Anisotropic dissociation and spectral response of 1-Bromo-4-chlorobenzene under static directional electric fields

3.1 Geometric configuration of C₆H₄BrCl at ground state

Initial structural optimizations of 1-Bromo-4-chlorobenzene were performed using the methods and basis sets listed in Table 1 under zero-field conditions. The B3LYP/6-311G(d,p) methodology demonstrated optimal agreement with experimental bond lengths (R) and bond angles (A) from the NIST Chemistry WebBook database, and was therefore selected for subsequent electric field simulations. As shown in Figure 1, the optimized molecular geometry adopts a Cartesian coordinate system (x, y, z), with halogen atoms (Br and Cl) aligned along the X-axis. This spatial arrangement guided the application of external electric fields along the ±X-axis to systematically probe the molecule’s electronic behavior and dissociation mechanisms.

Figure 1:

Stable structure of 1-Bromo-4-chlorobenzene molecule without external electric field (DFT B3LYP 6-311G(d,p)basis, 6C–11Br bond length is 1.91609 Å, 3C–12Cl bond length is 1.75736 Å, energy is −3265.471570 a.u.).

It should be emphasized that density functional theory (DFT) calculations fundamentally depend on the harmonic oscillator approximation. This approach may introduce errors due to truncation of the potential energy surface’s Taylor expansion, particularly affecting predicted bond dissociation and molecular degradation pathways in systems exhibiting significant anharmonic effects. Computational accuracy – especially for Raman spectra and vibrational properties – is substantially influenced by methodological choices, particularly the selection of functionals and basis sets [18]. To evaluate this sensitivity, we employed the B3LYP functional (demonstrating <0.3 ppm mean absolute error and >0.98 correlation with experimental Raman intensities [19]) with comparative basis sets (def-TZVP and 6-311G(d,p)), with detailed benchmarking data provided in Supplementary Materials.

3.2 Physical properties of C₆H₄BrCl molecule under an applied external electric fields

The 1-Bromo-4-chlorobenzene molecule was optimized using the B3LYP/6-311G(d,p) methodology. External electric fields ranging from −0.025 to 0.025 atomic units were systematically applied along the ±X-axis. The resulting geometric parameters of the molecule under these conditions are comprehensively detailed in Table 2.

As shown in Figure 2, the C–Br bond length increases progressively with increasing electric field strength, while the C–Cl bond length decreases accordingly. This anisotropic trend arises from the directional application of the electric field along the C–Br bond axis. Under this field, the electron density within the molecule is redistributed asymmetrically, generating an internal polarization field that enhances the asymmetry of the bonding environment [20], 21]. Specifically, the C–Br bond, being more polar and associated with the more polarizable Br atom, experiences a net weakening under the applied field, leading to bond elongation and a reduction in dissociation energy. In contrast, the C–Cl bond lies opposite to the field direction and is subjected to a compressive electrostatic effect, resulting in bond shortening and potential strengthening [22]. This field-induced differential response is further supported by the polar nature of the molecule and the Stark-like modulation of frontier orbital energies, which alters the bonding–antibonding orbital overlap. Such asymmetric structural evolution under the electric field provides mechanistic insight into bond-selective weakening and offers a theoretical basis for the field-controlled dissociation pathways discussed in later sections.

Figure 2:

The change of C₆H₄BrCl bond length under different external electric field.

Our comparative analysis of B3LYP/6-311G(d,p) and B3LYP/def2-TZVP computational results (Supplementary Tables S1) reveals minimal dependence on methodology for C–Br and C–Cl bond length variations. Both methods show identical directional changes, demonstrating consistent bond elongation trends regardless of functional or basis set selection. Although slight differences exist in absolute bond length values between methods, these variations fall within accepted computational tolerances. Thus, qualitative dissociation trends remain reliable while absolute values may exhibit minor method-dependent fluctuations.

Figure 3 demonstrates a progressive increase in molecular dipole moment with rising electric field strength (±X-axis). This polarization effect arises from charge separation – positive and negative charges migrate in opposing field directions, elongating the molecular structure and enhancing polarity [23]. Total molecular energy initially increases then decreases with field intensification, following the potential energy relationship.

Figure 3:

The change of C₆H₄BrCl total energy and dipole moment under different external electric fields.

At 0.025 atomic units field strength, directional electron migration significantly enhances Coulombic attraction between charged moieties. Concurrent dipole moment amplification increases the absolute potential energy value in the Hamiltonian (H), thereby reducing total system energy. The inverse relationship holds for field reversal, confirming the bidirectional control of electronic behavior through applied fields. This behavior reflects a second-order (quadratic) Stark effect in the total energy, where the external electric field perturbs the molecular Hamiltonian through the dipole interaction term (μ·F) and higher-order polarizability contributions. At higher field strengths (e.g., ±0.025 a.u.), enhanced charge redistribution and field-induced orbital reordering reduce the net system energy by stabilizing the dipolar configuration aligned with the field. Consequently, the dipole moment and total energy exhibit inverse trends, indicating that the system becomes more stable as its polarization increases [21]. Moreover, the asymmetric energy profile with respect to field direction highlights the critical role of the intrinsic dipole orientation, confirming that the applied field can be exploited to bidirectionally tune the electronic structure, potential energy surface, and molecular reactivity [22].

3.3 The effect of an external electric field on molecular charge and molecular orbitals

Using the aforementioned methodology and basis set, we analyzed the Natural Bond Orbital (NBO) charge distribution of 1-bromo-4-chlorobenzene under external electric fields ranging from −0.025 to +0.025 a.u., as summarized in Table 3. The results indicate that the applied electric field significantly modulates intramolecular electron distribution. Pairs of symmetry-related atoms (e.g., 1C–5C, 2C–4C, 7H–10H, 8H–9H) maintain nearly identical charge values throughout the field range, confirming the molecule’s partial symmetry. Notably, the halogen atoms respond strongly to the applied field. At +0.025 a.u., atom 12Cl exhibits the most negative charge (−0.358), while 11Br displays the largest positive charge (+0.313) at −0.025 a.u. With increasing positive field strength (aligned along the C–Br bond axis), 11Br accumulates additional negative charge, while the adjacent carbon atom 6C becomes more electron-deficient. This charge redistribution reflects the electrostatic polarization of the molecule, wherein the external field enhances the electron-withdrawing effect of Br. As a result, electron density is pulled toward 11Br, effectively elongating the C–Br bond due to increased Coulombic repulsion and weakened orbital overlap between C and Br. Conversely, 12Cl shows a gradual increase in positive charge at higher positive fields, intensifying its electrostatic interaction with 3C and thus contributing to a shortening of the C–Cl bond. These trends are consistent with the bond length variations observed in Figure 2 and further confirm the field-induced charge-driven mechanism underlying bond asymmetry. Such analysis links localized atomic charges to global structural reorganization, and reveals the essential role of electronic polarization in determining field-responsive reactivity.

Using the same method and basis set, we computed the LUMO energy (E _L), HOMO energy (E _H), and the energy gap (E _G) for the C₆H₄BrCl molecule under varying external electric fields ranging from −0.025 a.u. to 0.025 a.u. where the energy gap (E _G) was calculated by Eq (3).

Variations in the LUMO energy (E _L) reflect a molecule’s electron-accepting capacity, with lower E_L values indicating enhanced electron affinity and a greater tendency for reduction reactions. Conversely, shifts in the HOMO energy (E _H) reveal electron-donating tendencies, where elevated E _H values correlate with reduced electron retention and increased likelihood of oxidation processes [24]. The HOMO-LUMO energy gap (E_G) further serves as a critical indicator of chemical reactivity: narrower E_G values correspond to diminished molecular stability and heightened propensity for chemical interactions [25]. Together, these parameters provide a comprehensive framework for understanding redox behavior and reaction dynamics under external stimuli.

As shown in Figures 4 and 5, the lowest unoccupied molecular orbital energy (E _L) initially increases before decreasing with rising field strength, while the highest occupied molecular orbital energy (E _H) follows an inverse trend, decreasing first and then increasing. This field-induced modulation of orbital energies reflects a second-order Stark effect, where the spatial redistribution of electron density in response to the field perturbs the molecular Hamiltonian. As a result, the energy gap (E _G) widens near zero field and narrows significantly as the field strength approaches ±0.025 a.u. The reduced energy gap facilitates electronic excitation, enhancing the probability of charge transfer and exciton generation. This is particularly relevant for optical absorption and photoreactivity, as lower excitation thresholds increase the likelihood of π → π* or n → π* transitions under external stimuli. Moreover, the narrowing of E _G under strong electric fields correlates with structural distortions – such as C–Br bond elongation and C–Cl bond contraction – observed in Figure 2. This indicates a coupled electronic–structural response: field-induced polarization not only reshapes the molecular geometry but also modifies its electronic reactivity landscape. The observed trends underline the potential for precise field control over reactivity, optical behavior, and electron transport in polar π-conjugated molecules like 1-bromo-4-chlorobenzene [22].

Figure 4:

Changes of E _L and E _H in C₆H₄BrCl under different external electric fields.

Figure 5:

Variation of C₆H₄BrCl molecular energy gap in external electric fields.

To achieve more accurate characterization of charge-transfer excitations and long-range electron interactions, we employed the CAM-B3LYP functional with long-range correction. This method effectively mitigates known deficiencies in electronic gap prediction associated with conventional DFT approaches such as B3LYP [26]. Supporting Information S4 presents the CAM-B3LYP/6-311G(d,p) calculated energy gap (E _G) evolution of 1-bromo-4-chlorobenzene under electric fields (−0.025 to +0.025 a.u.). The gap exhibits non-monotonic behavior – initially widening before narrowing, with maximum values occurring near zero field. This response pattern originates from electric-field-induced molecular polarization and frontier orbital reorganization. Notably, while CAM-B3LYP yields systematically larger E _G values than B3LYP/6-311G(d,p) due to enhanced treatment of long-range electron interactions, both methods demonstrate consistent gap modulation trends. This consistency confirms the intrinsic nature of field-responsive gap variation rather than computational artifacts. The observed agreement with GW method predictions further validates the theoretical framework for electric-field-controlled molecular responses [27].

3.4 The infrared spectral characteristics of the molecule under different external electric field

Structural optimization of 1-Bromo-4-chlorobenzene was performed using the B3LYP/6-311G(d,p) methodology. Subsequent analysis under external electric fields (0 a.u.∼0.025 a.u.) applied along the +X-axis revealed significant field-dependent modifications to the infrared spectral profile. As shown in Figure 6, the IR spectrum exhibits five prominent absorption bands. The strongest peak at 1,118.44 cm⁻¹ arises from 3C–12Cl stretching vibrations coupled with collective bending modes of 4C–9H, 5C–10H, 2C–8H, and 1C–7H. A secondary peak at 1,499.15 cm⁻¹ originates from bending vibrations of the aromatic 4C–9H, 5C–10H, 2C–8H, and 1C–7H groups. The 1,000.44 cm⁻¹ band corresponds to in-plane deformation vibrations of 3C–4C and 2C–3C bonds, combined with 5C–11Br stretching. Out-of-plane deformation modes of aromatic C–C and C–H bonds dominate the 825.84 cm⁻¹ absorption, while stretching vibrations of the 3C–12Cl and 6C–11Br bonds contribute to the 477.33 cm⁻¹ feature. These vibrational assignments highlight the interplay between molecular symmetry, bond dynamics, and external field effects.

Figure 6:

The variations of IR spectra of C₆H₄BrCl in external.

Magnified spectral analysis (Figure 7a) reveals a systematic redshift across the 142∼1,054 cm⁻¹ range under increasing electric fields, indicating reduced vibrational frequencies for all modes in this region. At 218.70 cm⁻¹, the enhanced Coulombic interaction between 6C and 11Br intensifies the C–Br stretching vibration amplitude. Conversely, the dominant 1,118.44 cm⁻¹ peak (3C–12Cl stretching mode) exhibits a blueshift with field intensification, as shown in Figure 7b. This counterintuitive blueshift arises from 12Cl’s electron-withdrawing nature. The X-axis-aligned field redistributes electron density toward 11Br, increasing net positive charge on 3C–12Cl. The amplified charge disparity elevates the C–Cl bond’s force constant, thereby increasing its vibrational frequency through the relationship ν ∝ k / μ . Field-induced C–Br redshift correlates with decreased bond dissociation energy, while the C–Cl blueshift reflects enhanced stability under identical conditions. These opposing trends underscore the bond-specific electronic responses to directional field effects.

Figure 7:

The variations of IR spectra of C₆H₄BrCl in external field (a) 142∼1,054 cm⁻¹; (b) 1,058∼1,200 cm⁻¹.

3.5 The Effect of an external electric field on the excited states of C₆H₄BrCl

To elucidate field effects on 1-Bromo-4-chlorobenzene properties, we employed TD-DFT/B3LYP with the 6-311G(d,p) basis set to calculate excitation energies, wavelengths, and oscillator strengths for the first nine excited states under positive-oriented electric fields (0 a.u.∼0.025 a.u.). These computational results are systematically presented in Table 4.

Excitation energy, defined as the energy difference between the ground and excited states, provides direct insight into the electronic excitation characteristics of 1-bromo-4-chlorobenzene under external electric fields. As shown in Table 4, all excitation energies (except the second excited state) decrease monotonically with increasing field strength, indicating that the applied field facilitates electronic excitation by lowering the energy barriers to higher-lying states. This trend is particularly pronounced for low-lying states, whose energy values decrease from 4.9843 eV to 3.1944 eV (S₁) as the field increases from 0 to 0.025 a.u. The corresponding redshift in excitation wavelengths – from 248.75 nm to 388.13 nm for S₁ – further confirms this behavior. The origin of this redshift lies in the field-induced narrowing of the energy gap (as seen in Figure 5), which reduces the energy required for π → π* transitions. Additionally, changes in oscillator strength (f) reveal that several transitions become allowed or forbidden depending on field intensity. For example, the S₈ state has a finite oscillator strength at 0 a.u. but vanishes at 0.025 a.u., suggesting that the field modulates transition dipole moments via changes in orbital symmetry and spatial overlap. From a physical standpoint, these observations can be attributed to the external field’s ability to polarize the molecular electron cloud and distort its geometry. This affects both the delocalization of frontier orbitals and the charge-transfer characteristics of excited states.

To address the systematic underestimation of excited-state energies by conventional hybrid functionals like B3LYP and approach GW-level accuracy, we performed complementary calculations using the long-range corrected CAM-B3LYP functional. As shown in Supporting Information S5, significant differences exist between B3LYP and CAM-B3LYP predictions for both absolute excitation energies and field-response trends of 1-bromo-4-chlorobenzene. The incorporation of long-range exchange in CAM-B3LYP raises excitation energies by 0.3∼1.0 eV compared to B3LYP, substantially improving descriptions of charge-transfer states and long-range excitations. Regarding field responses: while B3LYP shows a continuous decrease (redshift) in S₁ excitation energy with increasing field strength, CAM-B3LYP exhibits non-monotonic behavior – reaching a minimum at 0.020 a.u. before rising at 0.025 a.u. – reflecting heightened sensitivity to orbital reorganization and polarization effects. For higher excited states, B3LYP predicts more pronounced energy reductions versus CAM-B3LYP’s gradual variations, highlighting inherent methodological differences. Crucially, both functionals effectively capture essential field-responsive excitation phenomena relevant to optoelectronic studies.

3.6 Stepwise dissociation of molecules under external electric field

To investigate the electric field-driven dissociation behavior of 1-bromo-4-chlorobenzene, we conducted potential energy surface (PES) scans along the C–Cl and C–Br bond coordinates under varying external electric fields using the B3LYP/6-311G(d,p) level of theory. Figures 8 and 9 show the energy profiles for bond lengths ranging from ∼1 Å to ∼17 Å under field strengths between −0.030 and +0.030 a.u., with the field direction oriented along the C–Br bond axis. Under zero-field conditions, both bonds exhibit steep energy descents to global minima, followed by gradual increases in energy as the bond extends – reflecting their intrinsic covalent stability. However, the application of external fields alters this stability significantly and directionally. For the C–Cl bond (Figure 8), increasing negative electric fields progressively destabilize the bond. As the field strength grows from −0.005 to −0.030 a.u., the depth of the energy well shallows, and the dissociation energy drops notably. This is attributed to field-induced polarization, which drives electron density away from the C–Cl region, weakening orbital overlap and reducing the energy barrier for dissociation [28], 29]. Conversely, the C–Br bond (Figure 9) responds to positive electric fields, showing a clear reduction in dissociation energy as field strength increases from 0 to +0.030 a.u. Here, the highly polarizable Br atom accumulates excess negative charge under the field, increasing repulsion with the adjacent carbon and weakening the C–Br bond [30]. This effect becomes pronounced at field strengths beyond 0.020 a.u., where the dissociation process becomes nearly barrierless. These findings establish a field-dependent and directionally selective bond cleavage mechanism: negative fields facilitate C–Cl bond rupture, while positive fields promote C–Br dissociation. This behavior arises from asymmetric charge redistribution and modified electrostatic forces, illustrating the external field’s role in modulating molecular potential energy surfaces [31]. Such insights are valuable for designing field-assisted reaction pathways, targeted halogen bond cleavage, and environmental degradation of halogenated pollutants.

Figure 8:

The potential energy curves of C₆H₄BrCl along 3C–12Cl bond at various external electric fields.

Figure 9:

The potential energy curves of C₆H₄BrCl along 6C–11Br bond at various external electric fields.

As noted, the harmonic approximation in DFT calculations may introduce errors affecting predicted bond dissociation and degradation pathways. Our comparative calculations using B3LYP/6-311G(d,p) and B3LYP/def2-TZVP basis sets (Supplementary Materials, Tables S2-S3) reveal that C–Br bond dissociation energy exhibits minimal variation (<2 % difference), indicating its relative insensitivity to computational methodology. In contrast, C–Cl dissociation energy shows greater basis set dependence. Crucially, both basis sets produce consistent potential energy curves for bond elongation and dissociation pathways. This demonstrates that while absolute dissociation energies are method-dependent, the qualitative field-induced degradation mechanisms remain robust across computational approaches. Therefore, the findings of this study demonstrate robust reliability.

3.7 Comparison with pevious studies

Furthermore, our results were compared with previous studies on chlorobenzene under electric fields Liu et al. [32]. Their work reported progressive C–Cl bond elongation, HOMO–LUMO gap narrowing, and spectral redshifts with increasing positive field strength, which are fully consistent with our findings. By additionally considering the C–Br bond, the present study reveals field-selective degradation behavior: C–Cl bonds are preferentially destabilized under negative fields, whereas C–Br bonds are more susceptible under positive fields. This provides a more comprehensive mechanistic picture of field-controlled halogen bond rupture and extends the applicability of external-field modulation strategies to halogenated aromatic systems.