Vibrational Analysis of Benziodoxoles and Benziodazolotetrazoles

: Tetrazoles are well known for their high positive enthalpy of makes them attractive as propellants, explosives, and energetic materials. As a step towards a deeper understanding of the stability of benziodazolotetrazole (BIAT)-based materials compared to their benziodoxole (BIO) counterparts, we investigated in this work electronic structure features and bonding properties of two monovalent iodine precursors: 2-iodobenzoic acid and 5-(2-iodophenyl)tetrazole and eight hypervalent iodine (III) compounds: I -hydroxybenzidoxolone, I -methoxybenziodoxolone, I -ethoxybenziodoxolone, I - iso -propoxybenziodoxolone and the corresponding I -hydroxyben ziodazolotetrazole, I -methoxybenziodazolotetrazole, I -ethoxybenziodazolotetrazole and I - iso -propoxybenziodazolotetrazole. As an efﬁcient tool for the interpretation of the experimental IR spectra and for the quantitative assessment of the I − C, I − N, and I − O bond strengths in these compounds reﬂecting substituent effects, we used the local vibrational mode analysis, originally introduced by Konkoli and Cremer, complemented by electron density and natural bond orbital analyses. Based on the hypothesis that stronger bonds correlate with increased stability, we predict that, for both series, i.e., substituted benziodoxoles and benziodazolotetrazoles, the stability increases as follows: allow design new controlled performance iodine three local mode monitor the bond potential trigger bonds. We hope that this article will foster future collaboration between the experimental and computational community being engaged in vibrational spectroscopy.


Introduction
Organic polyvalent iodine (III) and (V) reagents have gained popularity as oxidants, electrophiles, and radical sources in various synthetically useful organic transformations [1][2][3][4][5][6][7][8], as well as in organometallics [9], materials, and polymer chemistries [10]. These compounds contain an iodine atom which bonds to a carbon atom via conventional 2-center-2-electron (2c-2e) covalent bond, but also to two or more ligands (L) via 3-center-4-electron (3c-4e) bonds [11,12], dubbed hypervalent (HV) [13]. According to this model, only p-orbitals of the central atom are involved in the formation of the 3c-4e bonds. Since publication of the aforementioned pioneering works, a number of additional studies have appeared in the literature discussing in more detail the nature of HV bonds [14][15][16][17]. The presence of weak HV bonds is largely responsible for the characteristic structural features of HV iodine (HVI) molecules (e.g., presence of the near-linear L−I−L fragment(s)), as well as for their stability and reactivity [18,19]. Donor atoms of the ligands must be electronegative (e.g., F, O, N, or Cl) to promote stability. Among said ligands, carboxylates are the most widely studied and HVI(III) compounds such as (dicarboxyloxy)iodo arenes (ArI(O 2 CR) 2 ) [20] with linear arrangements of O atoms from the ligands and the central iodine atom) and benziodoxoles (where the carboxylate ligand and the HVI atom form a ring) [8,21] have found numerous applications. Tetrazolates (RCN -4 ) resemble carboxylates (RCO -2 ) in many respects (e.g., basicity, nucleophilicity, and complexation ability [22]), which prompted Tsarevsky et al. to investigate the propensity of tetrazole (TZ) for bonding to iodine(III) atoms. Several examples of TZ-containing HVI(III) compounds were synthesized and studied, including acyclic [23], pseudocyclic (with iodonium-like structure) [24], and heterocyclic benziodoazotetrazole (BIAT) derivatives [25]. Each of these compounds, like their carboxylate analogues, are strong oxidants. However, unlike the caboxylates, when heated BIATs decompose vigorously and even explosively. TZs are well known for their high positive enthalpy of formation (∆H f ) [26][27][28][29], which makes them attractive as propellants, explosives, and energetic materials [30], but HV compounds with one or more tetrazolate ligands are markedly more unstable than the parent free ligands [23,24].
An important question has been raised: which molecular parameters make TZs so explosive, and, even more importantly, how can their thermal stability be controlled. To answer this question, Tsarevsky et al. determined the enthalpies of thermal decomposition (∆H d ) for BIAT derivatives with axial Cl, OH, OMe, and OAc ligands. However, they did not find any significant correlation between ∆H d and structural parameters (e.g., lengths of either of the HV bonds or L−I−N valence angles), nucleophilicity, or field electronic parameters of the ligand [25]. It has been suggested that crystal packing in the solid state, i.e., the shearing force between packing layers may well account for the (in)stability of TZs, influencing both temperatures of decomposition and ∆H d , which complicates any direct comparison between ∆H d and structural parameters [31][32][33]. A common way to answer this question from a theoretical perspective is to use bond dissociation energies (BDE) [34,35] as a tool to identify the so-called trigger bond, which is first to break and therefore assesses the stability of a material [36]. However, a caveat is needed. BDE is not a suitable way to measure the intrinsic strength of a chemical bond because it also contains geometry relaxation and electronic structure reorganization of the dissociated fragments [37][38][39][40][41][42][43]. Therefore, this work refers to the local vibrational mode (LMV) theory originally proposed by Konkoli and Cremer [44][45][46][47][48], which provides a quantitative measure of intrinsic bond strength based on vibrational spectroscopy [49].
As a step towards understanding more about the nature and stability of TZ-based energetic materials from an electronic structure perspective, this work investigates the iodinecontaining bond strengths in two precursor monovalent iodine compounds, 2-Iodobenzoic acid (IBA) and 5-(2-Iodophenyl)tetrazole (IPT), as well as in HVI(III) compounds derived thereof, namely substituted BIOs 1-4 and BIATs 5-8 (shown in Figure 1), utilizing local vibrational force constants derived from LVM. This work is complemented with electron density information and natural bond orbitals (NBOs) to assess and predict chemical bond properties which correlate with explosive capabilities, and to explore the suggestion that a strongly positive molecular center (i.e., iodine) may serve as a reliable indicator for sensitive materials [50][51][52]. In addition, this work applies another feature of the LMV theory: the comprehensive analysis of experimental (exp) IR spectra [46,48]. An overarching aim of this research is to inspire the experimental and theoretical chemistry communities working in the field of vibrational spectroscopy to foster future collaborations.   ) of iodine (purple), oxygen (red), carbon/hydrogen (black), and nitrogen (blue); calculated at the ωB97X-D/Def2-TZVP level of theory. Summed NBO charges of hydroxyl/alkoxy, carboxylate ester (OCO), tetrazole (TZ), and ortho-substituted benzene (Ar) groups are shown below each respective molecule. Note: For BIOs 2-4 and BIATs 6-8, the charges shown in black font to the left of molecule numbers are the total charges of the Me, Et, and iPr groups, respectively.

Computational and Experimental Methods
To validate the model chemistry used in this work, experimental geometry coordinates and IR frequencies of BIO-1 (see Tables 1 and 2) were utilized as benchmarks for several levels of theory. Table 1 shows comparison between experimental (exp) and theor geometry parameters, and Table 2 summarizes the statistical analysis of exp IR frequencies (ω (exp) ) and theor normal mode frequencies (ω µ ) of BIO-1; calculated using 13 levels of theory. The B3LYP [53][54][55][56], B3LYP-D3 [57], B3LYP-D3BJ [58], M06-2X [59], and ωB97X-D [60] density functionals were combined with the following basis sets: aug-cc-pVTZ-[PP for iodine] (acpVTZ-PP) [61][62][63][64][65][66], Def2-TZVP (TZVP) [67,68], Def2-TZVPP (TZVPP) [69,70]. The Def2-TZVPD basis set was also included, but only in combination with M06-2X because this level of theory was recently applied successfully for a computational study of phenomenal molecular systems containing λ 3 -iodanes acting as biaxial halogen bond (XB) donors [71]. For the theor vibrational frequencies, the following scaling factors were applied to correct for the harmonic approximation of the Morse potential [72][73][74][75][76][77][78][79]   The results of the first attempts to determine the molecular structure of I-hydroxyben ziodoxolone (BIO-1) were published in 1964 by Shefter and Wolf [80], who noted that the endocyclic I−O bond was markedly longer (2.30 Å) than the sum of the covalent radii of the two atoms, which was attributed to steric strain or greater ionic character compared to the normal covalent I−O bond. A more detailed analysis, including all bond lengths and valence angles in the molecule, was provided a year later by the same authors [81]. Unfortunately, the published structure is imprecise (which becomes apparent by simple inspection of the clearly nonplanar benzene ring) and no further structural data have been reported since the publication of the two aforementioned papers. We therefore prepared crystals of BIO-1 (by recrystallization from water) and were able to obtain a more accurate structure ( Figure 2). The complete experimental details and structural data are provided in the Supporting Materials. This new structure was used for the analyses and comparison with the computed structural parameters, which allowed for proper selection of the computational method to be employed.
Calculations performed at the ωB97X-D/Def2-TZVP level of theory were in closest agreement with exp IR frequencies (average % error = 1.50, MAE = 12.99, standard deviation = 16.25, RMSE = 20.48), whereas comparison of exp and theor geometry parameters is less conclusive. Therefore, said model chemistry was utilized for the remainder of this work. All DFT calculations were performed with tight convergence criteria and superfine integration grids [82], and all stationary points were confirmed to be minima by the absence of imaginary normal mode frequencies. In addition to serving as a popular analytical tool, modern vibrational spectroscopy [83][84][85] is an excellent source of information on the electronic structure a molecule. Specifically, a new quantitative measure for the intrinsic strength of a chemical bond is derived from vibrational force constants. However, one has to consider that normal vibrational modes are generally delocalized over the molecule due to coupling of the atomic motions [86][87][88]. Therefore, one cannot directly derive an intrinsic measure of bond strength from said normal modes, a fact that has already been discussed since the early days of vibrational spectroscopy. (The reader may refer to review articles, e.g., by Quack [89], Halonen [90], and Jensen [91] for a more in-depth discussion and to Ref. [49] for a historical overview.) Furthermore, it can be difficult to assign a peak on an experimental spectrum to a normal mode involving the vibrations of a particular functional group, particularly in the mid and lower frequency domains. Both problems are addressed by Local Vibrational Mode (LVM) theory, originally introduced by Konkoli and Cremer [44][45][46][47][48]. In Ref. [49], a comprehensive discussion of the underlying theory of LVMs is provided; therefore, in the following, only some essential features are summarized.
As outlined in Ref. [49], LVMs have a number of unique properties. Zou, Kraka, and Cremer [46,47] verified the uniqueness of the LVMs via an adiabatic connection scheme between local and normal vibrational modes. In contrast to normal mode force constants, LVM force constants have the advantage of not being dependent on the choice of coordinates used to describe the target molecule. The latter are highly sensitive to electronic structure differences (e.g., caused by changing a substituent) and directly reflect the intrinsic strength of a bond or weak chemical interaction, as has been shown by Zou and Cremer [92]. Thus, LVM stretching force constants have been utilized as a unique measure of the intrinsic strength of chemical bonds [38,39,48,[93][94][95][96][97][98][99][100][101][102][103][104] and weak chemical interactions [19,40, based on vibrational spectroscopy. LVM theory has previously been applied for the description of bonding in a diverse set of 34 HVI compounds, the majority of which are λ 3 -iodanes [19]. In this work, LVM theory and associated LVM stretching force constants were applied to investigate the I−C, I−N, and I−O bonds composing the 'T'-shaped molecular frameworks in a set of four BIATs and four BIOs.
In addition to local force constants and frequencies, the LVM analysis has led to a new way of analyzing vibrational spectra. Any normal vibrational mode l µ can be decomposed into LVM contributions [46,48], leading to detailed analysis of vibrational spectra and a wealth of information about structure and bonding [97,107]. Decomposition of normal modes into percent LVM contributions, also called Characterization of Normal Modes (CNM), calculates for each normal mode l µ the overlap S nµ with each local mode vector a x n , with both vectors given in Cartesian coordinates x, according to [46,48]: ; with a x n = La n (1) (a, b) in Equation (1) is the short notation for the scalar product of two vectors of a and b O ij is an element of the metric matrix O. We generally use the force constant matrix f x as metric, namely O = f x to account for the influence of the electronic structure [46,48]. This leads to the contribution C nµ of local mode a n to the normal mode l µ given by: i.e., a completely localized normal mode l µ has a C nµ value of 1 (corresponding to 100% if C nµ is given as a percentage). The CNM procedure was recently applied to assess the usefulness of Vibrational Stark Effect probes [102], and to analyze π-hole interactions between aryl (Ar) donors and small molecule acceptors [126]. In this work, CNM is used to interpret exp and theor spectra. DFT calculations were carried out with GAUSSIAN16 [127] and the standard frequency calculations were followed by LVM analysis, performed with the LModeA program [49,128]. The spectroscopic analysis was complemented with NBO populations calculated with the NBO6 package [129][130][131]. Electron densities (ρ(r b )) and energy densities (H(r b )) at the I−C, I−O, and I−N bond critical points r b determined with the AIMAll package [132]. The covalent nature of the bonds was assessed following the Cremer-Kraka criterion, which implies that covalent bonding is characterized by a negative energy density, whereas electrostatic interactions are indicated by positive energy density values [133][134][135].
Commercially available IBA (98% purity) was purchased from Sigma-Aldrich, St Louis. IPT, BIO-1 [25,136], and BIAT-5 [25] were prepared using previously reported procedures. The identity and purity of synthesized compounds were confirmed by nuclear magnetic resonance (NMR) spectroscopy. Infrared (IR) spectra were collected on a Nicolet iS5 IR spectrometer with iD7 attenuated total reflectance (ATR) accessory and diamond crystal, and were formatted using OriginPro 9.1.0 (64 bit) [137]. Data were recorded in the domain of 4000-400 cm −1 . The number of scans were set to 16 with spectral resolution of 4 cm −1 . To ensure no contamination during the analysis, a background spectrum was collected every time before collecting the sample spectrum. All experiments were performed under ambient conditions. Figure 3a,b show the exp and theor IR spectra of IBA, respectively. All exp compounds were in the solid phase under standard conditions, whereas theor normal mode vibrational frequencies were calculated in the gas phase. This difference in phase is responsible for the sharper, more well-defined peaks of the theor IR spectra. Additionally, corresponding peaks of the theor spectra have higher frequencies compared to the exp spectra which is also attributable to the phase difference. Discrepancies in peak height and shape are due to the signal intensities being given in transmittance for the exp spectra, and molar absorption coefficient (ε) for the theor spectra. To report the exp spectra with values of ε, amounts (i.e., film thickness or concentration) must be known and they are difficult to measure accurately using conventional spectral acquisition techniques. Likewise, to convert the theor spectra to absorbance, concentrations must be known, which are irrelevant for isolated molecules in the gas phase.

Experimental and Theoretical IR-Spectra
The small peak at 3814 cm −1 of the exp spectrum corresponds with the peak at 3642 cm −1 of the theor spectrum. In this case, mapping the exp signal to the theor signal is straightforward because the theor peak at 3642 cm −1 is the highest normal vibrational mode, and the only signal close to 3814 cm −1 , with the nearest theor signal at 3086 cm −1 . Mapping exp to theor frequencies of lower resolution is less straightforward, but can be done by comparing IR intensities, using common functional group frequency characteristics, and comparing distances between signals. In the 3058 to 2510 cm −1 domain of the exp spectrum, there are six weak signals. The theor spectrum shows only one peak at 3086 cm −1 , but there are three more weak signals from 3093 through 3062 cm −1 , which have low intensities at the given scale. These theor peaks correspond with the exp peaks in the domain of 3058 through 2809 cm −1 . In both spectra, there are 14 prominent signals between 1800 and 400 cm −1 .  Figure 4a,b show the exp and theor IR spectra for IPT. There is an intense, sharp signal at 3507 cm −1 of the theor spectrum, which is not pronounced in the exp spectrum. This is likely due to the effects of intermolecular hydrogen bonding (HB) in the solid phase. Between 2900 and 2300 cm −1 of the exp spectrum, there is a multitude of signals, whereas there is only a single peak at 3084 cm −1 in the theor spectrum. As in the case of IBA for IBA, there are several low-intensity theor signals in the 3200 to 2800 cm −1 domain. On the other hand, none of the exp signals between 2700 and 2300 cm −1 are pronounced in the theor spectrum; this is also the case for the broad signal at 1823 cm −1 . From 1700 through 400 cm −1 , the signals match up well between exp and theor spectra. Figure 5a,b are the exp and theor IR spectra of BIO-1, respectively. BIO-1 is a Ihydroxylated HV derivative of the monovalent IBA. The exp and theor spectra of IBA are quite similar to the spectra of BIO-1. However, the spectra of IBA and BIO-1 diverge in the 3100 to 2400 cm −1 domain, where BIO-1 has fewer signals and no pronounced signals in the 3600 to 4000 cm −1 domain. In addition, the prominent signals at 733 and 1250 cm −1 of IBA have higher relative frequencies for BIO-1. Notably, the latter signal is nearly 90 cm −1 higher in BIO-1. For the theor spectrum of BIO-1, the peaks at 3701 and 3083 cm −1 have higher frequencies by 59 and 3 cm −1 , respectively, compared to the corresponding signals of IBA. On the other hand, many of the signals between 1800 and 400 cm −1 have lower frequencies in BIO-1 compared to IBA.   Figure 6a,b show the exp and theor IR spectra of BIAT-5, respectively. The exp spectrum has six broad peaks between 3500 and 2400 cm −1 and several weak signals between 2400 and 1500 cm −1 . There are two signals at 3394 and 3463 cm −1 which are not pronounced in the spectrum of IPT. The other three peaks at 3062, 2970, and 2901 cm −1 are more than 100 cm −1 higher than corresponding signals for IPT. At 2408 cm −1 , there is a single peak, whereas IPT has several signals in the same domain. There is an absence of pronounced signals between 1900 and 1500 cm −1 , but this domain contains noise which may be significant. There are three weak signals from 1454 to 1377 cm −1 , which are almost 20 cm −1 lower than the corresponding signals of IPT. The theor spectrum of BIAT-5 contains sharp peaks at 3697 and 3085 cm −1 , with the former having high intensity. The theor and exp spectra of BIAT-5 match well, with the exception being the exp signal at 2408 cm −1 , which is not pronounced in the theor spectrum. Comparison between theor spectra of BIAT-5 and IPT reveals all of the signals between 3697 and 1235 cm −1 have higher frequencies in BIAT-5, with the peak at 3697 cm −1 being 190 cm −1 higher compared to the corresponding peak of IPT. Conversely, between 1235 and 400 cm −1 , IPT has higher frequencies, the exception being at 738 cm −1 in BIAT-5 and 736 cm −1 in IPT.
There are significant differences between exp and theor IR spectra which are mostly attributable to the phase difference in this case, but it is evident that the two can be mapped to one another. LVM analysis not only confirms the accurate mapping of exp to theor vibrational frequencies, but it also provides a probe of vibrational spectra with a level of detail otherwise unobtainable, as is demonstrated in the following subsection.

CNM Analysis
There are many common IR signatures and numerous charts exist to help with assigning functional groups for the most recognizable signals, but doing so neglects the fact that normal vibrational modes are delocalized. In other words, most vibrational frequencies are composed of several molecular motions rather than a single C−C or C−N stretch for example. This is where LVM theory provides valuable new insights for the analysis of vibrational spectra through decomposition of normal vibrational modes into individual LVM contributions from local parameters bond distance (R), angle (θ), and dihedral/torsion (ϕ). Figure 7 shows CNM, for IBA, including normal mode frequencies 439 through 3507 cm −1 . IBA has eight normal modes with frequencies below 400 cm −1 , but the CNM plots do not include these frequencies in accordance with the exp IR spectrum. Most of these eight frequencies are related to the LVMs of iodine, and this is consistent for CNM of IPT, BIO-1, and BIAT-5. In addition, included in Figure 7   H9 The IR spectra of 5-phenyltetrazole derivatives with various substituents in the phenyl rings, including the spectrum of the ortho-iodo derivative, IPT, have been reported [138]. Six of the absorption bands in the spectrum of IPT, listed as 1467(s), 1269(w), 1048(s), 1018(m), 1005(s), and 767(m) cm −1 , were assigned to vibrations of the TZ ring. Each of these bands were also observed in this work (shown in italics in Figure 4a), and are within 3 to 4 cm −1 of the previous literature values. The authors in [138] provide an in-depth discussion on the IR spectrum of 5-phenyltetrazole and the combinations of vibrations responsible for the occurrence of all absorption bands are in agreement with the above assignments. For example, the band at 1465 cm −1 in the spectrum of 5-phenyltetrazole (likely of similar origin as the band at 1467 (1471 in this work) cm −1 ) in the spectrum of IPT was attributed to a combination of vibrations from C−NH (37%), C− −N (36%), N−NH (16%), and N− −N (15%). In addition, more complex vibrations involving three atoms, such as N−N− −N (12%) and C− −N−N (9%), were reported [139]. In the current work, LVM contributions to the frequencies observed in the IR spectrum of IPT are discussed in more detail. Figure 8 is the CNM plot of IPT, including normal modes at 439 through 3507 cm −1 . The highest theor frequency at 3507 cm −1 is a pure N−H stretch. This peak is not in the exp spectrum, which is likely due to intermolecular hydrogen bonding in the solid phase. No other normal modes for IPT contain more than 59% contributions from a single local mode. Figure 9 is the CNM plot of BIO-1, including frequencies spanning 418 through 3701 cm −1 . The highest theor frequency at 3701 cm −1 is a pure N−H stretch; this peak is not pronounced in the exp spectrum, which is again attributable to intermolecular HBs in the solid phase. Important LVM contributions are as follows: 3081/3059 (exp) − − → 3093 (theor), symmetric ortho-C10−H13 and meta-C9−H15; 3083 (theor), symmetric stretch meta-C7−H14, para-C8−H12. The other two C−H stretches are asymmetric; 3073, asymmetric stretch of the two meta-C−H bonds C7−H14 (meta), C9−H15 (meta), C8−H12 (para), plus ortho-C10-H13; 3061: asymmetric stretch of the two meta-C−H bonds meta-C7−H14, C9−H15 (meta), C8−H12 (para). O2

NBO Analysis
In Figure 1, atomic and group NBO charges for all molecules (reference systems IBA and IPT, BIOs 1-4, and BIATs 5-8) investigated in this work are reported (see also Table 3). NBO atomic charges of iodine are shown in purple, carbon in black, oxygen in red, and nitrogen in blue. Figure 1 also shows the total NBO charge of the Ar group in black, the TZ group in blue, and the alkoxy group in red. The iodine-atomic NBO charge in IBA is slightly more positive compared to IPT (0.179 and 0.158 e, respectively) and the total charge of the Ar group in IBA is significantly more negative compared to IPT (−0.213 and −0.126 e, respectively); while the total charges of COOH in IBA and TZ in IPT are both close to zero, with COOH having a net positive charge (0.035 e) and TZ having a net negative charge (−0.032 e).
Comparing NBO charges of IBA with those of IPT reveals some significant electronic differences which extend to BIOs 1-4 and BIATs 5-8, namely the following: charge (and electronic density) distribution are more polar in IBA compared to IPT, and NBO charge/electronic density is significantly higher/more negative on the Ar ring in IBA compared to IPT. On the other hand, in IPT, more electron density is transferred to TZ, which becomes more negative relative to the total COOH charge in IBA, showing a stronger electron withdrawing effect of the TZ group. It is also interesting to note that the presence of the TZ group in IPT increases the electron density/negative charge on the Ar-carbon atom bound to iodine relative to that of IBA (NBO charges of −0.133 and −0.129 e, respectively). Consequently, iodine is less positive in IPT compared to IBA (NBO charge values of 0.158 and 0.179 e, respectively).
To reiterate some of the aforementioned observations, 1-8 show similar trends in charge and electron density distribution with respect to the comparison of IBA and IPT. The iodine-atomic charge in BIO-1 is slightly more positive compared to BIAT-5 (1.329 and 1.294 e, respectively), the charge of the Ar group is significantly more negative (−0.224 e BIO and −0.120 e BIAT, respectively), and the charge on TZ in 5 is more negative than COOin 1 (−0.639 and −0.569 e, respectively). However, in contrast with IBA and IPT, the Ar-C atomic charge (bound to iodine) in 1 is slightly more negative relative to 5 (−0.195 and −0.178 e, respectively). COOgroups in BIOs 2-4 show similar charge differences compared with TZ groups in BIATs 6, 7, and 8, which show a similar increase in electron withdrawing abilities of the TZ groups in the BIATs, as was observed in IPT.
The electron withdrawing ability of the TZ groups in BIATs 5-8 increases in series, as the charges of these groups become more negative (−0.639, −0.642, −0.644, and −0.648 e, respectively), which correlates to more negative charges on the Ar groups (−0.120, −0.125, −0.128, and −0.130 e, respectively). A methyl group is a stronger σ-electron donor than H, and the increasing number of methyl substituents in the alkoxy groups MeO − − → EtO − − → iPrO increases electron density transfer to the Ar and TZ groups in series. This causes increased negative charges, despite the fact that both the TZ and the Ar groups are not directly bound to the alkoxy groups. It is also interesting to note that, in the same series, the charge on iodine becomes more positive (1.294, 1.302, 1.307, and 1.308 e, respectively). A similar trend is observed for BIOs 1-4. Increasing the number of carbon atoms in the alkoxy groups results in increasingly more negative charges on the COOgroups (−0.569, −0.571, −0.573, and −0.575 e, respectively), and the Ar groups (−0.224, −0.228, −0.231, and −0.232 e, respectively), while the iodine-atomic charges become more positive (1.329, 1.336, 1.341, and 1.343 e, respectively). The iodine atoms in this case, similar to I 2 , show both σ-electron donor and acceptor capabilities [140]. In addition to the special properties of HVI, iodine can form an efficient bridge between molecular groups of different electron donor/acceptor abilities. The I-atomic charge becomes more positive in the same series, i.e., the I-atomic charge increases in magnitude as the mass of the hydroxyl/alkoxy group increases. NBO charge of the Ar rings become slightly more negative in the same series (−0.224 to −0.232 e in BIOs 1-4 and −0.120 to −0.130 e in BIATs 5-8, respectively). With the exception of the hydroxyl/alkoxy O-atoms, the difference in atomic NBO charges between O, N, and Catoms bound to iodine remains relatively constant. The NBO charge on iodine varies, but to a lesser extent compared to he hydroxyl/alkoxy O-atoms; ∆ NBO = 0.014 e and 0.218 e, respectively. Generally, more insights into the differences in electronic structure, density, and populations are obtained by considering the net NBO charge of the entire functional group rather than the charge on the atom which bonds directly to iodine. Table 3. Theoretical bond lengths R (Å), local mode vibrational force constants k a (mDyn/Å), local mode vibrational frequencies ω a (cm −1 ), electronic densities at the bond critical points ρ(r b ) (e/Å 3 ), energy densities at the bond critical points H(r b ) (Hartree/Å 3 ), and atomic NBO charges (e) for all I−C, I−N, and I−O bonds in IBA, IPT, and 1-8, calculated at the ωB97X-D/Def2-TZVP level of theory.
Most notable is the difference in NBO charges of the whole Ar rings between BIOs and BIATs. For the BIOs, Ar NBO charges are more negative compared to BIATs by up to 0.104 e (60.5% difference). On the other hand, BIAT TZ group charges are more negative compared to BIO OCO group charges by up to 0.079 e. This is a result of the ability of TZs, particularly pronounced in amino-TZs to withdraw electrons [141][142][143]. Iodine can also accept an electronic charge from an Ar ring through a σ-hole interaction. However, given the abundance of lone pairs electrons (lp) in iodine and comparatively low electronegativity, iodine is as likely to be an electron donor as it is an acceptor. This result seems subtle, but it points to the C−C bond between TZ/OCO and Ar as a channel for the transfer of negative charge from the latter to the former. This finding naturally draws interest in the LVMs as well as electronic density (ρ(r b )) of this connecting C−C bond. The importance of this connector C−C bond is addressed in the following subsection. Table 3 depicts chemical bond strength of all iodine-containing bonds: I−C, I−N, and I−O, expressed as LVM stretching force constants k a , along with ionic character described by the local energy density H(r b ). In Figure 11a   In Figure 12a Table 4 summarizes LVM, QTAIM, and NBO results for the C−C bonds which link Ar and OCO/TZ groups in IBA, IPT, BIOs 1-4, and BIATs 5-8. In addition to the I−N bonds, this bridging C−C bond is a potential weak point, as well as a location for electron transfer. These C−C bonds are significantly stronger than the iodine-related bonds but are significantly weaker than the C−C, C−O, C−N, and N−N bonds. According to Table 4, the C−C bond is stronger for IPT compared to IBA (the k a values of 4.468 and 4.408 mDyn/Å, respectively), is shorter (R values of 1.469 and 1.495 Å, respectively), and has a more covalent character (the H(r b ) values of −1.782 and −1.688 Hartree/Å 3 ). The difference between the NBO charges of both C atoms in this bond for IPT is smaller compared to IBA (∆ NBO values of 0.4368 and 0.9691 e, respectively), which indicates less polarization of this bond in IPT and is consistent with larger covalent character [144]. The chemical differences of the C−C bonds in IPT and IBA is explained by more π-electron delocalization in the TZ group of IPT, which leads to a less positive charge of the TZ-carbon compared to the OCO-carbon atom of IBA (NBO charge values are 0.3025 and 0.7700 e, respectively), resulting in the C−C bond in IPT being less polar but stronger. Similar correlations are observed in calculations for BIOs 1-4 and BIATs 5-8. The C−C bonds in BIATs 5-8 are generally stronger, shorter, and have more covalent character (correlating with a less polar bond) compared to BIOs 1-4, and the TZ-carbon atoms have less positive NBO charges in contrast with the OCO-carbon atoms. It is also interesting to note that the C−C 'bridge' bond in BIAT-5 is much stronger than that of IPT, where both systems have TZ groups (k a values of 5.587 and 4.468 mDyn/Å, respectively), thus indicating more π-electron delocalization in 5. This is corroborated by the TZ-carbon atom charge in BIAT-5 less positive compared with the IPT-carbon atom (NBO charges of 0.2483 and 0.3025 e, respectively), and the bridging C−C bond being less polar in BIAT-5 compared with IPT (∆ NBO values of 0.3509 and 0.4368 e, respectively). The analogous C−C bonds in BIATs 6-8 are very similar to BIAT-5 in terms of all of the aforementioned properties, indicating that formation of the I−N bond in the BIATs increases the π electron delocalization in the TZ group, making these C−C bonds stronger. Table 4. Theoretical R (Å), k a (mDyn/Å), ω a (cm −1 ), ρ(r b ) (e/Å 3 ), H(r b ) (Hartree/Å 3 ), and NBO atomic charges (e) for the C−C bonds linking Ar groups and TZ/OCO groups in IBA, IPT, and BIOs/BIATS 1-8.

Conclusions and Outlook
There are fundamental differences between exp and theor IR spectroscopy which are mostly attributable to the phase difference in this case, but it is evident that the two can be mapped to one another with relative ease if corrections to the harmonic approximation are considered. LVM analysis not only confirms the accurate mapping of exp to theor vibrational frequencies, but opens the door to the analysis of vibrational spectra at a level of detail and accuracy not previously known. This work demonstrates the importance of the often overlooked fact that normal vibrational modes are delocalized. LVM theory takes this into consideration, and reveals valuable new insights by decomposing normal vibrational modes into fundamental LVM contributions in terms of R, θ, and ϕ.
The sensitivity of LVM stretching force constants has also revealed subtle but important differences in the intrinsic nature of iodine-related bonds between a set of four alkoxybenziodoxoles, which are relatively stable, and four tetrazolated derivatives which decompose explosively. The I−N bonds in BIATs 5-8 are generally weaker than the comparable I−OCO bonds in BIOs 1-4 by as much as 0.300 mDyn/Å. Moreover, strength of the I−N bond in BIATs 5-8 decreases with the increasing size of the hydroxyl/alkoxy group: OH > MeO > EtO > iPrO. Based on LVM analysis, I−N is most likely the trigger bond responsible for initiation of explosive decomposition in BIATs 5-8. For comparison, trigger bonds were recently identified as C−N bonds in the high-energy compounds 1fluoro-2,4,6-trinitrobenzene and 2,4,6-trinitrobenzaldehyde [31]. Our calculations predict the C−C bond linking Ar and aldehyde groups to be the weakest in the latter, but both bonds in question have k a values between 3.400 and 3.900 mDyn/Å, whereas the possible I−N trigger bonds, I−C, and I−O bonds in this work have k a values between 1.300 and 2.620 mDyn/Å. With regard to the I−N bonds, it is interesting to note that explosive compounds with I−N bonds have been known as long as elemental iodine itself. The formation of the highly friction-sensitive black compound NI 3 (or more precisely, its adduct with ammonia), achieved by mixing iodine with aqueous ammonia, was first reported by Bernard Courtois in 1813 in the paper where the discovery of the new element was announced [145]. The composition of the unstable compound was confirmed as NI 3 · NH 3 in 1903 [146]. Based on strength of the I−C, I−N, and I−O bonds, where stronger bonds will correlate with increase in stability, we predict stability of BIATs 5-8 as follows: BIAT-8 < BIAT-7 < BIAT-6 < BIAT-5. The finer details obtained from this work regarding the characteristics of iodine-containing bonds can lead to new structure-property relationships. Some additional key differences between the BIOs 1-4 and BIATs 5-8 are as follows: Future goals are to investigate the effects other types of substituents will have on the physical properties of benziodazolotetrazoles, which encompasses modifications to the TZ group as well as the Ar group. Furthermore, we plan to investigate the mechanism of detonation using the Unified Reaction Valley Approach to reveal in what order the most important changes in electronic structure occur and determine the most prevalent reaction products. Lastly, we wish to investigate and develop better methods for approximating the anharmonic nature of vibrational frequencies.