Interaction of cisplatin anticancer drug with C 20 bowl: DFT investigation

Abstract

This study investigated the cisplatin (anticancer drug) interaction with C₂₀ bowl and C₂₀H₁₀(Bowl) molecule including hydrogen-saturated with using mPW1PW91 functional. The stability of the various isomers of drug interaction with C₂₀ bowl was investigated. The interaction energy values were estimated in these systems. Changes in the structural parameters and the frontier orbital energy and HOMO-LUMO gap values were evaluated. Charge transfer between fragments were shown with electrophilicity-based charge transfer (ECT). The Octanol–water partition coefficient (log P) and molecular volume (V_m) of these drug precursor molecules were studied. Also, Pt-C bond characterizations were illustrated using QTAIM analysis. The results showed that C₂₀ bowl can be a promising nanocarrier for cisplatin anticancer drug.

Keywords

cisplatin drug electrophilicity-based charge transfer (ECT)quantum theory of atoms in molecules (QTAIM) analysis

1 Introduction

Cisplatin (Cis-diamminedichloroplatinum (II)) is the first-line treatment for different types of solid tumors [1]. Previously studies demonstrated that cisplatin can bind to nuclear DNA and mitochondria DNA (mtDNA) [2, 3]. But it has a several side effects against normal tissues and cells [4, 5]. Recent studies apply novel carriers for delivery of cisplatin to reduction of its side effects [6, 7].

Application of nanomaterials for drug delivery (active or inactive drug delivery), enhancement of therapeutic efficacy of the traditional anticancer drugs as well as prevention of its side effects is the goals of nanomedicine. Fullerene derivatives have been employed as drug delivery agent [8]. In a few years ago, C₆₀ was covalently attached to paclitaxel (anticancer drug) via an ester bond [9]. In another study, doxorubicin was attached to the fullerene and results showed that doxorubicin- fullerene complex was distributed mostly in the cytoplasm instead of the cell nucleus [10]. Prylutska et al. demonstrated that C₆₀ combined with cisplatin effectively induced tumor cell death, inhibited tumor growth, and overcoming drug resistance [11].

In other side, Prylutska et al. showed that the cytotoxic effect of cisplatin against normal cells was prevented at complexation with C₆₀ fullerene. It indicates that nanocomplex of fullerene(C₆₀)-cisplatin has a potential to be used for the minimization of anticancer drug side effects [6]. The C₂₀ by multifunctionalized can be considered as an interesting nanocarrier at drug delivery systems.

Fullerene is one of the allotrope of carbon that are individual molecules with an in finite number of discrete. It discovered after diamond and graphite, and unlike them, each type of Fullerenes has its own unique properties [8]. Fullerene generally produced by electric arc vaporizes, laser ablation, pyrolysis or combustion [12 –16]. The lowest energy members of the C₂₀ family are cage 1, bowl 2 and ring 3. While Fullerene molecule is insoluble in water, but it showed very low solubility in common organic solvents [17]. Then, partially mask the a polar fullerene surface or covalently modify the aromatic structure were used to overcome its compatibility limitation with biological media [17].

In this paper, we investigated interaction cisplatin drug with C₂₀ bowl. The four possible isomers of cisplatin interaction with C₂₀ bowl and C₂₀H₁₀ (Bowl) molecule including hydrogen-saturated were considered. The frontier orbital energy and HOMO-LUMO gap values, changes in the structural parameters and the interaction energy values were calculated. Finally, Pt-C bond characterizations were illustrated using QTAIM analysis.

2 Computational methods

Gaussian 09 software package was used for calculations [18]. The standard 6-311G(d,p) basis set [19 –22] and the Def2-TZVPPD basis set [23] were applied for main groups of elements and the Pt element, respectively. The studied molecules were considered in the neutral form and singlet state. For exclude direct calculation of the exchange and correlation integrals related to 60 electrons of the Pt atom, pseudo-potential effective core potential (ECP) was applied to the Def2-TZVPPD basis set [24].

The one-parameter hybrid functional with adapted Perdew-Wang exchange and correlation (mPW1PW91) was used for Geometry optimizations [25]. In compared with B3LYP, the mPW1PW91 functional revealed better results in the transition metal complexes [26 –29].

For prove that the optimized structures have no imaginary frequency, harmonic vibrational frequencies were evaluated.

In this study, we applied a self-consistent reaction field (SCRF) method to investigate of the solvation impacts. Specially, non-electrostatic terms for Solvent Model Density (SMD) solvation model and the conductor-like polarizable continuum model (CPCM) [30, 31] with radii was used [32].

The partition coefficient octanol/water (c log P) [33] was calculated by the following equation: $c log P = \frac{Δ G_{sol}^{aqua} - Δ G_{sol}^{Octanol}}{2.303 RT}$

These thermodynamic parameters were provided from frequency calculations on the optimized structures of gas phase at the same level of theory in the corresponding solvents.

Quantum theory of atoms in molecules (QTAIM) analyses were performed on the optimized geometries with the used level of theory for optimization using Multiwfn 3.8 software package [34, 35].

Contour map of electrostatic potential was provided using the Multiwfn 3.8 package [34, 36].

3 Results and discussion

3.1 Energetic aspects

Four possible isomer structures of C₂₀(Bowl) . . . cis-PtCl₂(NH₃)₂ nanocomplex are demonstrated in Fig. 1. Also, cis-PtCl₂(NH₃)₂ complex with C₂₀H₁₀(Bowl) molecules including hydrogen-saturated (H-saturated) are considered (Fig. 1). The relative and absolute energies of the studied isomers are listed in Table 1. According to results, the order of stability of these isomers is: I > II > III > IV. As seen, the I-isomer is most stable between other isomers. It can be observed, relative energy values of the studied isomers are larger in the molecules including hydrogen-saturated (H-saturated).

Fig. 1

The structures of various isomers of cis-Pt(NH₃)₂Cl₂ with C₂₀(bowl) and H-saturated form of this molecule.

Table 1

Absolute energy (E, a.u), relative energy (ΔE, kcal/mol), basis set superposition error (E(BSSE), kcal/mol), interaction energy (ΔE_int, kcal/mol), octanol–water partition coefficient (log P) and molecular volume (V_m, cm³/mol)values of the various isomers of cis-Pt(NH₃)₂Cl₂with C₂₀(bowl)and its H-saturated form

Isomer	E(gas)	ΔE	E(BSSE)	ΔE_int	V_m	clog P
Non-H-saturated
I	–1914.6647	0.00	3.42	–97.18	187.32	–4.02
II	–1914.5975	42.19	3.73	–59.11	251.39	–3.75
III	–1914.5801	75.94	4.76	–57.49	240.87	–3.58
IV	–1914.5633	63.65	4.86	–42.75	225.51	–3.53
H-saturated
I	–1921.2813	0.00	4.11	–66.14	318.21	–3.82
II	–1921.2510	19.02	3.57	–41.16	229.99	–3.87
III	–1921.2540	17.13	4.11	–45.29	250.59	–4.38
IV	–1921.2420	24.66	4.15	–38.86	209.45	–4.60

3.2 Interaction energy values

The interaction energy (ΔE_int) is typically measured as follows: $\begin{matrix} Δ E_{int} = E (C_{20} or C_{20} H_{10} \dots cis - PtC l_{2} {(N H_{3})}_{2}) \\ - E (C_{20} or C_{20} H_{10}, sp) - E (cis - PtC l_{2} {(N H_{3})}_{2}, sp) + E (BSSE) \end{matrix}$

Where E(C₂₀,sp) and E(cis-PtCl₂(NH₃)₂,sp) are the energy values of isolated C₂₀ or C₂₀H₁₀(Bowl) and cis-PtCl₂(NH₃)₂ molecules in the optimized C₂₀(Bowl) or C₂₀H₁₀(Bowl) . . . cis-PtCl₂(NH₃)₂, respectively. E(C₂₀ or C₂₀H₁₀(Bowl) . . . cis-PtCl₂(NH₃)₂) is the energy of cis-PtCl₂(NH₃)₂ interacted with C₂₀(Bowl) or C₂₀H₁₀(Bowl). E(BSSE) is the basis set superposition error (as corrected of interaction energy) [37, 38].

Interaction energy and E(BSSE) values of numerous isomers of cis-PtCl₂(NH₃)₂ complexation with the C₂₀(Bowl) are listed in Table 1. It was revealed from the negative ΔE_int values that the complex formation is energetically favorable. The interaction energies demonstrated that the I-Isomer has more tendency to interaction cis-PtCl₂(NH₃)₂ molecule compared with the C₂₀(Bowl). The weakness interaction is observed in IV-isomer. Weakness interactions are favorable for drug delivery because in this case because of easy desorption process in these cases. Also, interaction energy values show the stronger interaction between cisplatin and non-H-saturated molecule than H-saturated molecule.

3.3 Molecular orbital analysis

The frontier orbitals energy, hardness, electrophilicity, the corresponding HOMO–LUMO energy gaps, chemical potential values of C₂₀(Bowl) or C₂₀H₁₀(Bowl) . . . cis-PtCl₂(NH₃)₂ isomers, C₂₀(Bowl) or C₂₀H₁₀(Bowl) and cis-PtCl₂(NH₃)₂ molecules are given in Table 2.

Table 2
Frontier orbital energy (eV), HOMO-LUMO gap (eV) values of the Pt(NH₃)₂Cl₂, C₂₀(bowl)\\ and various isomers of cis-Pt(NH₃)₂Cl₂with C₂₀(bowl) and its H-saturated form

Molecule E(HOMO) E(LUMO) Gap

C₂₀ –7.49 –3.37 4.12

C₂₀H₁₀ –6.49 –1.76 4.73

cis-PtCl₂(NH₃)₂ –6.45 –1.10 5.35

Non-H-saturated

I –6.89 –3.03 3.86

II –6.65 –3.63 3.02

III –6.76 –3.28 3.48

IV –6.19 –3.44 2.76

H-saturated

I –6.32 –2.43 3.88

II –5.64 –2.83 2.81

III –5.86 –2.13 3.73

IV –5.51 –2.55 2.96

Molecule	E(HOMO)	E(LUMO)	Gap
C₂₀	–7.49	–3.37	4.12
C₂₀H₁₀	–6.49	–1.76	4.73
cis-PtCl₂(NH₃)₂	–6.45	–1.10	5.35
Non-H-saturated
I	–6.89	–3.03	3.86
II	–6.65	–3.63	3.02
III	–6.76	–3.28	3.48
IV	–6.19	–3.44	2.76
H-saturated
I	–6.32	–2.43	3.88
II	–5.64	–2.83	2.81
III	–5.86	–2.13	3.73
IV	–5.51	–2.55	2.96

Comparison of the HOMO-LUMO gap values in the C₂₀(Bowl) or C₂₀H₁₀(Bowl) . . . cis-PtCl₂(NH₃)₂ isomers with C₂₀ bowl showed that cis-PtCl₂(NH₃)₂ adsorption meaningfully decrease the HOMO-LUMO gap values. Thus, these results indicated that the C₂₀ bowl may be a suitable nano-carrier for cis-PtCl₂(NH₃)₂. On the other hand, there are larger gap values for H-saturated isomers than non-H-saturated isomers.

It was demonstrated that the HOMO-LUMO gap of I-isomer was largest among other isomers. These variations between isomers are compatible with the principles of maximum hardness (MHP) and minimum energy (MEP) [39 –43]. In most cases, the energy increases and the hardness decreases when a conformer changes from the most stable to other less stable species.

Frontier orbitals plots of the studied isomers of C₂₀(Bowl) . . . cis-PtCl₂(NH₃)₂ nano-complex are presented in Fig. 2. For most stable isomer (I-isomer), between d-orbital of Pt and carbon atoms of C₂₀ bowl in HOMO there is π^*-interaction. The most contributions in HOMO and LUMO of I-isomer belong to C₂₀ bowl.

Fig. 2

Plots of frontier orbitals of various isomers of cis-Pt(NH₃)₂Cl₂. . . C₂₀(bowl) complex.

Figure 3 shows PDOS (partial density of state) and DOS (density of states) diagrams in the C₂₀(Bowl) . . . cis-PtCl₂(NH₃)₂ nano-complex. The PDOS determined the composition of the fragment orbitals that are contributing at the molecular orbitals. The contribution percent of fragments in frontier orbital of the studied isomers are mentioned in Table 3. The most fragments which contribute in HOMO and LUMO are belongs to C₂₀ and cis-PtCl₂(NH₃)₂ nano-complex in the studied isomers, respectively.

Fig. 3

(a) DOS and (b) PDOS diagrams of frontier orbitals of various isomers of cis-Pt(NH₃)₂Cl₂. . . C₂₀(bowl) complex.

Table 3

Percent of contribution of fragments in the frontier orbitals for various isomers\\ of cis-Pt(NH₃)₂Cl₂with C₂₀(bowl)

	HOMO		LUMO
Isomer	C₂₀	drug	C₂₀	drug
I	82	18	99	1
II	52	48	81	19
III	65	35	99	1
IV	61	39	82	18

3.4 Electrophilicity-based charge transfer (ECT)

Calculation of the electrophilicity-based charge transfer (ECT) of C₂₀(Bowl) . . . cis-PtCl₂(NH₃)₂ isomers was evaluated. The difference between ΔN_max values of interacting molecules is defined as ECT [44]: $ECT = Δ N_{max} (cis - PtC l_{2} {(N H_{3})}_{2}) - Δ N_{max} (C_{20} (Bowl) or C_{20} H_{10} (Bowl))$

Where ΔN_max is defined as: ${(Δ N_{\max})}_{i} = \frac{μ_{i}}{η_{i}}$

μ and η are global chemical potential and hardness, respectively. They are determined on the basis of Koopman’s theorem [45] and defined as global reactivity descriptors [46 –49]. These values for C₂₀(Bowl), C₂₀H₁₀(Bowl), cis-PtCl₂(NH₃)₂ and C₂₀(Bowl) or C₂₀H₁₀(Bowl) . . . cis-PtCl₂(NH₃)₂ isomers are calculated by the following equations and results are mentioned in Table 2. $η = \frac{E (LUMO) - E (HOMO)}{2}$ $μ = \frac{E (HOMO) + E (LUMO)}{2}$

The calculated ΔN_max value is +0.859 and –0.032 for interaction of drug with C₂₀(Bowl) or C₂₀H₁₀(Bowl), respectively. The positive value of ECT reveal charge flow from C₂₀(Bowl) to cis-PtCl₂(NH₃)₂. On the other hand, the negative value of ECT show charge flow from cis-PtCl₂(NH₃)₂ to C₂₀H₁₀(Bowl).

3.5 Structural parameters

Pt-C bond distances in the optimized isomers of C₂₀(Bowl) . . . cis-PtCl₂(NH₃)₂ nano-complex are shown in Fig. 1. According to Fig. 1, the average of Pt-C bond lengths are 2.026 Å (I-isomer), 2.074 Å (II-isomer), 2.126 Å (III-isomer), and 2.158 Å (IV-isomer). It can be found, Pt-C bonds are longer in the presence of H-saturated C₂₀(Bowl) than C₂₀(Bowl). The shortest bond length is observed in I-isomer. Thus, it can be seen stronger interaction between C₂₀(Bowl) and cis-PtCl₂(NH₃)₂ complex in I-isomer in compared to II-isomer. This result is compatible with EDA prediction. As expected, Pt-C bond distances are increased, when ΔE_int values increased.

3.6 Quantum theory of atoms in molecules (QTAIM) analysis

Now, we employed QTAIM analysis for illustration of chemical and physical properties of the Pt-C bonds in the studied systems. The electron density and Laplacian of electron density values (ρ_BCP and ▿² ρ_BCP) at bond critical points of Pt-C of the studied systems are gathered in Table 4. The positive ▿² ρ_BCP values are compatible with closed-shell interactions in the Pt-C bonds. Total electron energy density (H) values at bond critical points of Pt-C are listed in Table 4. the negative H values are taken as an indicator of covalency [50]. The positive ▿² ρ values and negative H values at BCP(Pt-C) are compatible with similar results for the metal–carbon bonds in organometallic complexes [51] and transition metal carbonyl clusters [52]. These values reveal a combination of the closed-shell and shared interactions for the metal–ligand bonds.

Table 4
Bond distance (r) and QTAIM results at bond critical points of Pt-Cof four possible isomers of cis-Pt(NH₃)₂Cl₂with C₂₀(bowl) and its H-saturated form

r(Å) ρ(e.Å^–3) ∇² ρ(e.Å^–5) H (a.u)

Complex Pt-C1 Pt-C2 Pt-C1 Pt-C2 Pt-C1 Pt-C2 Pt-C1 Pt-C2

Non-H-saturated

I 2.036 2.016 0.1414 0.1347 0.1409 0.1718 –0.0721 –0.0652

II 2.178 1.969 0.1553 0.1091 –0.0873

III 2.131 2.12 0.1147 0.1156 0.1162 0.1247 –0.0500 –0.0506

IV 2.154 2.161 0.1054 0.1077 0.1387 0.1248 –0.0422 –0.0441

H-saturated

I 2.104 2.092 0.1208 0.1243 0.1168 0.1006 –0.0550 –0.0584

II 2.131 2.208 0.1110 0.0949 0.1085 0.1611 –0.0477 –0.0336

III 2.01 2.135 0.1101 0.0977 0.1317 0.1509 –0.0461 –0.0356

IV 2.173 2.179 0.1020 0.1004 0.1308 0.1412 –0.0396 –0.0383

	r(Å)	ρ(e.Å^–3)	∇² ρ(e.Å^–5)	H (a.u)
Non-H-saturated
I	2.036	2.016	0.1414	0.1347	0.1409	0.1718	–0.0721	–0.0652
II	2.178	1.969	0.1553	0.1091	–0.0873
III	2.131	2.12	0.1147	0.1156	0.1162	0.1247	–0.0500	–0.0506
IV	2.154	2.161	0.1054	0.1077	0.1387	0.1248	–0.0422	–0.0441
H-saturated
I	2.104	2.092	0.1208	0.1243	0.1168	0.1006	–0.0550	–0.0584
II	2.131	2.208	0.1110	0.0949	0.1085	0.1611	–0.0477	–0.0336
III	2.01	2.135	0.1101	0.0977	0.1317	0.1509	–0.0461	–0.0356
IV	2.173	2.179	0.1020	0.1004	0.1308	0.1412	–0.0396	–0.0383

3.7 Contour map of electrostatic potential

Contour map of electrostatic potential of the most stable isomer of C₂₀(Bowl) . . . cis-PtCl₂(NH₃)₂ nano-complex are presented in Fig. 4 (in xy-plane of molecules). The solid and dashed lines reveal the region having positive and negative value of ESP, respectively. The bold blue line relates to vdW surface.

Fig. 4

Contour map of electrostatic potential of the I- isomer of C₂₀(Bowl) . . . cis-PtCl₂(NH₃)₂ nano-complex in xy-plane of molecules.

3.8 Partition coefficient

Lipophilicity is a material properties that determine interactions between a drug and its biological receptor. Lipophilicity usually estimated by log P. The greater log P value demonstrate the more lipophilic character. Log P values of the studied systems are mentioned in Table 1. The largest and smallest Log P values are observed for IV-isomer and I-isomer of non-H-saturated molecules, respectively. On the other hand, there are the largest and smallest Log P values for I-isomer and IV-isomer of H-saturated molecules, respectively.

3.9 Molecular volume

The calculated molecular volume (V_m) of the studied isomers are gather in Table 1. It can be found that the I-isomer of non-H-saturated molecule has smallest V_m. Smallest V_m of H-saturated molecules has been found for IV-isomer. Compounds with small V_m, cannot interact with the biological receptor. Besides, the bigger V_m gives higher biological activity.

4 Conclusion

Computational evaluation of the interaction behavior of fullerene C₂₀ bowl with cisplatin revealed that I-isomer was most stable isomer between four possible isomers. Relative energy values of the studied isomers were larger in the molecules including hydrogen-saturated (H-saturated). Interaction energy calculations indicated the most interaction between two fragments in the I-isomer. Interaction energy values indicated the stronger interaction between cisplatin and non-H-saturated molecule than H-saturated molecule. PDOS results illustrated that the most contribution of fragments in HOMO and LUMO were belonged to C₂₀ and cis-PtCl₂(NH₃)₂ nanocomplex in the studied isomers, respectively. The results from ECT showed a charge flow from C₂₀(Bowl) to cis-PtCl₂(NH₃)₂. QTAIM results revealed a combination of the closed-shell and shared interactions for the Pt-C bonds in the studied systems. The largest and smallest Log P values were observed for IV-isomer and I-isomer of H-saturated species, respectively. In summary, our study suggested that C₂₀(Bowl) and C₂₀H₁₀(Bowl) could be a promising nano-carrier for cisplatin (cis-PtCl₂(NH₃)₂) anticancer drug.

References

Giacomini

, Ragazzi

, Pasut

and Montopoli

, International journal of molecular sciences 2020, 21.

Wang

F.-Y.

, Tang

X.-M.

, Wang

, Huang

K.-B.

, Feng

H.-W.

, Chen

Z.-F.

, Liu

Y.-N.

and Liang

, European Journal of Medicinal Chemistry 2018, 155.

Wang

and Lippard

S.J.

, Nature Reviews Drug Discovery 2005, 4.

Wang

T.-E.

, Lai

Y.-H.

, Yang

K.-C.

, Lin

S.-J.

, Chen

C.-L.

and Tsai

P.-S.

, Antioxidants 2020, 9.

Federico

, Sun

, Muz

, Alhallak

, Cosper

P.F.

, Muhammad

, Jeske

, Hinger

, Markovina

, Grigsby

, Schwarz

J.K.

and Azab

A.K.

, International Journal of Radiation Oncology*Biology*Physics 2021, 109.

Prylutska

, Grynyuk

, Skaterna

, Drobot

, Slobodyanik

and Matyshevska

, Biotechnologia Acta 2020, 13.

González-López

M.A.

, Gutiérrez-Cárdenas

E.M.

, Sánchez-Cruz

, Hernández-Paz

J.F.

, Pérez

, Olivares-Trejo

J.J.

and Hernández-González

, Cancer Nanotechnology 2020, 11.

Chan

, The Journal of Physical Chemistry A 2020, 124.

Zakharian

T.Y.

, Seryshev

, Sitharaman

, Gilbert

B.E.

, Knight

and Wilson

L.J.

, Journal of the American Chemical Society 2005, 127.

10.

Liu

J.-H.

, Cao

, Luo

P.G.

, Yang

S.-T.

, Lu

, Wang

, Meziani

M.J.

, Haque

S.A.

, Liu

and Lacher

, ACS Applied Materials & Interfaces 2010, 2.

11.

Prylutska

, Panchuk

, Gołuński

, Skivka

, Prylutskyy

, Hurmach

, Skorohyd

, Borowik

, Woziwodzka

and Piosik

, Nano Research 2017, 10.

12.

Fulcheri

, Schwob

, Fabry

, Flamant

, Chibante

and Laplaze

, Carbon 38 (2000), 797.

13.

Lamb

L.D.

and Huffman

D.R.

, Journal of Physics and Chemistry of Solids 1993 54.

14.

Takehara

, Fujiwara

, Arikawa

, Diener

M.D.

and Alford

J.M.

, Carbon 2005, 43.

15.

Crowley

, Taylor

, Kroto

H.W.

, Walton

D.R.

, Cheng

P.-C.

and Scott

L.T.

, Synthetic Metals 1996, 77.

16.

Dubrovsky

, Bezmelnitsyn

and Eletskii

, Carbon 2004, 42.

17.

Montellano

, Da Ros

, Bianco

and Prato

, Nanoscale 2011, 3.

18.

Frisch

M.J.

, Trucks

G.W.

, Schlegel

H.B.

, Scuseria

G.E.

, Robb

M.A.

, Cheeseman

J.R.

, Scalmani

, 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.J.A.

, Peralta

, Ogliaro

J.E.

, Bearpark

, Heyd

J.J.

, Brothers

, Kudin

K.N.

, Staroverov

V.N.

, Keith

, 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.

and Ciwski

, Fox

D.J.

Gaussian 09, Revision D.01, Gaussian, Inc.: Wallingford CT, 2013.

19.

Hay

P.J.

, The Journal of Chemical Physics 1977, 66.

20.

Krishnan

, Binkley

J.S.

, Seeger

and Pople

J.A.

, The Journal of Chemical Physics 1980, 72.

21.

McLean

A.D.

and Chandler

G.S.

, The Journal of Chemical Physics 1980, 72.

22.

Wachters

A.J.H.

, The Journal of Chemical Physics 1970, 52.

23.

Rappoport

and Furche

, The Journal of Chemical Physics 2010, 133.

24.

Andrae

, Häußermann Dolg

, Stoll

and Preuß

, Theoretica Chimica Acta 1990 77, 123.

25.

Adamo

and Barone

, The Journal of Chemical Physics, 1998 108, 664.

26.

Dunbar

R.C.

, The Journal of Physical Chemistry A 2002, 106.

27.

Porembski

and Weisshaar

J.C.

, The Journal of Physical Chemistry A 2001, 105.

28.

Porembski

and Weisshaar

J.C.

, The Journal of Physical Chemistry A 2001, 105.

29.

Zhang

, Guo

and You

X.-Z.

, Journal of the American Chemical Society 2001, 123.

30.

Barone

and Cossi

, The Journal of Physical Chemistry A 1998, 102.

31.

Cossi

, Rega

, Scalmani

and Barone

, Journal of Computational Chemistry 2003, 24.

32.

Marenich

A.V.

, Cramer

C.J.

and Truhlar

D.G.

, The Journal of Physical Chemistry B 2009, 113.

33.

Kim

and Park

, Journal of Molecular Graphics and Modelling 2015, 60.

34.

and Chen

, J Comp Chem 2012 33, 580.

35.

and Chen

, J. Mol. Graph. Model, 2012 38, 314.

36.

Zhang

14, J Chem Theory Comput 2018, 572.

37.

Simon

, Duran

and Dannenberg

, The Journal of Chemical Physics 1996, 105.

38.

Richard

R.M.

, Bakr

B.W.

and Sherrill

C.D.

, Journal of Chemical Theory and Computation 2018, 14.

39.

Ayers

P.W.

and Parr

R.G.

, Journal of the American Chemical Society 2000, 122.

40.

Parr

R.G.

and Chattaraj

P.K.

, Journal of the American Chemical Society 1991, 113.

41.

Pearson

R.G.

, Journal of Chemical Education 1987, 64.

42.

Pearson

R.G.

Accounts of Chemical Research, 1993, 26.

43.

Pearson

R.G.

Journal of Chemical Education, 1999, 76.

44.

Padmanabhan

, Parthasarathi

, Subramanian

and Chattaraj

P.K.

, The Journal of Physical Chemistry A 2007, 111.

45.

Parr

R.G.

and Yang

Density functional Theory of Atoms and Molecules; Oxford University Press, Oxford, New York, (1989).

46.

Geerlings

, De Proft

and Langenaeker

, Chemical Reviews 2003, 103.

47.

Parr

R.G.

and Pearson

R.G.

, Journal of the American Chemical Society 1983, 105.

48.

Parr

R.G.

, Szentpály

L.v.

and Liu

, Journal of the American Chemical Society 1999, 121.

49.

Flippin

L.A.

, Gallagher

D.W.

and Jalali-Araghi

, The Journal of Organic Chemistry 1989, 54.

50.

Cremer

and Kraka

, Croat. Chem. Acta, 1984 57, 1259.

51.

Palusiak

, J Organometallic Chem 2005 692, 3866.

52.

Macchi

and Sironi

, Coordination Chemistry Reviews 2003 239, 383.