A Comprehensive Theoretical Investigation of the Molecular Properties of Methyl Bromide (CH3Br)

VSEPR Theory and Molecular Geometry
VSEPR Theory and Molecular Geometry

Abstract

The properties of the ground and the lowest excited state of methyl bromide (CH3Br) have been studied with and without inclusion of the solvent effects in this work. The geometric parameters, energies, and frequencies of the ground state and the triplet state are calculated by using the MP2(full)/6-311++G** level of theory. The vertical excitation for the singlet state is also investigated. It is found that the theoretical results performed by the TDDFT/B3P86/6-311++G** method are in the best agreement with the experimental results. In addition, the dissociation energy of CH3Br molecule is computed at MP2(full)/6-311++G** level of theory for the gas phase and in water. The ionisation potential (IP), electron affinity (EA), electronegativity (χ), electrophilicity index (ω), hardness (η), softness (S), and chemical potential (μ) values are calculated from HOMO-LUMO energies both in the gas phase and in solvent (water). These theoretical results could serve as a guide for future experimental investigations.

1 Introduction

Because of its ozone depletion potential, methyl bromide (CH3Br) has received a great deal of attention recently [1]. A recent report shows that methyl bromide is the largest container of atmospheric bromide and accounts for 10% of the loss of stratospheric ozone on Earth [2]. Produced from natural and anthropogenic sources, bromine atoms could destroy the atmospheric ozone with a 40 times more efficient rate than chlorine atoms [3]. Compared to the corresponding chlorine-containing molecules, the ultraviolet absorption bands of bromine-containing molecules are red-shifted by several tens of nanometers. The first absorption band in CH3Br ranges between 170 nm and 270 nm. The strongest absorption feature is centered at 200 nm [4] and a lifetime of 120 fs [5].

Excitation from the ground state can result in three excited states denoted as 3Q0, 3Q1, and 1Q1 as defined by Mulliken [6]. It has been experimentally found [5] that two dissociation channels (i) CH3Br+hν→CH3+ Br(2P3/2) and (ii) CH3Br+hν→CH3+Br(2P1/2) take place in CH3Br. Experimental studies about the molecule’s photodissociation have been performed in several laser wavelengths [7–11]. A recent experiment of photodissociation of CH3Br at 193 nm shows the CH3· radical in four vibrational states and three continuous bands [12]. Until now, very few studies have reported the properties of CH3Br in excited states [13], whereas the properties of CH3Br in the ground and low-lying excited states are necessary to be addressed. Hence, we investigate the properties of CH3Br in this work.

This article is outlined as follows. In Section 2, the theoretical method and calculation details are introduced. The results of the geometric parameters, the HOMO-LUMO analysis, and the dissociation energy of CH3Br are demonstrated in Section 3. The conclusion part in Section 4 gives a summary.

2 Computation Methods

All the calculations are accomplished using the Gaussian 09 package [14]. The geometries and energies of electronic states are computed by the second-order Moller-Plesset perturbation-theory (MP2) [15, 16] in adjunction with 6-311++G** basis set. Vibration frequency calculation at the same level of theory is performed to ensure that the geometry is really stable. In addition, the dissociation energy of CH3Br is obtained at the same theoretical level. The absorption spectra of CH3Br are investigated as well. The results calculated by the TDDFT/B3P86/6-311++G** method [17, 18] are found to be in the best agreement with the experimental data.

Frontier molecular orbital (HOMO and LUMO) analysis of CH3Br has been performed to obtain information about ionisation potential (IP), electron affinity (EA), electronegativity (χ), electrophilicity index (ω), hardness (η), softness (S), and chemical potential (μ). In this work, we evaluate the solvent effects on the properties of the CH3Br molecule with the integral equation formalism polarisable continuum model (IEFPCM) [19]. The water molecule was chosen as the solvent because of the abundance of water molecules in the atmosphere.

3 Results and Discussion

3.1 The Ground State and the Triplet State of CH3Br

Table 1 demonstrates the ground state geometric parameters of CH3Br using a myriad of methods and basis sets. It can be found that the geometric parameters at the MP2(full)/6-311++G** level of theory are in best agreement with the experimental data [20]. Therefore, the MP2(full)/6-311++G** level of theory is chosen for CH3Br. Figure 1 exhibits the ground state geometry of CH3Br with C1 symmetry. The C-Br bond length of 1.932 Å is smaller than the experimental value by 0.001 Å, whereas the C-H bond length of 1.087 Å is larger than the experimental value by 0.001 Å. The calculated HCH bond angle is 110.6°, which is in good agreement with the experimental value of 111.2°. The calculated HCBr bond angle is 108.4°, whereas there is no corresponding experimental data.

The calculated geometric parameters and experimental results of CH3Br at various methods and basis sets.

Level r(C-Br) r(C-H) ∠HCH
Observed [20] 1.933 1.086 111.2
CCSD/6-311++G** 1.945 1.089 110.6
CCSD(full)/6-311++G** 1.942 1.089 110.6
CCSD/aug-cc-pVDZ 1.955 1.097 111.1
MP2(full)/6-311++G** 1.932 1.087 110.6
MP2/6-311++G(2d,2p) 1.942 1.080 110.8
MP2(full)/6-311++G(2d,2p) 1.937 1.079 110.7
MP2/aug-cc-pVDZ 1.946 1.096 110.9
MP2/aug-cc-pVTZ 1.925 1.083 110.9
DFT/B3LYP/6-311++G** 1.964 1.086 111.1
DFT/B3LYP/6-31++G(d) 1.968 1.089 111.2
DFT/B3LYP/6-31++G(d,2p) 1.965 1.086 111.5

The unit of the bond length is Å, and the unit of the bond angle is °.

Figure 1: The ground state geometry of CH3Br in vacuum. The unit of the bond length is Å.

The ground state geometry of CH3Br in vacuum. The unit of the bond length is Å.

The triplet state’s geometry and energy at the MP2(full)/6-311++G** level of theory are computed either. The ground state energy is –1639462.98 kcal/mol, and the triplet state energy is –1639387.68 kcal/mol. The energy of the triplet state is higher than the energy of the ground state by 75.3 kcal/mol, which implies that the triplet state might be unstable. Figure 2 presents the triplet state geometry of CH3Br with C1 symmetry. The C-Br and C-H bond lengths are predicted to be 4.502 and 1.079 Å respectively, when the molecule is excited to the triplet state (13A). The substantial increase in C-Br bond length indicates strongly that the triplet state potential energy surface has the characteristics of a repulsive nature. The corresponding product channel is to form a CH3· radical and a Br atom. The stability of the ground state and triplet state geometries is further confirmed by vibration frequency analysis as shown in Table 2. It can be seen from the table that all the frequencies are real, which means that these geometries are stable. It can also be seen that the vibrational strengths are the largest at wave numbers of 1385 and 3126 cm−1, which correspond to the CH3 umbrella vibration and stretching vibration, respectively. As for the triplet state, the vibrational strength is the largest at a wave number of 470 cm−1, which corresponds to the CH3 rocking vibration.

Figure 2: The triplet state geometry of CH3Br in vacuum. The unit of the bond length is Å and the unit of the bond angle is °.

The triplet state geometry of CH3Br in vacuum. The unit of the bond length is Å and the unit of the bond angle is °.

Vibrational frequencies (in cm−1) of the ground and triplet state of bromomethane.

State Frequencies (with corresponding strength in the brackets)
Ground 649 (9.17), 993 (5.19), 993 (5.20), 1385 (25.78), 1489 (5.06), 1490 (5.05), 3126 (18.57), 3241 (2.44), 3242 (2.41)
Triplet 44 (0.01), 49 (0.01), 94 (0.23), 470 (90.17), 1442 (4.27), 1445 (2.11), 3176 (0.77), 3367 (3.47), 3372 (0.97)

To have a good comprehension of the charge transfer in the excitation processes, we have also analyzed the charge distribution for CH3Br in different electronic states. Figure 3 exhibits the charge distributions in the ground state, the triplet state, and the first excited state for CH3Br. It can be inferred from the figure that the CH3· radical donates an electron, and the Br atom accepts an electron when the molecule is induced to the first excited state. On the contrary, there is the electron transfer from the Br atom to the C atom when the molecule transitions from the singlet state to the triplet state. These charge transfer processes are interesting, because each atom plays very different roles when CH3Br is excited to different states. These phenomena will have potential use in optical-electronics conversion.

Figure 3: The charge distribution diagrams for CH3Br in the ground state, the triplet state, and the first excited state.

The charge distribution diagrams for CH3Br in the ground state, the triplet state, and the first excited state.

3.2 Excitation and Emission Properties of CH3Br

The vertical excitation energies of the singlet excited states of CH3Br are calculated based on the ground state geometry. Table 3 presents the vertical excitation energies obtained from different methods (TDDFT and CIS) and basis sets. TDDFT results are more adequate than the CIS results compared with the experimental data. The results calculated by the TDDFT/B3P86 method are the closest to the experimental data. In addition, the energies calculated by B3P86/aug-cc-pVDZ are much closer to the experimental data than the values calculated by B3P86/6-311++G**. Overall, the results obtained from the TDDFT (B3P86/aug-cc-pVDZ) method are in best agreement with the experimental data.

Vertical excitation energies (in nm) for low-lying excited electronic states of CH3Br based on the geometry of MP2(full)/ 6-311++G** level along with the experimental results.

CH3Br X1A′→11A″ X1A′→21A″
Experiment [4, 5] 200 160.46
TD-PBE/6-311++G** 217.94 195.40
TD-PW91/6-311++G** 219.15 196.19
TD-B3P86/6-311++G** 202.77 175.25
TD-B3LYP/aug-cc-pVDZ 208.95 185.84
TD-PBE/aug-cc-pVDZ 218.10 196.14
TD-PW91/aug-cc-pVDZ 219.03 198.14
TD-B3P86/aug-cc-pVDZ 202.66 (197.73) 174.93 (171.33)
TD-B3LYP/6-311++G** 208.93 185.42
RCIS/6-311++G** 175.83 156.23

The data in brackets stands for the calculated results considering the solvent effects.

The absorption spectrum is presented in Figure 4. Some peaks (in blue color) in the absorption spectrum correspond to the excitation to different states from the ground state. The emission energies from the low-lying excited states to the ground state are also computed at TDDFT/B3LYP level. The fluorescence emission spectrum is also exhibited in Figure 4, with the blue peak corresponding to the transition from the first excited state to the ground state. It is found that the emission energies using different basis sets are quite different. The emission wavelength at TD-B3LYP/6-31G(d) level is 1226 nm, whereas the wavelength at TD-B3LYP/aug-cc-pVDZ is 1467 nm. Because there is no equivalent experimental data for comparison, it is difficult to judge which method gives the most satisfactory result.

Figure 4: The absorption spectrum of CH3Br at the TD-B3LYP/6-31G(d) level (a) and the fluorescence emission spectrum from the lowest excited state to the ground state at the same theoretical level (b); the absorption spectrum of CH3Br at the TD-B3LYP/aug-cc-pVDZ level (c) and the fluorescence emission spectrum from the lowest excited state to the ground state at the same level (d).

The absorption spectrum of CH3Br at the TD-B3LYP/6-31G(d) level (a) and the fluorescence emission spectrum from the lowest excited state to the ground state at the same theoretical level (b); the absorption spectrum of CH3Br at the TD-B3LYP/aug-cc-pVDZ level (c) and the fluorescence emission spectrum from the lowest excited state to the ground state at the same level (d).

3.3 Dissociation Energy and Frontier Molecular Orbital Analysis of CH3Br

The dissociation energies for the ground state and the triplet state of CH3Br are listed in Table 4. The dissociation energies for the singlet state and the triplet state are 68.96 kcal/mol and 177.39 kcal/mol, respectively. Because the triplet state needs more dissociation energy than the counterpart of the ground state, the channel of CH3Br(X1A′)→CH3(2A)+1/2Br is much easier to happen than the channel of CH3Br(X3A′)→CH3(2A)+1/2Br.

Dissociation energies of the ground and triplet state of bromomethane (in kcal/mol).

State Dissociation energy (kcal/mol)
CH3Br(X1A′)→CH3(2A)+1/2Br 68.96 (69.47)
CH3Br(X3A′)→CH3(2A)+1/2Br 177.39

The data in brackets stands for the calculated result incorporating the solvent effects.

It is known that the highest occupied molecular orbital (HOMO) and the lowest-lying unoccupied molecular orbital (LUMO) are regarded as frontier molecular orbitals (FMOs). The FMOs have important roles in the electric and optical properties, with wide applications in quantum chemistry, chemical reactions, and UV–VIS spectra [21]. The HOMOs contain electrons with the ability to donate an electron, whereas LUMOs have no electrons, acting as electron acceptors. There is a HOMO–LUMO energy gap (EGap) between these orbitals, and it determines the kinetic stability, chemical reactivity, optical polarisability, chemical hardness or softness, and the eventual charge transfer processes within the molecule. A large energy gap means a hard molecule, and a small energy gap means a soft molecule [22]. In this study, the HOMO and LUMO orbital energies of CH3Br were calculated at MP2(full)/6-311++G** level of theory in the gas phase and in water (IEF-PCM model). The results show that CH3Br has 22 occupied molecular orbitals. As is shown in Figure 5, the HOMO and LUMO energies along with the energy gap (EGap) for CH3Br are –10.935, 1.044, and 11.979 eV in the gas phase; the corresponding values in solvent (water) are –11.167, 1.244, and 12.411 eV, respectively.

Figure 5: The frontier molecular orbitals (HOMO and LUMO) of the CH3Br molecule calculated at MP2(full)/6-311++G** level for gas phase and in solvent (water).

The frontier molecular orbitals (HOMO and LUMO) of the CH3Br molecule calculated at MP2(full)/6-311++G** level for gas phase and in solvent (water).

The energies of HOMO and LUMO are also related to the ionisation potential (IP=–EHOMO) and electron affinities (EA=–ELUMO). The other important properties, such as global hardness (η=(IP–EA)/2), global softness (S=1/η), electronegativity (χ=(IP+EA)/2), chemical potential (μ=–χ), and electrophilicity index (ω=μ2/2η), are also calculated from HOMO and LUMO energy values [23, 24]. All of these parameters were computed and the results are presented in Table 5. As can be seen from Figure 5 and Table 5, the CH3Br molecule presents high chemical stability because of a high energy gap and low reactivity. The chemical potential (μ) value of CH3Br is negative, which indicates that the molecule is stable. The chemical hardness (η) value is considerably high; hence, CH3Br is chemically stable. As an important parameter for a molecule, the calculated dipole moment values in the gas phase and in water for CH3Br are high. This means that the CH3Br molecule has strong intermolecular interactions.

Frontier molecular orbital energies, HOMO–LUMO energy gap (EGap) and global reactivity descriptors for CH3Br at MP2(full)/ 6-311++G(d,p) level both gas phase and in solvent (water).

Parameters Gas phase Solvent (water)
EHOMO (eV) –10.935 –11.167
ELUMO (eV) 1.044 1.244
EGap (eV) 11.979 12.411
Ionisation potential, IP (eV) 10.935 11.167
Electron affinity, EA (eV) –1.044 –1.244
Electronegativity, χ (eV) 4.946 4.962
Chemical hardness, η (eV) 5.990 6.206
Chemical softness, S (eV−1) 0.1669 0.1611
Chemical potential, μ (eV) –4.946 –4.962
Global electrophilicity index, ω (eV) 2.042 1.984
Dipol moment (D) 2.230 2.321

3.4 Evaluation of the Solvent Effects on the Properties of the CH3Br Molecule

It is necessary to evaluate the solvent effects on the properties of the CH3Br molecule because there are plenty of water molecules in the atmosphere. In this work, the integral equation formalism polarisable continuum model (IEFPCM) [19] is adopted to evaluate the solvent effects on the properties of the CH3Br molecule. The excitation energies including the solvent effects can be seen in the parentheses of Table 3.

In the current work, we have calculated 20 allowed excitation transitions both in the gas phase and in water. The lowest-lying excited states are selected to make a comparison between the experimental results and the calculated results. The listed results show that the solvent effect could result in blue-shift in the absorption spectra. The calculated dissociation energy with the inclusion of solvent effects is shown in Table 4 in parentheses. The similar dissociation energies in the gas phase and in water imply the minor role of solvent effects on the CH3Br molecule. Let us look at how solvent affects molecular orbital energies. In Figure 5, the HOMO energy is –10.935 eV in the gas phase, whereas it is lowered to –11.167 eV in solvent (water). As for the LUMO energy, it is 1.044 eV in the gas phase while increased to 1.244 eV in solvent (water). Therefore, the solvent has induced a larger energy gap (12.411 eV) in water than the corresponding value (11.979 eV) in the gas phase.

Table 6 presents the geometric parameters and energies for the ground state (11A) and triplet state (13A) of CH3Br at the MP2(full)/6-311++G** level of theory, with the results incorporating the solvent effects in parentheses. It has been found that the geometries are only slightly changed when incorporating the solvent effects. Overall, the solvent effect is not very obvious in the properties of the CH3Br molecule.

The geometric parameters and energies of the ground state (11A), triplet state (13A) of methyl bromide.

State r(C-H) r(C-Br) ∠HCH Energy
Observed [20] 1.086 1.933 111.2
Ground 1.087 (1.087) 1.938 (1.938) 110.9 (110.9) –1639462.98
Triplet 1.080 4.402 120.0 –1639387.68

The data in brackets stands for the calculated result incorporating the solvent effects. The unit of the bond length is Å, the unit of the bond angle is °, and the unit of energy is in kcal/mol.

4 Conclusions

The ground and low-lying excited states of the CH3Br molecule have been investigated in this work. The geometric parameters, energies, and frequencies of the ground state and the triplet state have been calculated. Based on the triplet state structure, the repulsive nature of the triplet state potential energy surface is explained. It has been found that the excitation energies obtained by the TDDFT/B3P86/aug-cc-pVDZ method are in best agreement with the experimental data. We understand that the CH3Br molecule has a high chemical stability after the frontier molecular orbital and other related analyses. In addition, the solvent effects are found to be minor in the properties of CH3Br. This work represents a comprehensive study of CH3Br, which could serve as a guide for future research.

Acknowledgments

We thank Shenyang National Lab of Material Science and Ondokuz Mayis University for supporting this research. The reviewers are also acknowledged for many helpful and constructive suggestions.

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