Realgar, α-As4S4, is an ancient compound that has many important applications in diverse fields. It can be used as photoresists in optical and ultraviolet lithography, optical memory devices, and so on[1]. It can also be employed to obtain AsS3, As2S3, As2S, and AsS ligands that react as electron donors for transition-metal complexes in coordinating chemistry[2-6]. In addition, as traditional Chinese medicine, realgar has been administered to treat a variety of diseases, including syphilis, "malignant" sores, malaria and several other parasitic infections since ancient time. Modern studies have shown that realgar can offer therapeutic benefits to different types of leukemia[7-12] and a variety of cancer[13-17], whether given alone or in combination with other Chinese herbal medicines.
There have been many reports on the structures, polymorphs and the phase transformation of realgar[18-35]. α-As4S4 (P21/n)[18-21] is a low-temperature phase of realgar. The structure of α-As4S4 is a cradle shaped eight-membered ring with D2d symmetry[22]. β-As4S4 (C2/c)[21, 23, 24] is a higher-temperature phase, which is stable above about 260 ℃ and slowly reconverts to the α-As4S4 upon cooling. The β-As4S4 can be obtained by heating natural realgar above the transition temperature 252 ℃ or heating a mixture of As and S in stoichiometric proportion. Both α-As4S4 and β-As4S4 have the same D2d symmetric geometry but different packing in solid state[24]. Upon exposure to visible light, both α-As4S4 and β-As4S4 transform into another As4S4 polymorph termed pararealgar (P21/n) which has a CS molecular symmetry, different from α-As4S4 and β-As4S4[25, 26]. As4S4(II) is the fourth As4S4 polymorph, which has the same molecular structure as pararealgar but different spatial accumulation patterns. As4S4(II) can be synthesized by re-crystallizing quenched As4S4 melt from 500~600 ℃ to room temperature[27]. Another phase termed χ-As4S4 was found to be an intermediate between realgar and pararealgar[28]. Subsequently, χ-As4S4 was identified not to be polymorph of As4S4, but a mixture of β-As4S4 and As4S5 in essence[29].
For arsenic can readily change its oxidation state and molecular configuration in the natural environment, it is difficult to study the structure, polymorphs and their transformations of As4S4. As referred above, there have been four known As4S4 polymorphs, i.e., α-As4S4, β-As4S4, pararealgar and As4S4(II). And there have been two known geometries of As4S4 with D2d and CS molecular symmetries, respectively. Is there any other possible geometry of As4S4 that has not been characterized? How is the thermodynamic stability of these isomers? To answer these questions, the As4S4 isomers were investigated in the present paper by computational quantum chemistry. It is hoped to provide some valuable information for the widely-used realgar and its relative isomers.
All calculations were carried out using the Gaussian 09 program package[36]. The geometries of the ten As4S4 isomers were fully optimized at the B3LYP/6-31G*, B3LYP/6-311+G*, B3LYP/6-311+G(3df, 2p), and MP2/(6-311+G*, LanL2MB) levels of theory. Harmonic vibrational frequency analyses were carried out at the same levels to check whether the obtained structure is a local minimum (frequencies are all real) or a transition state (having imaginary frequency). Natural bond orbital (NBO) analyses were carried out at the B3LYP/6-31G* level of theory for some As4S4 isomers. Throughout this paper, bond lengths were provided in angstroms (Å), bond angles in degrees and relative energies in kcal⋅mol-1 unless otherwise stated.
As shown in Fig. 1 and Table 1, ten isomers of As4S4 (isomers 1 to 10) are located as minima. As realgar molecule, isomer 1 is the most stable structure among the ten isomers. The molecular geometry of isomer 1 was firstly established due to the work of Buerger[18], Lu and Donohue[22] and Ito et al.[19]. It consists of a tetrahedron of As atoms bisected by a square planar arrangement of sulfur atoms. Babić and Rabii[37, 38] performed local-density pseudopotential calculation and putted forward that it is the As–As bond contributes largely to the stability of isomer 1. Later, Banerjee et al.[39] performed a theoretical study on the bonding, infrared and Raman spectra of the D2d symmetric As4S4. For isomer 1, the experimental bond lengths for As–S and As–As are 2.24 and 2.57 Å, respectively[40]. The present study shows that the calculated bond length for As–S is 2.230 (B3LYP/6-31G*), 2.070 (B3LYP/6-311+G*), 2.252 (B3LYP/6-311+G(3df, 2p)), and 2.309 Å (MP2/(6-311+G*, LanL2MB)). The calculated bond length for As–As is 2.532, 2.643, 2.632, and 2.916 Å at the above four levels of theory, respectively. It can be seen that the calculated results at the B3LYP/6-31G* level of theory compare well with the experimental ones. However, because of the included f orbital function, the result obtained at the B3LYP/6-311+G (3df, 2p) level is usually considered to be more reliable than those at the B3LYP/6-31G* and B3LYP/6-311+G* levels. It can also be seen that the bond length calculated at the MP2/(6-311+G*, LanL2MB) level of theory is longer than those of B3LYP levels. The covalent radii of As and S atoms are 1.19 and 1.02 Å, respectively. Clearly, the present calculated As–S bond length approaches to the sum of the covalent radii of As and S atoms (2.21 Å), and the calculated As–As bond length is a little larger than the doubleness of the covalent radius of As atom (2.38 Å). According to the present natural bond orbitals (NBO) study at the B3LYP/6-31G* level of theory, the Wiberg bond indexes (WBI)[41] of As–S and As–As are 0.85 and 0.98, respectively, which are close to the standard values of covalent single bond (1.0). Mulliken charge analysis shows that all positive charges distribute on the As atoms (about +0.05 per atom) while all negative charges on the S atoms (about –0.05 per atom). According to the bond lengths, WBI, and the charge distribution analysis, the As–S and As–As are covalent bonds.
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| Complexes | B3LYP/6-31G* | B3LYP/6-311+G* | MP2/6-311+G*, LanL2MB | B3LYP/6-311+G(3df, 2p) |
| Isomer 1(D2d) | –10528.05290 | –10536.59187 | –1614.65361 | –10536.63229 |
| Isomer 2(CS) | –10528.04172 | –10536.58618 | –1614.63850 | –10536.62533 |
| Isomer 3(CS) | –10528.00492 | –10536.55942 | –1614.61580 | –10536.60049 |
| Isomer 4(C2v) | –10528.00470 | –10536.55721 | –1614.61200 | –10536.59833 |
| Isomer 5(C1) | –10528.01073 | –10536.55382 | –1614.60907 | ---------- |
| Isomer 6(C1) | –10527.99901 | –10536.54309 | –1614.59512 | –10536.58640 |
| Isomer 7(C2) | –10527.98878 | –10536.53378 | –1614.58898 | –10536.57672 |
| Isomer 8(D2h) | –10527.99386 | –10536.53395 | –1614.57765 | –10536.57349 |
| Isomer 9(D2d) | –10527.98327 | –10536.52623 | –1614.57852 | –10536.57140 |
| Isomer 10(CS) | –10527.92224 | –10536.47718 | –1614.54028 | –10536.52637 |
Nucleus-independent chemical shift (NICS) is one of the criteria in probing aromaticity, which was proposed by Schleyer et al.[42]. NICS is based on the negative of the magnetic shielding computed, e.g., at or above the geometrical centers of rings or clusters. Systems with (significant) negative NICS values are aromatic. The more negative NICS, the more aromatic the system is[43]. In the present study, at the HF/6-311+G* level of theory, we calculated NICS (0.0) by placing a ghost atom at the geometric center of the molecule, as shown in Fig. 2. For isomer 1, the calculated NICS value is –16.6. According to the yardstick of the NICS value of benzene (–9.4 at the geometric center of benzene molecule and –11.3 above the geometric center of benzene molecule by 1.0 Å), it is suggested that isomer 1 may be aromatic.
The frontier molecular orbitals (FMOs) theory involving the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are one of the best theories to explain the chemical stability of a molecule[44]. The negative magnitude of HOMO and LUMO energies and their energy gap reflect the stability of molecules[45]. The energy levels of the frontier orbitals of isomer 1 were investigated at the B3LYP/6-31G* level of theory. For isomer 1, the energies are –6.73 and –2.36 eV for HOMO and LUMO, respectively. The HOMO-LUMO gap for isomer 1 is 4.37 eV, suggesting its thermodynamic stability.
To further investigate the bonding nature in isomer 1, as shown in Fig. 3, molecular orbital analyses were performed at the B3LYP/6-31G* level of theory. Including 3s and 3p electrons of the S atoms and 4s and 4p electrons of As atoms, there are in all 44 electrons, or 22 doubly occupied molecular orbitals (MOs) to analyze. As shown in Fig. 2, these orbitals range from the HOMO, MO98, down to MO77. All MOs contour figures were made by using the MOLDEN 3.7 program[46]. The MO77 is an A1 symmetric orbital with energy of –0.81199 a.u. As shown in Fig. 2, the MO77 is a completely delocalized σ-bonding MO formed from the s atomic orbitals (AOs) of all the As and S atoms. The presence of delocalized σ-bonding may render isomer 1 to be σ-aromatic and, consequently, to possess extra stability. The MO78 and MO79 are degenerate orbitals with E symmetry. Both of these two MOs are σ-bonding, consisting of the s AOs of one As and its two neighboring S atoms. The MO81 of B2 symmetry is an σ-bonding MO, which is formed from the s AOs of two adjacent As atoms. The MO85 of B2 symmetry has contribution mainly from the p AOs of As and S atoms. The two adjacent As atoms form σ- and π-bonding, and so do the two adjacent S atoms. The MO87 of A1 symmetry is mainly composed of p AOs of the As and S atoms. It is noted that the in-plane p AOs of the four S atoms form a delocalized four-centered σ-bonding that may make σ-aromatic, which contributes in stabilizing isomer 1. The MO90 and MO91 are degenerate orbitals with E symmetry. Both of these two MOs have σ-antibonding between the two adjacent As atoms, and σ- and π-bonding between the two adjacent S atoms. The MO94 is σ- and π-bonding between the two adjacent S atoms. The MO95 and MO96 are degenerate orbitals that consist of the p AOs of S atoms. Both two MOs are π-bonding. The MO97 of B2 symmetry mainly consists of the p AOs of As atoms, being σ- and π-bonding. The MO98 is the HOMO of A1 symmetry. It has σ- and π-antibonding between the adjacent S atoms. Because the HOMO is antibonding, isomer 1 is ready to lose electrons in chemical reaction. Although MO85, MO90, MO91, MO94, MO95 and MO96 all have π-bonding component, they seem to contribute a little in stabilizing isomer 1, which may be attributed to the long distance between the two adjacent S atoms. Moreover, owning to the high energy of MO97, it is inferred that the As–As bond is ready to break in chemical reaction. According to the investigation on the bonding in isomer 1, it seems that the delocalized σ-bonding plays an important role in stabilizing isomer 1, which also renders it to be σ-aromatic.
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| MO | Energy | Symmetry | MO | Energy | Symmetry | |
| MO77 | –0.811 99 | A1 | MO88 | –0.375 09 | E | |
| MO78 | –0.757 05 | E | MO89 | –0.375 09 | E | |
| MO79 | –0.757 05 | E | MO90 | –0.316 99 | E | |
| MO80 | –0.708 94 | B1 | MO91 | –0.316 99 | E | |
| MO81 | –0.667 57 | B2 | MO92 | –0.310 60 | B1 | |
| MO82 | –0.569 54 | A1 | MO93 | –0.297 90 | A1 | |
| MO83 | –0.549 05 | E | MO94 | –0.292 80 | B2 | |
| MO84 | –0.549 05 | E | MO95 | –0.278 28 | E | |
| MO85 | –0.412 90 | B2 | MO96 | –0.278 28 | E | |
| MO86 | –0.396 48 | A2 | MO97 | –0.248 24 | B2 | |
| MO87 | –0.380 64 | A1 | MO98 | –0.247 51 | A2 |
As listed in Table 3, isomer 2 is higher in energy than isomer 1 by 4.5 kcal⋅mol-1 at the B3LYP/6-311+G(3df, 2p) level of theory. Isomer 2 was found as a distinct mineralogical species and was termed as pararealgar by Roberts et al.[25]. Later, the crystal structure of isomer 2 was investigated by Bonazzi et al.[26]. As shown in Fig. 1, the geometry of isomer 2 is quite different from isomer 1. For isomer 2, the experimental bond lengths for As–S and As–As are 2.24 and 2.51 Å, respectively[40]. The present calculated bond lengths of As–S and As–As are compared with the experimental value. NBO analysis shows that the WBIs of S1–As5, S2–As5, S2–As7, S4–As7, S4–As6, and As5–As6 are 0.95, 0.97, 0.95, 0.93, 1.03, and 0.91, respectively, approaching to the standard values of covalent single bond (1.0). The calculated Mulliken charge distribution on the S1, S2, S4, As5, As6, and As7 atoms is –0.1, –0.06, –0.04, 0.07, 0.05, and 0.06, respectively. Obviously, both As–S and As–As are covalent bonds.
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| Complexes | B3LYP/6-31G* | B3LYP/6-311+G* | MP2/(6-311+G*, LanL2MB) | B3LYP /6-311+G(3df, 2p) |
| Isomer 1 (D2d) | 0.0 | 0.0 | 0.0 | 0.0 |
| Isomer 2 (CS) | 7.2 | 3.8 | 9.6 | 4.5 |
| Isomer 3 (CS) | 30.7 | 21.0 | 24.3 | 20.6 |
| Isomer 4 (C2v) | 30.8 | 22.3 | 26.7 | 21.9 |
| Isomer 5 (C1) | 26.9 | 24.3 | 28.1 | ---------- |
| Isomer 6 (C1) | 37.2 | 31.0 | 37.0 | 29.1 |
| Isomer 7 (C2) | 40.6 | 36.9 | 40.9 | 35.2 |
| Isomer 8 (D2h) | 37.3 | 36.7 | 48.1 | 37.2 |
| Isomer 9 (D2d) | 44.4 | 41.8 | 47.7 | 38.7 |
| Isomer 10 (CS) | 83.0 | 72.6 | 71.7 | 67.1 |
The energy levels of the frontier orbitals of isomer 2 were investigated at the B3LYP/6-31G* level of theory. The energies of the frontier orbitals are –6.63 and –2.45 eV for the HOMO and LUMO, respectively. The HOMO-LUMO gap for isomer 2 is 4.18 eV, suggesting it should be thermodynamically stable.
Isomers 3 to 10 are firstly reported in the present paper, detailed parameters of bond lengths and bond angles of eight optimized structures of As4S4 at the B3LYP/6-31G*, B3LYP/6-311+G*, B3LYP/6-311+G(3df, 2p), and MP2/(6-311+G*, LanL2MB) levels of theory are shown in Fig. 1. The lowest harmonic vibrational frequencies for each structure at these four levels of theory are listed in Table 4. It is clear that all these eight isomers are local minima on their potential energy surfaces.
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| Complexes | B3LYP/6-31G* | B3LYP/6-311+G* | MP2/(6-311+G*), LanL2MB) | B3LYP/6-311+G(3df, 2p) |
| Isomer 1 (D2d) | 112 | 107 | 104 | 107 |
| Isomer 2 (CS) | 114 | 109 | 106 | 107 |
| Isomer 3 (CS) | 57 | 50 | 51 | 50 |
| Isomer 4 (C2v) | 71 | 57 | 56 | 57 |
| Isomer 5 (C1) | 80 | 60 | 93 | ---------- |
| Isomer 6 (C1) | 79 | 70 | 76 | 73 |
| Isomer 7 (C2) | 100 | 87 | 87 | 90 |
| Isomer 8 (D2h) | 64 | 54 | 50 | 51 |
| Isomer 9 (D2d) | 72 | 73 | -7 | 62 |
| Isomer 10 (CS) | 56 | 50 | 64 | 51 |
The geometries of isomers 3 and 4 are both eight-membered rings formed by eight As–S bonds. Isomer 3 is CS symmetric, while isomer 4 is C2v symmetric. The energy of isomer 4 is very close to that of isomer 3, and is 0.1, 1.3, 2.4, and 1.3 kcal⋅mol-1 higher than that of isomer 3 at the B3LYP/6-31G*, B3LYP/6-311+G*, B3LYP/6-311+G(3df, 2p) and MP2/(6-311+G*, LanL2MB) levels of theory, respectively.
For isomers 3 and 4, Mulliken charge analysis shows that almost all positive charges distribute on the As atoms while all negative charges distribute on the S atoms. The energy levels of the frontier orbitals of isomers 3 and 4 were investigated at the B3LYP/6-31G* level of theory. The energies of the frontier orbitals of isomer 3 are –6.37 and –2.36 eV for the HOMO and LUMO, respectively, while the corresponding values for isomer 4 are –6.58 and –2.67 eV, respectively. The HOMO-LUMO gaps for isomers 3 and 4 are 4.01 and 3.91 eV, respectively, suggesting they should be thermodynamically stable. If isomers 3 and 4 could be found or synthesized, they might be used as widely as realgar (isomer 1) and pararealgar (isomer 2).
The symmetries of isomers 5, 6, and 7 are very low among the ten As4S4 isomers. Isomers 5 and 6 are both C1 symmetric, and isomer 7 is C2 symmetric. Although isomers 8 and 9 have higher symmetries than isomers 5~7, they have lower energies than these three isomers. It may be due to the volume repulsion, charge repulsion and ring tension caused by four adjacent arsenic atoms. Isomer 10 is CS symmetric containing a ternary ring. Compared with isomers 1~9, the energy of isomer 10 is significantly higher, indicating its thermodynamic stability is very poor. The ternary ring tension may be the main factor for the instability of isomer 10. Since the thermodynamic energies of isomers 5 to 10 are too high, it is speculated that some of them exist only as short-lived molecules. Except for isomer 8, isomers 5, 6, 7, 9, and 10 all contain -S–Sdisulfide bond, which may make them have certain biological activity.
As shown in Fig. 1, all of the As4S4 isomers have one common characteristic, i.e., each As atom connects with three atoms to form three chemical bonds, while each S atom connects with two atoms to form two chemical bonds. Among all structures tested, only those satisfying the above "rule" are finally found to be local minima. In addition, it is found that structures containing more five-membered rings are more stable than those containing less five-membered rings, and structures containing five-membered rings are more stable than those containing four-membered ring. For example, isomer 1 is more stable than isomer 2, and they both are more stable than isomers 5, 6, 7, and 8. These bonding and structural characteristics along with the relative stability could be attributed to the following facts: (1) For arsenic sulphide, the chemical bond and molecular structure are mainly determined by the electronic structure of the outermost shells of As and S atoms. In other words, the s and p orbitals of As and S atoms contribute mainly to the bonding. (2) Close-formed structure of arsenic sulphide exhibits maximum repulsive interaction between lone electron pairs. This kind of interaction not only affects the geometrical parameters of structures, but is one of dominant terms that determine the relative stability. Obviously, the repulsive interaction between lone electron pairs in a five-membered ring is smaller than that in a four-membered one. (3) The ring strain is another reason to explain why structures containing five-membered rings are more stable than those containing four-membered rings.
This work provides some valuable information for the widely-used realgar and its relative isomers. The geometries of ten isomers of As4S4 were fully optimized at the B3LYP/6-31G*, B3LYP/6-311+G*, B3LYP/6-311+G(3df, 2p), and MP2/(6-311+G*, LanL2MB) levels of theory. Harmonic vibrational frequency analyses show that all the ten As4S4 isomers are thermodynamically stable. Among these ten isomers, isomers 3~10 are firstly reported in the present paper. If isomers 3~10 could be found or synthesized, they will play a certain role in promoting the scientific research of realgar. The calculated NICS value indicates that isomer 1 is aromatic. The molecular orbitals analyses suggest that there is delocalized σ-bonding in isomer 1, which may render it to be σ-aromatic. Moreover, structure analyses show that only those structures of which each As atom connects with three atoms and each S atom connects with two atoms would be local minima.
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Figure 1 Geometries and configuration parameters of ten As4S4 isomers optimized at the B3LYP/6-31G*, B3LYP/6-311+G*, B3LYP/6-311+G(3df, 2p), and MP2/(6-311+G*, LanL2MB) levels of theory (Displayed distances are in Å and angles are in degrees)
Figure 2 Schematic diagram for the calculation of NICS (a ghost atom "Du(9)" at the geometric center of isomer 1)
Table 1. Total Energies (a.u.) and Zero-point Energies (kcal⋅mol-1) of Various Isomers at the B3LYP/6-31G*, B3LYP/6-311+G*, B3LYP/6-311+G(3df, 2p), and MP2/(6-311+G*, LanL2MB) Levels of Theory
| Complexes | B3LYP/6-31G* | B3LYP/6-311+G* | MP2/6-311+G*, LanL2MB | B3LYP/6-311+G(3df, 2p) |
| Isomer 1(D2d) | –10528.05290 | –10536.59187 | –1614.65361 | –10536.63229 |
| Isomer 2(CS) | –10528.04172 | –10536.58618 | –1614.63850 | –10536.62533 |
| Isomer 3(CS) | –10528.00492 | –10536.55942 | –1614.61580 | –10536.60049 |
| Isomer 4(C2v) | –10528.00470 | –10536.55721 | –1614.61200 | –10536.59833 |
| Isomer 5(C1) | –10528.01073 | –10536.55382 | –1614.60907 | ---------- |
| Isomer 6(C1) | –10527.99901 | –10536.54309 | –1614.59512 | –10536.58640 |
| Isomer 7(C2) | –10527.98878 | –10536.53378 | –1614.58898 | –10536.57672 |
| Isomer 8(D2h) | –10527.99386 | –10536.53395 | –1614.57765 | –10536.57349 |
| Isomer 9(D2d) | –10527.98327 | –10536.52623 | –1614.57852 | –10536.57140 |
| Isomer 10(CS) | –10527.92224 | –10536.47718 | –1614.54028 | –10536.52637 |
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Table 2. Energies (a.u.) and Symmetries of Some Molecular Orbitals (MOs) of Isomer 1 at the B3LYP/6-31G* Level of Theory
| MO | Energy | Symmetry | MO | Energy | Symmetry | |
| MO77 | –0.811 99 | A1 | MO88 | –0.375 09 | E | |
| MO78 | –0.757 05 | E | MO89 | –0.375 09 | E | |
| MO79 | –0.757 05 | E | MO90 | –0.316 99 | E | |
| MO80 | –0.708 94 | B1 | MO91 | –0.316 99 | E | |
| MO81 | –0.667 57 | B2 | MO92 | –0.310 60 | B1 | |
| MO82 | –0.569 54 | A1 | MO93 | –0.297 90 | A1 | |
| MO83 | –0.549 05 | E | MO94 | –0.292 80 | B2 | |
| MO84 | –0.549 05 | E | MO95 | –0.278 28 | E | |
| MO85 | –0.412 90 | B2 | MO96 | –0.278 28 | E | |
| MO86 | –0.396 48 | A2 | MO97 | –0.248 24 | B2 | |
| MO87 | –0.380 64 | A1 | MO98 | –0.247 51 | A2 |
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Table 3. Energy Differences Relative to Isomer 1 (kcal⋅mol-1) at the B3LYP/6-31G*, B3LYP/6-311+G*, B3LYP/6-311+G(3df, 2p), and MP2/(6-311+G*, LanL2MB) Levels of Theory
| Complexes | B3LYP/6-31G* | B3LYP/6-311+G* | MP2/(6-311+G*, LanL2MB) | B3LYP /6-311+G(3df, 2p) |
| Isomer 1 (D2d) | 0.0 | 0.0 | 0.0 | 0.0 |
| Isomer 2 (CS) | 7.2 | 3.8 | 9.6 | 4.5 |
| Isomer 3 (CS) | 30.7 | 21.0 | 24.3 | 20.6 |
| Isomer 4 (C2v) | 30.8 | 22.3 | 26.7 | 21.9 |
| Isomer 5 (C1) | 26.9 | 24.3 | 28.1 | ---------- |
| Isomer 6 (C1) | 37.2 | 31.0 | 37.0 | 29.1 |
| Isomer 7 (C2) | 40.6 | 36.9 | 40.9 | 35.2 |
| Isomer 8 (D2h) | 37.3 | 36.7 | 48.1 | 37.2 |
| Isomer 9 (D2d) | 44.4 | 41.8 | 47.7 | 38.7 |
| Isomer 10 (CS) | 83.0 | 72.6 | 71.7 | 67.1 |
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Table 4. The Lowest Frequency of Various Isomers at the B3LYP/6-31G*, B3LYP/6-311+G*, B3LYP/6-311+G(3df, 2p), and MP2/(6-311+G*, LanL2MB) Levels of Theory
| Complexes | B3LYP/6-31G* | B3LYP/6-311+G* | MP2/(6-311+G*), LanL2MB) | B3LYP/6-311+G(3df, 2p) |
| Isomer 1 (D2d) | 112 | 107 | 104 | 107 |
| Isomer 2 (CS) | 114 | 109 | 106 | 107 |
| Isomer 3 (CS) | 57 | 50 | 51 | 50 |
| Isomer 4 (C2v) | 71 | 57 | 56 | 57 |
| Isomer 5 (C1) | 80 | 60 | 93 | ---------- |
| Isomer 6 (C1) | 79 | 70 | 76 | 73 |
| Isomer 7 (C2) | 100 | 87 | 87 | 90 |
| Isomer 8 (D2h) | 64 | 54 | 50 | 51 |
| Isomer 9 (D2d) | 72 | 73 | -7 | 62 |
| Isomer 10 (CS) | 56 | 50 | 64 | 51 |
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