), 6174–6191.

27.

Kar

and Pal

, Effect of solvents having different dielectric constants on reactivity: a conceptual DFT approach, International Journal of Quantum Chemistry 110 (2010), 1642–1647.

28.

Jovića

, Nikolića

, Petrovićb

, Kordića

, Đaković-Sekulića

and Stojanović

, FTIR investigation of solvent effects of N-methyl and N-tert-butyl benzamide, Journal of Structural Chemistry 55 (2014), 1616–1622.

29.

Y.-K.

, Wu

H.-Y.

, Zhu

, Fu

K.-X.

and Li

X.-Y.

, Solvent effect on the UV/Vis absorption spectra in aqueous solution: The nonequilibrium polarization with an explicit representation of the solvent environment, Computational and Theoretical Chemistry 971 (2011), 65–72.

30.

Basavaraja

, Inamdar

S.R.

and Kumar

H.M.S.

, Solvents effect on the absorption and fluorescence spectra of 7-diethylamino-3-thenoylcoumarin: Evaluation and correlation between solvatochromism and solventolarity parameters. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 137 (2015), 527–534.

31.

Ersan

, Apul

O.G.

and Karanfil

, Linear solvation energy relationships (LSER) for adsorption of organic compounds by carbon nanotubes, Water Research 98 (2016), 28–38.

32.

Ouennoughi

, Karce

H.E.

, Aggoun

, Lanez

and Morallon

, A novel ferrocenic copper(II) complex Salen-like, derived from 5-chloromethyl-2-hydroxyacetophenone and N-ferrocenmethylaniline: Design, spectral approach and solvent effect towards electrochemical behavior of Fc+/Fc redox couple, Journal of Organometallic Chemistry 848 (2017), 344–351.

33.

Aydin

and Akins

D.L.

, DFT studies on solvent dependence of electronic absorption spectra of free-base and protonated porphyrin, Computational and Theoretical Chemistry 1132 (2018), 12–22.

34.

C.-l.

, Zhang

S.-h.

, Gou

R.-j.

, Ren

F.-d.

and Zhu

S.-f.

, Theoretical insight into the effect of solvent polarity on the formation and morphology of 2,4,6,8,10,12-hexanitrohexaazaisowurtzitane (CL-20)/2,4,6-trinitro-toluene(TNT) cocrystal explosive, Computational and Theoretical Chemistry 1127 (2018), 22–30.

35.

Dos Santos

H.F.

, Chagas

M.A.

, De Souza

L.A.

, Rocha

W.R.

, De Almeida

M.V.

, Anconi

C.P.A.

and De Almeida

W.B.

, Water Solvent Effect on Theoretical Evaluation of 1H NMR Chemical Shifts: o-Methyl-Inositol Isomer, The Journal of Physical Chemistry A 121 (2017).

36.

Ganesan

, Vedamanickam

and Paranthaman

, Studies of intramolecular H-bond interactions and solvent effects in the conformers of glycolic acid—A quantum chemical study, Journal of Theoretical and Computational Chemistry 17 (2018), 1850009.

37.

Shen

, Su

and Wu

, What kind of neutral halogen bonds can be modulated by solvent effects? Phys Chem Chem Phys 20 (2018), 26126.

38.

T.-J.

, Xu

L.-K.

, Wang

and Li

X.-Y.

, Solvent effects for vertical absorption and emission processes in solution using a self-consistent state specific method based on constrained equilibrium thermodynamics, Phys Chem Chem Phys 20 (2018), 13178.

39.

Sizova

O.V.

, Ivanova

N.V.

, Lyubimova

O.O.

and Sizov

V.V.

, Electronic structure and spectra of binuclear bridged nitrosyl ruthenium complexes, Russian Journal of Coordination Chemistry 33 (2007), 523–529.

40.

Shamsiev

R.S.

and Drobyshev

A.V.

, Study of the effect of the solvent nature on cis-trans isomerization in Bis(allyl)nickel by the density functional theory method, Russian Journal of Inorganic Chemistry 58 (2013), 1506.

41.

Milani

N.N.

, Ghiasi

and Forghaniha

, The Impact of Solvent Polarity on the Stability, Electronic Properties, and 1H NMR Chemical Shift of the Conformers of 2-Chloro-3-Methylcyclohexan-1-One Oxime: a Conceptual DFT Approach, Journal of Applied Spectroscopy 86 (2020), 1123–1131.

42.

Kamrava

, Ghiasi

and Marjani

, The conductor-like polarizable continuum model study of indenyl effect on the ligand substitution reaction in the (η5-C9H7)Co(CO)2 complex, International Journal of Chemical Kinetics 53 (2021), 901–912.

43.

Parsa

, Ghiasi

and Marjani

, Unveiling the influence of solvent polarity on structural, electronic properties, and 31P NMR parameters of rhenabenzyne complex, Inorganic Chemistry Communications 127 (2021), 108497.

44.

Kamrava

, Ghiasi

and Marjani

, Structure, electronic properties and slippage of cyclopentadienyl and indenyl ligands in the (η5-C5H5) (η3-C5H5) W(CO)2 and (η5-C9H7) (η3-C9H7)W(CO)2 complexes: A C-PCM investigation, Journal Molecular Liquid 329 (2021), 115535.

45.

Ghiasi

, Emami

and Sofiyani

M.V.

, Cyclometalation in the (η3-C5H5)Co(η2-C2H2)(PMe3) and (η3-C9H7)Co(η2-C2H2) (PMe3) complexes: A computational investigation, Journal of Molecular Liquid 325 (2021), 115097.

46.

Ghiasi

and Milani

N.N.

, Exploring of the solvent effect on the electronic structure and 14N NMR chemical shift of cyclic-N3S3Cl3: A computational investigation, Russian Journal of Physical Chemistry B 15 (2021), S14.

47.

Frisch

M.J.

, Trucks

G.W.

, Schlegel

H.B.

, Scuseria

G.E.

, Robb

M.A.

, Cheeseman

J.R.

, Scalman

, Barone

, Mennucci

, Petersson

G.A.

, Nakatsuji

, Caricato

, Li

, Hratchian

H.P.

, Izmaylov

A.F.

, Bloino

, Zheng

, Sonnenberg

J.L.

, Hada

, Ehara

, Toyota

, Fukuda

, Hasegawa

, Ishida

, Nakajima

, Honda

, Kitao

, Nakai

, Vreven

, Montgomery

J.A.

Jr , Peralta

J.E.

, Ogliaro

, Bearpark

, Heyd

J.J.

, Brothers

, Kudin

K.N.

, Staroverov

V.N.

, Kobayashi

, Normand

, Raghavachari

, Rendell

, Burant

J.C.

, Iyengar

S.S.

, Tomasi

, Cossi

, Rega

, Millam

J.M.

, Klene

, Knox

J.E.

, Cross

J.B.

, Bakken

, Adamo

, Jaramillo

, Gomperts

, Stratmann

R.E.

, Yazyev

, Austin

A.J.

, Cammi

, Pomelli

, Ochterski

J.W.

, Martin

R.L.

, Morokuma

, Zakrzewski

V.G.

, Voth

G.A.

, Salvador

, Dannenberg

J.J.

, Dapprich

, Daniels

A.D.

, Farkas

, Foresman

J.B.

, Ortiz

J.V.

, Cioslowski

and Fox

D.J.

, Gaussian 09, Gaussian, Inc., Wallingford CT, 2009.

48.

Hariharan

P.C.

and Pople

J.A.

, The influence of polarization functions on molecular orbital hydrogenation energies, Theo Chim Acta 28 (1973), 213.

49.

Hariharan

P.C.

and Pople

J.A.

, Accuracy of AH n equilibrium geometries by single determinant molecular orbital theory, Mol Phys 27 (1974), 209.

50.

Adamo

and Barone

, Exchange functionals with improved long-range behavior and adiabatic connection methods without adjustable parameters: The m PW and m PW1PW models, J Chem Phys 108 (1998), 664.

51.

Dunbar

R.C.

, Metal Cation Binding to Phenol: DFT Comparison of the Competing Sites, J Phys Chem A 106 (2002), 7328–7337.

52.

Porembski

and Weisshaar

J.C.

, Kinetics and Mechanism of the Reactions of Ground-State Y (4d 15s 2, 2D) with Ethylene and Propylene: Experiment and Theory, J Phys Chem A 105 (2001), 6655–6667.

53.

Porembski

and Weisshaar

J.C.

, Singlet and Triplet Reaction Paths for Gas-Phase Zr + C2H4 by Density Functional Theory, J Phys Chem A 105 (2001), 4851–4864.

54.

Zhang

, Guo

and You

X.-Z.

, Hydrolysis Theory for Cisplatin and Its Analogues Based on Density Functional Studies, J Am Chem Soc 123 (2001), 9378–9387.

55.

Keleiman

D.A.

, Nonlinear dielectric polarization in optical media, Phy Rev 126 (1962), 1977.

56.

Barone

and Cossi

, Quantum calculation of Molecular Energies and Energy Gradients in Solution by a Conductor Solvent Model, J Phys Chem A 102 (1998), 1995.

57.

Cossi

, Rega

, Scalmani

and Barone

, Energies, structures, and electronic properties of molecules in solution with the C-PCM solvation model, J Comp Chem 24 (2003), 669.

58.

McRae

E.G.

, Theory of solvent effects on molecular electronic spectra. Frequency shifts, J Phys Chem 61 (1957), 562–572.

59.

Suppan

, Local polarity of solvent mixtures in the field of electronically excited molecules and exciplexes, J Chem SOC, Faraday Trans 83 (1987), 495.

60.

Onsager

, Electric moments of molecules in liquids, J Am Chem Soc 58 (1936), 1486–1493.

61.

Clays

and Persoons

, Hyper-Rayleigh scattering in solution, Phys Rev Lett 66 (1991), 2980.

62.

Lee

, An

S.-Y.

and Cho

, Nonlinear optical (NLO) properties of the octupolar molecule: Structure– function relationships and solvent effects, J Phys Chem B 103 (1999), 4992–4996.

63.

Ray

P.C.

and Leszczynski

, First hyperpolarizabilities of ionic octupolar molecules: structure–function relationships and solvent effects, Chem Phys Lett 399 (2004), 162.

64.

Bauer

and Magat

, Sur la déformation des molécules en phase condensée et la < <liaison hydrogène> > , J Physique Radium 9 (1938), 319.

65.

Reichardt

and Welton

, Solvents and Solvent Effects in Organic Chemistry. Fourth ed., Editor, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2011.