Chiral Molecular Structures of Substituted Indans: Ring Puckering, Rotatable Substituents, and Vibrational Circular Dichroism.

The chiral molecular structures of four different substituted indans, namely, (S)-1-methylindan, (R)-1-methylindan-1-d, (R)-1-aminoindan, and (S)-1-indanol, were investigated using experimental vibrational absorption and vibrational circular dichroism spectra and corresponding spectra predicted using quantum chemical (QC) calculations. All of these molecules possess two ring puckering conformations, with ring puckering leading to the pseudoequatorial substituent being approximately four times more abundant over that leading to the pseudoaxial substituent. The amino group in 1-aminoindan has three conformations arising from the rotation of NH2 group, for each ring puckering conformation, resulting in a total of six conformations. Whereas 1-indanol in the nonhydrogen-bonding solvent CCl4 also has six conformations similar to those of 1-aminoindan, 1-indanol in the hydrogen-bonding solvent DMSO-d 6 adopts numerous conformations, of which 30 conformers are considered to have at least ∼1% or more population. In DMSO solution, ring puckering leading to pseudoequatorial substituent accounts for 77% population and 23% for pseudoaxial substituent. The QC spectra predicted for the geometry optimized conformers are found to be in excellent quantitative agreement with corresponding experimental spectra in all of the molecules considered. The procedures suggested in this work are hoped to provide successful pathways for future chiral molecular structural analyses.

Introduction

Determining the molecular structures of chiral molecules is often a challenging task. X-ray crystallography offers the most direct approach to establish molecular structures, but its utility is restricted due to the difficulty in obtaining good quality single crystals for the samples of interest. The second popular approach is the use of NMR, where chiral shift reagents are needed for studying chiral molecules. Furthermore, the NMR time scale limits the achievable information to average molecular structures. Optical spectroscopy suitable for studying chiral molecules is referred to as chiroptical spectroscopy[1,2] and represents an important alternative to X-ray and NMR methods. Four different methods, optical rotatory dispersion (ORD),[1−3] electronic circular dichroism (ECD),[1,2,4] vibrational circular dichroism (VCD),[1,2,5,6] and vibrational Raman optical activity (VROA),[1,2,6,7] fall under the umbrella of chiroptical spectroscopy. Since optical transitions occur on a much faster time scale, chiroptical spectroscopy is more appropriate for investigating the molecular conformers and is increasingly becoming popular for probing the structures of chiral molecules. As molecular vibrational transitions are expected to be sensitive to minor structural changes, the vibrational transition-based VCD and VROA methods offer greater promise for chiral molecular structure determination. The electronic transition-based ECD and ORD methods are also sensitive for certain structural changes.

Substituted indans have attracted interest for their chiroptical properties since early 1970s, mainly in terms of ECD associated with n−σ*, σ–π*, π–-σ*, and π–π* transitions.[8,9] More recently, various jet-cooled spectroscopies were undertaken for substituted indans, where low-frequency ring puckering modes were investigated.[10−15] In the early stages of VCD research, emphasis was placed on spectra–structure correlations and qualitative interpretations. In this connection, the methine-hydrogen bending mode has been suggested to generate a VCD band with its sign correlating with the absolute configuration (AC) in a series of related compounds. This observation was further investigated[16] for (S)-1-methylindan and (R)-1-methylindan-1-d and (R)-1-aminoindan, by measuring the experimental vibrational absorption (VA) and VCD spectra for neat liquid samples and identifying the VCD associated with methine-hydrogen (or deuterium) bending mode. The sign of VCD band associated with methine-hydrogen bending mode in these three indans was also suggested[16] to correlate with the AC.

In recent years, the advances in VCD theory[17−19] and quantum chemical (QC) computational methods[20,21] have shifted the focus of VCD research to interpreting the experimental VCD spectra using QC predictions of corresponding spectra and deducing the chiral molecular structures therefrom. This approach has facilitated probing not only the AC but also the molecular conformational space, in a variety of systems, containing both small and large molecules. The availability of faster computer processors with larger memory and storage space has led to the use of molecular dynamics (MD) for generating the geometries of solute–solvent clusters and simulating the QC-predicted spectra for solvated species.[22−24] Attempts to analyze the experimental chiroptical spectra using corresponding QC-predicted spectra have now become a routine practice.[25] Recent works have also emphasized on quantitative comparisons between experimental and calculated spectra using the similarity index[26] and spectral similarity overlap (SSO) plots.[27−29]

The puckering of a five-membered ring common to substituted indans can shed light on the role of ring puckering conformation on VCD spectra. The contributions to vibrational absorption (VA) and VCD spectra from the ring puckering conformations have not been identified before, and there is a need to identify conformer-specific VA and VCD bands. Second, (R)-1-aminoindan has a freely rotatable amino group whose influence on VCD spectra needs to be explored. A similar situation, with a freely rotatable O–H group, exists for (S)-1-indanol whose experimental VA and VCD spectra in CCl4 and dimethyl sulfoxide (DMSO) solvents were reported recently.[30] In this manuscript, we identify the puckering conformer-specific VA/VCD bands in 1-methylindans and the conformational sensitivity of rotatable NH2/OH groups to VA/VCD spectra. In addition, comparison of the experimental and QC-predicted VA and VCD spectra of (S)-1-methylindan, (R)-1-methylindan-1-d, (R)-1-aminoindan, and (S)-1-indanol, using quantitative SSO measures, are carried out.

Investigations presented here on four 1-substituted indans lead to consistent conclusions as follows: (a) the positive ring puckering of a five-membered ring, leading to a pseudoequatorial substituent at the 1-position, dominates the contributions to VCD spectra in all molecules. Nevertheless, evidence for the signatures of negative ring puckering, leading to a pseudoaxial substituent, is also present in the experimental spectra. (b) Even though the rotatable NH2 and OH substituents at 1-position add additional conformational complexity, the observed VA and VCD spectra are reproduced remarkably well by QC predictions at the optimized geometries. (c) Hydrogen-bonding DMSO solvent facilitates the formation of the 1-indanol/DMSO complex, requiring exploration of numerous conformers. Even then, with proper care in probing the conformational space, the experimental spectra of 1-indanol/DMSO-d6 complex are remarkably well reproduced by QC predictions at the optimized geometries. (d) The excellent correlation of experimental spectra with corresponding QC-predicted spectra, obtained for all four substituted indans, including for a complex with a hydrogen-bonding solvent, identifies successful pathways for future chiral molecular structure determination.

Results and Discussion

The details on the conformational analysis, QC predictions of VA and VCD spectra, and spectral similarity analysis are given in the Methods section.

(S)-1-Methylindan

Relaxed energy scan (see the Supporting Information) for 1-methylindan as a function of 9–4–3–2 dihedral angle (see Figure ) using the B3LYP functional[31−33] and 6-311++G(2d,2p) basis set,[34] indicates two minima at +17 and −15°. Thus, two conformers with opposite ring puckering angles are possible for this molecule. The energies and populations of these conformers for the isolated molecule are summarized in Table . These conformers, along with atom numbering for identifying the ring puckering angle, are shown in Figure .

Figure 1

Two conformers of (S)-1-methylindan with opposite puckering of the 5-membered ring. Positive 9–4–3–2 dihedral angle leads to methyl group in the pseudoequatorial position and in pseudoaxial position for negative 9–4–3–2 dihedral angle.

Table 1

Energies and Populations of Conformers of 1-Methylindan at B3LYP/6-311++G(2d,2p) Level

conf #	Gibbs energy (hartrees)	ΔE (kcal/mol)	population	dihedral angle C9–C4–C3–C2
1	–388.25842	0	0.75	17.0
2	–388.25741	0.63	0.25	–15.2

The conformation with a positive 9–4–3–2 dihedral angle has the lowest Gibbs energy and is expected to be present with ∼75% population in vacuum. The experimental VA and VCD spectra obtained for the neat liquid sample are compared to the population-weighted QC-predicted spectra for the isolated molecule in Figure .

Figure 2

Comparison of experimental and predicted VA (bottom panel), VCD (middle panel), and vibrational dissymmetry factor (VDF, top panel) spectra for (S)-1-methylindan. Although the experimental VA spectra are shown until 1425 cm–1, the experimental VCD was not displayed above 1320 cm–1 due to excessive absorbance present in the 1325–1425 cm–1 region. The left vertical panels display overlaid spectra after scaling the calculated vibrational frequencies with 0.9785, whereas the right vertical panels display stacked spectra with unscaled vibrational frequencies and labeled band positions. Experimental VA and VCD spectra are taken from ref (16).

In Figure , the left vertical panels display predicted spectra with vibrational frequencies scaled with 0.9785 (which corresponds to maximum SSO of VCD spectra) as overlaid with experimental spectra whereas the right vertical panels provide stacked display of predicted spectra with unscaled frequencies. From the overlaid experimental and predicted spectra, it can be seen that the predicted spectra faithfully reproduce the bands seen in the experimental spectra and band-by-band correlation in experimental and predicted spectra can be seen. The correlation of experimental (and corresponding unscaled predicted) VA band positions (in cm−1 units) noted from the stacked spectra is as follows: 1372 (1412), 1326 (1349), 1299 (1330), 1263 (1293), 1211 (1235), 1154 (1183), 1077 (1100), 1020 (1044), 1012 (1029), 950 (969), and 928 (950). Similarly, the correlation of experimental (and corresponding unscaled predicted) VCD band positions is as follows: 1301 (1329), 1275 (1302), 1262 (1293), 1212 (1236), 1166 (1194), 1157 (1174), 1075 (1100), 1065 (1082), 1019 (1045), 1013 (1026), 967 (976), and 900 (910). This comparison indicates that almost all experimental bands are satisfactorily reproduced in the predicted spectra. The same type of correlation can also be seen in VDF spectra, as is clearly apparent from the overlaid spectra.

The agreement between experimental and predicted spectra is quantified using maximum SimVA, SimVCD, and SimVDF values (see SSO plots in Figure A), which are respectively, 0.87, 0.65, and 0.66 for (S)-1-methylindan. The SimVCD and SimVDF values obtained here are excellent, because these higher magnitudes are not that routine, and for typical cases, they can be as low as ∼0.4.[35]

Figure 3

SSO plots (A–F) for investigated substituted indans.

Since there are two ring puckering conformers, it is useful to understand how the experimental spectra are influenced by the individual conformers. The spectra predicted for individual conformers and their Boltzmann population-weighted spectra are compared to the experimental spectra in Figure .

Figure 4

Comparison of individual conformer and population-weighted predicted VA (left panel), VCD (right panel) with corresponding experimental spectra of (S)-1-methylindan. The predicted frequencies are scaled as in Figure . Experimental VA and VCD spectra are taken from ref (16).

From this comparison, it can be seen that the major VA and VCD spectral features seen in the experimental spectra have counterparts in those predicted for the conformation with a positive puckering angle (#1 in Table ). However, it is important to note that the presence of both conformers is required for reproducing the experimental positive–negative bisignate VCD couplet (positive at 1075 and negative at 1065 cm–1), with positive VCD mostly coming from conformer 1 and negative VCD mostly coming from conformer 2. Similarly, the presence of both conformers is required for reproducing the experimental weak negative–positive bisignate VCD couplet (negative at 1166 and positive at 1157 cm–1), with negative VCD mostly coming from conformer 1 and positive VCD coming from conformer 2. This information on conformer-specific VCD bands is useful for future investigations on temperature-dependent conformer equilibrium and associated thermodynamic parameters.

(R)-1-Methylindan-1-d

Note that the substitution of hydrogen atom with deuterium does not alter the conformational space or the optimized geometries. However, Gibbs energies and hence populations of conformers can be different upon deuterium substitution. The energies, populations, and ring puckering angles for the two conformers are summarized in Table .

Table 2

Energies and Populations of Conformers of 1-Methylindan-1-d at B3LYP/6-311++G(2d,2p) Level

conf #	Gibbs energy (hartrees)	ΔE (kcal/mol)	population	dihedral angle C9–C4–C3–C2
1	–388.26188	0	0.74	17.0
2	–388.2609	0.61	0.26	–15.2

The deuterium substitution has changed the populations of the two conformers only slightly. The conformer with the positive 9–4–3–2 dihedral angle is now expected to be present with ∼74% population (as opposed to 75% in 1-methylindan) in vacuum. The experimental VA and VCD spectra obtained for the neat liquid sample are compared to the population-weighted QC-predicted spectra for isolated molecules in Figure . In the left vertical panels of Figure , predicted spectra with vibrational frequencies scaled with 0.978 (which corresponds to the maximum SSO of VCD spectra) are overlaid on experimental spectra. In the right vertical panels of Figure , predicted spectra with unscaled vibrational frequencies are stacked above experimental spectra and individual band peak positions are labeled. As with (S)-1-methylindan, it can be seen that the predicted spectra faithfully reproduce the bands seen in the experimental spectra for (R)-1-methylindan-1-d, and band-by-band correlation in experimental and predicted spectra can be seen. The correlation of experimental (and corresponding unscaled predicted) VA band positions noted from the stacked spectra is as follows: 1375 (1413), 1307 (1340), 1259 (1291), 1196 (1220), 1155 (1179), 1083 (1105), 1020 (1042), 971 (979), and 942 (960). Similarly, the experimental (and the corresponding unscaled predicted) VCD band positions are as follows: 1296 (1324), 1266 (1293), 1202 (1223), 1171 (1193), 1098 (1121), 1072 (1091), 1023 (1041), 971 (979), and 941 (960). This comparison indicates that almost all of the experimental bands are satisfactorily reproduced in the predicted spectra. The same type of correlation is apparent in the overlaid VDF spectra.

Figure 5

Comparison of experimental and predicted VA (bottom panel), VCD (middle panel), and VDF (top panel) spectra for (R)-1-methylindan-1-d. Although the experimental VA spectra are shown until 1425 cm–1, the experimental VCD was not displayed above 1345 cm–1 due to excessive absorbance present for the 1375 cm–1 band. The left vertical panels display overlaid spectra after scaling the calculated vibrational frequencies with 0.978, whereas the right vertical panels display stacked spectra with unscaled vibrational frequencies and labeled band positions. Experimental VA and VCD spectra are taken from ref (16).

The agreement between experimental and predicted spectra is quantified using maximum SimVA, SimVCD, and SimVDF values (see SSO plots in Figure B), which are, respectively, 0.92, 0.72, and 0.66. These values are even better than those for (S)-1-methylindan (see the comparison in Table ) and reflect the excellent agreement between experimental and predicted spectra.

Table 3

Maximum SSO Values in Similarity Analysisa for Substituted Indans without Experimental Reliability Criterion

molecule	experimental region (in cm–1) used for analysis	SimVA	SimVCD	SimVDF
(S)-1-methylindan	925–1320	0.87	0.65	0.66
(R)-1-methylindan-1-d	920–1345	0.92	0.72	0.66
(R)-1-aminoindan	950–1450	0.89	0.60	0.47
(S)-1-indanol in CCl4	900–1700	0.86	0.43	0.36
(S)-1-indanol in CCl4	900–1350	0.94	0.63	0.62
(S)-1-indanol in DMSO-d6	1100–1700	0.89	0.61	0.66

see Methods section for information on the similarity analysis. Baseline ε tolerance used in obtaining VDF spectra are: 0.7, 0.5, 2, 1.4, and 0.5, respectively, for 1-methylindan, 1-methylindan-1-d, 1-aminoindan, 1-indanol in CCl4, and 1-indanol in DMSO-d6.

As with (S)-1-methylindan, the role of two individual conformer contributions to the experimental spectra of (R)-1-methylindan-1-d can be analyzed. For this purpose, the predicted spectra for two individual conformers and their population-weighted average are compared to the experimental spectra in Figure . The dominant VCD features seen in the experimental spectrum are clearly present in the predicted spectrum of conformer with a positive puckering angle (#1 in Table ). For example, the dominant positive–negative bisignate VCD couplet with positive VCD at 1098 cm–1 and negative VCD at 1072 cm–1 originates predominantly from conformer #1. It is of interest to note that the signs of intense VCD bands of conformer #2 are opposite to those of conformer #1. As a result, the experimental intensities of bisignate VCD couplets (1296(−)/1266(+) and 1202(−)/1171(+)) of (R)-1-methylindan-1-d can be seen to result from a significant reduction of the VCD band intensities of conformer #1 by the opposing contributions from conformer #2. As with (S)-1-methylindan, this information on conformer-specific VCD bands is useful for future investigations on temperature-dependent conformer equilibrium and associated thermodynamic parameters.

Figure 6

Comparison of individual conformer and population-weighted predicted VA (left panel), VCD (right panel) with corresponding experimental spectra for (R)-1-methylindan-1-d. The predicted frequencies were scaled as in Figure . Experimental VA and VCD spectra are taken from ref (16).

(R)-1-Aminoindan

The energies, populations, and ring puckering angles for the six conformers of 1-aminoindan are summarized in Table . The structures are displayed in Figure . Conformers 5, 3, and 1, with pseudoequatorial orientation (positive ring puckering angle) contribute to 80% of the population. Thus, as with 1-methylindans, the pseudoequatorial orientation is predicted to be the dominant contributor to vibrational spectra.

Table 4

Energies and Populations of Conformers of 1-Aminoindan at B3LYP/6-311++G(2d,2p) Level

				dihedral angle
conf #	Gibbs energy (hartrees)	ΔE (kcal/mol)	population	C9–C4–C3–C2	C9–C1–N–H1	C9–C1–N–H2
5	–404.31173	0.00	0.43	17.1	65.9	–174.8
3	–404.31144	0.18	0.32	16.8	–70.3	48.8
4	–404.31016	0.98	0.08	–13.7	–64.8	51.7
6	–404.30998	1.10	0.07	–14.4	55.9	175.2
2	–404.30985	1.18	0.06	–16.0	–172.7	–54.2
1	–404.30969	1.28	0.05	16.6	179.8	–63.0

Figure 7

Six conformers of (S)-1-aminoindan. Conformers 1, 3, and 5 have positive 9–4–3–2 dihedral angles, whereas the other three have negative dihedral angles. See Table for relative energies and populations of these conformers.

The experimental VA and VCD spectra obtained for the neat liquid sample are compared to the population-weighted QC-predicted spectra for isolated molecules in Figure . The predicted VA and VCD spectra of individual conformers are presented in the Supporting Information. In the left vertical panels of Figure , predicted spectra with vibrational frequencies scaled with 0.977 (which corresponds to maximum SSO of VCD spectra) are overlaid on experimental spectra. In the right vertical panels of Figure , predicted spectra with unscaled vibrational frequencies are stacked above experimental spectra and individual band peak positions are labeled. As with (S)-1-methylindan and (R)-methylindan-1-d, it can be seen that the predicted spectra faithfully reproduce the vibrational bands seen in the experimental spectra.

Figure 8

Comparison of experimental and predicted VA (bottom panel), VCD (middle panel), and VDF (top panel) spectra for (R)-1-aminoindan. The experimental region above 1450 cm–1 is associated with excessive absorbance and not displayed. The left vertical panels display overlaid spectra after scaling the calculated vibrational frequencies with 0.977, whereas the right vertical panels display stacked spectra with unscaled vibrational frequencies and labeled band positions. Experimental VA and VCD spectra are taken from ref (16).

The correlation of experimental (and corresponding unscaled predicted) VA band positions noted from the stacked spectra is as follows: 1377 (1413), 1317 (1349), 1296 (1327), 1259 (1293), 1215 (1240), 1184 (1204), 1153 (1175), 1121 (1141), 1101 (1120), 1070 (1080), 1019 (1044), 971 (985), and 953 (956). Similarly, the correlation of experimental (and corresponding unscaled predicted) VCD band positions is as follows: 1378 (1413), 1274 (1303), 1259 (1288), 1223 (1243), 1179 (1207), 1121 (1144), and 948 (959). Quantification of the agreement between experimental and predicted spectra can be gleaned from SSO plot (see Figure C and Table ), where the maximum SimVA, SimVCD, and SimVDF values are, respectively, 0.89, 0.60, and 0.47. The SimVCD and SimVDF magnitudes for 1-aminoindan are slightly smaller than those for 1-methylindan and 1-methylindan-1-d, which is probably because of the additional conformational degrees of freedom arising from the NH2 group (each of the two puckered ring conformers is associated with three different orientations of the NH2 group). Nevertheless, the agreement between experimental and predicted VA and VCD spectra of 1-aminoindan is remarkably good.

It is useful to note that the liquid-phase experimental spectra are satisfactorily reproduced by gas-phase calculations for 1-methylindan, 1-methylindan-1-d, and 1-aminoindan. This observation raises the relevance of solute–solute interactions in condensed media. Although polarizable continuum model (PCM)[36] calculations might not be useful for shining light on this issue, liquid-phase MD simulations might be able to.[37]

(S)-1-Indanol in Nonhydrogen-Bonding Solvent, CCl4

Whereas six stable conformations were found for 1-aminoindan, only four initial conformations of different energies were generated by CONFLEX.[38] To avoid missing the remaining two conformations, we have manually recreated the six conformations and optimized their geometries at B3LYP/6-311++G(2d,2p) level, followed by VA and VCD calculations at the same level of theory. These six conformers are identical to those reported recently by Zehnacker et al.[30] The geometries of conformers for (S)-1-indanol were also optimized, with PCM[36] representing CCl4 solvent at B3LYP/6-311++G(2d,2p) level, followed by VA and VCD calculations at the same level of theory. The use of PCM has only a minor influence on conformational populations and predicted spectra, as already pointed out by Zehnacker et al.[30] For this reason, the comparison of experimental spectra is restricted to the QC-predicted spectra obtained with PCM (see Table , Figures and 3).

Table 5

Gibbs Energies and Populations of Conformersa of 1-Indanol at B3LYP/6-311++G(2d,2p)/PCM(CCl4) Level

				dihedral angle
conf #	Gibbs energy (hartrees)	ΔE (kcal/mol)	population	C9–C4–C3–C2	C9–C1–O–H
5	–424.20196	0.00	0.33	16.5	54.6
4	–424.20152	0.27	0.21	–12.9	38.3
6	–424.20125	0.45	0.16	–14.5	–47.2
3	–424.20102	0.59	0.12	15.7	–76.8
1	–424.20098	0.62	0.12	16.1	–167.3
2	–424.200	1.01	0.06	–14.9	–176.1

The populations calculated from electronic energies are as follows: C5: 0.43; C4: 0.16; C6: 0.16; C3: 0.08; C1: 0.11; C2: 0.06.

Figure 9

Comparison of experimental and predicted VA (bottom panel), VCD (middle panel), and VDF (top panel) spectra for (S)-1-indanol in CCl4. The spectra in the left vertical panels display overlaid spectra after scaling the calculated vibrational frequencies with 0.98, whereas the right vertical panels display stacked spectra with unscaled vibrational frequencies and labeled band positions. Experimental VA and VCD spectra are taken from ref (30) with permission from the Royal Society of Chemistry.

The experimental VA, VCD, and VDF spectra obtained for (S)-1-indanol in CCl4 are compared to the population-weighted QC-predicted spectra, with PCM representing the solvent environment, in Figure . In the left vertical panels of Figure , predicted spectra with vibrational frequencies scaled with 0.98 (which corresponds to the maximum SSO of VCD spectra) are overlaid on experimental spectra. In the right vertical panels of Figure , predicted spectra with unscaled vibrational frequencies are stacked above experimental spectra and individual band peak positions are labeled. There is a good correlation of experimental (and predicted) bands, which in VA spectra is as follows: 1605 (1640), 1475 (1506), 1458 (1492), 1381 (1420), 1324 (1352), 1205 (1252), 1178 (1206), 1148 (1173), 1092 (1109), 1046 (1064), 1017 (1027), and 952 (964) and that in VCD is as follows: 1465 (1508), 1384 (1422), 1303 (1337), 1270 (1303), 1246 (1275), 1212 (1224), 1181 (1205), 1134 (1155), 1088 (1106), 1055 (1072), 1024 (1040), and 960 (966).

The overlaid VA and VCD spectra show an excellent match in the 1350–900 cm–1 region of the experimental spectrum. But neither VA nor VCD has a good match in the 1350–1450 cm–1 region of the experimental spectrum, mainly because the predicted VA spectrum has very large intensity at ∼1420 cm–1 compared to that of the corresponding experimental VA band at ∼1381 cm–1. The same discrepancy appears between the corresponding predicted VCD at ∼1422 cm–1 and experimental VCD at 1384 cm–1. The maximum SimVA, SimVCD, and SimVDF values obtained, for the 900–1700 cm–1 region of the experimental spectrum (Figure D and Table ), are 0.86, 0.43, and 0.36, respectively. Of these, SimVCD and SimVDF values are not as large as those seen for (S)-1-methylindan, (R)-1-methylindan-1-d, or (R)-1-aminoindan. The reason for lower SSO values for (S)-1-indanol in CCl4 is due to the mismatch of the large intensities associated with the predicted band at ∼1420 cm–1. Both absorption and VCD intensities predicted at ∼1420 cm–1 are significantly higher than the corresponding intensities observed in the experiment. If the region of similarity analysis is restricted to 900–1350 cm–1 region of the experimental spectra, then the SimVA, SimVCD, and SimVDF values increase to 0.94, 0.63, and 0.62, respectively (see Figure E), which are better than those for 1-aminoindan and closer to those of 1-methylindans (see Table ). The higher VA and VCD intensities predicted at ∼1420 cm–1 originate from coupled O–H and C–H bending motions at 1-position.

VA and VCD spectra of (S)-1-indanol in CCl4 have been analyzed previously by Zehnacker et al.[30] They reported predicted spectra using the B3LYP functional and 6-31++G(d,p) basis set and adopting two different approaches: (1) conventional static optimized geometries, nuclear velocity perturbation (NVP) theory[39−41] for calculating VCD, and PCM for representing the CCl4 solvent. This approach was referred to as static optimized geometry method. (2) Ab initio molecular dynamics for capturing the dynamical behavior of solute configurations, optimizing the geometries of snapshots extracted from the MD trajectories and NVP theory for predicting VCD. This approach was referred to as first-principle molecular dynamics (FPMD) method. The analysis of Zehnacker et al.[30] was limited to qualitative visual comparison of selected VCD bands. Their focus was on large intensities predicted for the ∼1420 cm–1 band and incorrect relative intensities predicted for the negative doublet at ∼1200 cm–1. Although these discrepancies were considered to have been corrected in their FPMD calculations,[30] the following negative points in the FPMD predictions can be noticed: the predicted spectrum in the FPMD approach did not show bands corresponding to the experimental positive VCD doublet at ∼1088 and 1055 cm–1; the FPMD-predicted spectrum also did not reproduce the experimental negative VCD band at 1465 cm–1 (instead the FPMD-predicted spectrum showed a negative VCD couplet; positive on the higher frequency side and negative on the lower frequency side) in the 1425–1475 cm–1 region. Thus, although FPMD calculations may have appeared to have corrected the deficiencies associated with the predicted band intensities at ∼1420 and 1200 cm–1, two other regions (1000–1100 and 1400–1500 cm–1) of the experimental spectra were negatively influenced. As a result, the overall spectral similarity between FPMD-predicted and experimental VCD spectra of (S)-1-indanol in CCl4 appears less than desired.

The current simulated spectra at the B3LYP/6-311++G(2d,2p) level, using conventional static optimized geometries, match the experimental spectra in the 1350–900 cm–1 region (see Table and Figure E, and overlaid spectra in Figure ) and also the 1450–1480 cm–1 region (see overlaid spectra in Figure ) reasonably well. The discrepancy associated with higher intensities predicted for the ∼1420 cm–1 band of (S)-1-indanol in CCl4 (compared with the corresponding experimental intensities), however, remains to be resolved.

It appears then that, identifying a method to correct for the overestimated intensities predicted for ∼1420 cm–1 band for 1-indanol in CCl4, without negatively influencing other regions of the spectra, will be useful. We pursued different directions for this purpose.

First, we followed the recent findings of Nicu et al.,[42] where the overestimated intensities in the 1160–1380 cm–1 region for vibrations involving C–O–H bending in 3-methyl-1-(methyldiphenylsilyl)-1-phenylbutan-1-ol could be satisfactorily corrected by averaging over the spectra obtained for thermal fluctuations in C–O–H angle. Taking cues from this study, we changed the C–O–H angle in the fully optimized geometries of 1-indanol conformers in three steps of +2° increment each and three steps of −2° increment each and performed constrained geometry optimizations. Some of the resulting geometries with positive increments were found to have imaginary frequencies. The Gibbs energy-derived Boltzmann population-weighted spectra, including those of additional C–O–H angle variations that did not have imaginary frequencies, are then compared to the experimental spectra and similarity analyses performed. Unfortunately, these results (SimVA = 0.80, SimVCD = 0.40, and SimVDF = 0.36 for the 900–1700 cm–1 region; see the SI) also did not provide improvement over the spectra shown in Figure and Table .

Second, individual conformer spectra (see the SI) indicate that out of the four lowest energy conformers, two of the conformers (C5 and C4) make dominant contributions to VA intensity and three conformers (C5, C4, and C3) make dominant contributions to VCD intensity at 1420 cm–1. The C6 conformer does not contribute to this band. Assuming that Boltzmann populations determined from Gibbs energies may not be reflecting the actual populations in the experiment, we considered the following: (a) the populations derived from electronic energies (see the footnote to Table ); (b) equal populations for all six conformers, and (c) the influence of increasing the population of C6 and decreasing C4. With these altered populations, spectra were simulated for each case and similarity analysis carried out. The spectra derived from populations with electronic energies yielded slightly inferior similarity values (SimVA = 0.84, SimVCD = 0.41, and SimVDF = 0.36) for the 900–1700 cm–1 region. The simulated spectra with equal populations yielded lower intensities for the 1420 cm–1 band and improved overall quantitative similarity for the 900–1700 cm–1 region in VA and VCD spectra slightly (SimVA = 0.87 and SimVCD = 0.48), but simVDF has decreased from 0.36 to 0.28. When the population of C6 was increased and that of C4 decreased, via the combination C5(0.29), C6(0.27), C3(0.14), C4(0.1), C2(0.1), and C1(0.1), the predicted intensities of the 1420 cm–1 band were lowered and some improvement was found for the similarity values for the 900–1700 cm–1 region (SimVA = 0.88, SimVCD = 0.46, and SimVDF = 0.40; see the SI) compared to those in Table . It turned out to be difficult to improve the similarity values further without negatively influencing the VCD doublet at ∼1088 and 1055 cm–1. Thus, a satisfactory procedure for fully correcting the overestimated intensities of the 1420 cm–1 band of 1-indanol in CCl4, without negatively influencing other regions of spectra, remained elusive. Even if a different combination of populations happens to improve the similarity values, the task of finding experimental proof for such hypothesized populations remains to be undertaken.

(S)-1-Indanol in a Hydrogen-Bonding Solvent, DMSO-d6

To analyze the experimental spectra of (S)-1-indanol obtained in DMSO-d6 solvent, two different calculations are undertaken: (a) one set of calculations is carried out with PCM representing the DMSO solvent. However, PCM cannot realistically represent the solute–solvent interactions, especially when hydrogen bonding is involved.[43] (b) DMSO solvent has very high propensity for forming hydrogen bonds with solute molecules containing O–H and N–H groups, and in such cases, successful reproduction of experimental spectra by the predicted spectra without incorporating explicit solvent molecules becomes a challenge. For this reason, an explicit DMSO molecule is added in two different orientations to each of the six conformations of (S)-1-indanol. These complexes are optimized at B3LYP/6-311++G(2d,2p) level with PCM representing DMSO solvent environment. The complexed DMSO molecule in each of the optimized structures is then rotated to 90, 180, and 270° around the hydrogen bond to explore the conformational space of the 1-indanol/DMSO complex. This process led to investigating a total of 48 conformers. The optimized 30 lowest energy structures at B3LYP/6-311++G(2d,2p) level, with PCM representing DMSO solvent environment, are used for VA and VCD calculations on the 1-indianol/DMSO-d6 complex at the same level of theory, and none of these structures had imaginary vibrational frequencies. The energies, populations, and dihedral angles associated with these 30 conformers are presented in Table and conformer structures displayed in Figure .

Table 6

Energies and Populations of Conformers of 1-Indanol/DMSO-d6 Complex at B3LYP/6-311++G(2d,2p)/PCM(DMSO) Level

				dihedral angle
conf #	Gibbs energy (hartrees)	ΔE (kcal/mol)	population	C9–C4–C3–C2	C9–C1–O–H	C1–O···O=S
18	–977.46953	0.00	0.11	16.46	–156.29	–78
14	–977.46924	0.19	0.08	16.46	–157.57	–91.8
38	–977.46922	0.20	0.08	16.44	–157.22	–63.5
16	–977.46903	0.32	0.07	16.47	–156.33	111.8
12	–977.46890	0.40	0.06	16.44	–156.31	144.5
35	–977.46886	0.42	0.06	16.40	–98.20	85.7
13	–977.46880	0.46	0.05	16.48	–158.42	97.8
54	–977.46862	0.57	0.04	16.31	59.84	–110.4
61	–977.46842	0.70	0.03	–14.25	–74.15	105
56	–977.46841	0.70	0.03	16.40	60.81	–173.6
32	–977.46840	0.71	0.03	16.38	–97.05	99.1
11	–977.46840	0.71	0.03	16.47	–157.76	–107.8
34	–977.46829	0.78	0.03	16.21	–83.62	–97.3
62	–977.46816	0.86	0.03	–14.11	–73.60	–129
21	–977.46815	0.87	0.03	–14.52	–169.88	–89.3
22	–977.46811	0.89	0.03	–14.55	–170.44	157.8
24	–977.46792	1.01	0.02	–14.47	–170.72	105.2
67	–977.46787	1.04	0.02	–14.32	–73.53	147.8
51	–977.46784	1.06	0.02	16.32	58.73	5.3
52	–977.46783	1.07	0.02	16.27	59.56	–102.2
57	–977.46767	1.17	0.02	16.43	58.51	95.5
64	–977.46765	1.18	0.02	–14.12	–74.14	–115.7
58	–977.46765	1.18	0.02	16.37	59.00	–5.1
23	–977.46763	1.19	0.02	–14.59	–170.75	140.2
53	–977.46760	1.21	0.01	16.41	58.85	112.2
42	–977.46741	1.33	0.01	–13.02	54.90	–101.1
65	–977.46738	1.35	0.01	–14.28	–73.85	111
41	–977.46718	1.48	0.01	–13.42	55.67	175.3
44	–977.46704	1.57	0.01	–13.21	55.06	126.2
43	–977.46673	1.76	0.01	–13.57	57.49	178.1

Figure 10

Different conformers of (S)-1-indanol–DMSO complexes. See Table for relevant dihedral angles.

Table lists some conformers with nearly the same C9–C4–C3–C2 and C9–C1–O–H dihedral angles. For example, the five lowest energy conformers (#18, #14, #38, #16, and #12) have nearly the same C9–C4–C3–C2 and C9–C1–O–H dihedral angles, making one wonder if they are in fact distinctly separate conformers. In this connection, it is useful to note that the orientation of DMSO molecules can be different even for the same C9–C4–C3–C2 and C9–C1–O–H dihedral angles. For this reason, an additional dihedral angle C1–O···O=S, relating the C1–O bond of the parent molecule to the S=O bond of the solvent molecule is also included in Table . With the three dihedral angles listed, one can identify the differences in conformers that have the C9–C4–C3–C2 and C9–C1–O–H dihedral angles. However, even with the use of these three dihedral angles, the two higher energy structures #41 and #43 do not appear to be significantly different. But they are in fact different in terms of the inversion at S atom of the solvent molecule (see Figure ).

It is important to note that (S)-1-indanol/DMSO complexes adopt both positive and negative ring puckering angles for the five-membered ring, with 77% population contribution coming from the conformers with positive ring puckering angle. Also, since O–H group can have free rotation around C–O bond, the hydrogen-bonded DMSO molecule is in a different relative orientation with respect to the parent molecule. This should not be viewed as a hydrogen-bonded DMSO molecule rotating with O–H group; instead, this could be viewed as a different DMSO molecule from the solvent bath hydrogen bonding to O–H in a different orientation.

The experimental VA and VCD spectra of 1-indanol in DMSO-d6 solvent are compared to the population-weighted QC-predicted spectra for 1-indanol/DMSO-d6 complex in Figure , and SSO plots are displayed in Figure F. The excellent correlation between experimental and predicted spectra features is surprising, given that modeling hydrogen-bonding interactions with the solvent is often challenging.[43] The correlation of experimental (and predicted) spectra is as follows. In VA spectra: 1602 (1633), 1476 (1488), 1457 (1456), 1323 (1332), 1284 (1316), 1261 (1284), 1209 (1225), 1178 (1204), 1151 (1172), and 1101 (1109); in VCD spectra: 1479 (1509), 1466 (1491), 1418 (1453), 1300 (1356), 1289 (1319), 1266 (1283), 1212 (1227), 1182 (1204), 1136 (1160), and 1101 (1109). Of these, there are three places where some differences are apparent: The weak positive VCD band at 1300 cm–1 seen in the experimental spectrum does not match in sign with the predicted VCD at 1356 cm–1. The weak negative experimental VCD band at 1289 cm–1 is not as well developed as the corresponding predicted negative VCD at 1319 cm–1. The weak positive VCD band seen in the experimental spectrum at 1241 cm–1 is not resolved in the predicted spectrum.

Figure 11

Comparison of experimental and predicted VA (bottom panel), VCD (middle panel), and VDF (top panel) spectra for (S)-1-indanol–DMSO-d6 complex. The left vertical panels display overlaid spectra after scaling the calculated vibrational frequencies with 0.9825, whereas the right vertical panels display stacked spectra with unscaled vibrational frequencies and labeled band positions. Experimental VA and VCD spectra are taken from ref (30) with permission from the Royal Society of Chemistry.

Except for the differences associated with weak bands mentioned above, the overlaid VA and VCD spectra show good match in the entire 1700–1100 cm–1 region of the experimental spectrum. The quantification of this match is reflected in a similarity analysis (see Figure H and Table ), which yields 0.89, 0.61, and 0.66 for SimVA, SimVCD, and SimVDF, respectively. The SimVCD and SimVDF values obtained here are better than those for 1-aminoindan and 1-indanol in CCl4. Also, the SimVDF value obtained for 1-indanol/DMSO-d6 complex is larger than that for 1-aminoindan and as high as that for 1-methylindan and 1-methylindan-1-d.

VA and VCD spectra of (S)-1-indanol in DMSO-d6 have been analyzed previously by Zehnacker et al.[30] They reported predicted spectra using NVP theory, B3LYP functional, and 6-31++G(d,p) basis set adopting different approaches: (1) conventional static optimized geometries and PCM representing the DMSO solvent continuum; (2) conventional static optimized geometries for 1:1 indanol/DMSO complex and PCM representing the DMSO solvent continuum; (3) conventional static optimized geometries for 1:2 indanol/DMSO complex and PCM representing the DMSO solvent continuum; and (4) FPMD for capturing the dynamical behavior of 1-indanol in a box of DMSO solvent molecules, optimizing the geometries of snapshots extracted from the MD trajectories. Optimization of snapshots from FPMD trajectories resulted in both pseudoequatorial and pseudoaxial conformers and provided improved comparison between predicted and experimental VCD spectra, although disagreement (resulting from a large negative doublet in the predicted spectrum) in the region around 1300 cm–1 still persisted.[30]

The main point leading to the differences in the previous and present results can be associated with the following aspect: in the previous conventional static optimized geometry calculations,[30] only four major geometries of the 1:1 indanol/DMSO complex, all with pseudoequatorial orientation of O–H group, were considered for VCD predictions on 1-indanol/DMSO-d6 complex. This is different from the current finding that nearly 30 different static geometries (with 77% population coming from pseudoequatorial conformers and 23% from pseudoaxial) are needed to describe the 1-indanol/DMSO conformational space. The critical point to recognize here is that rotating the O–H group around C–O bond and complexing a DMSO molecule in each of the new O–H orientations is important for exploring the conformational space of the 1-indanol/DMSO complex. With these precautions, the present conventional static optimized geometry calculations can be seen to be a successful (see Table , Figure and overlaid spectra in Figure ) alternative to FPMD simulations in reproducing the experimental VCD spectra in the 1700–1100 cm–1 region of the 1-indanol/DMSO-d6 complex. This observation should not be interpreted as discouraging the general use of MD simulations, because the analyses of solution-phase spectra using MD geometries have certainly helped in many situations.[22−24]

Conclusions

(S)-1-Methylindan, and (R)-1-methylindan-1-d have just two conformations resulting from opposite ring puckering angles. Ring puckering conformer populations that result in pseudoequatorial vs pseudoaxial substituent are in the ratio of ∼80:20. Ring puckering conformer-specific VCD bands could be clearly identified in the experimental spectra of 1-methylindans, and pseudoaxial contribution is important for reproducing the experimental spectra. (R)-1-Aminoindan and (S)-1-indanol in CCl4 have six conformations, resulting from the rotation of the NH2/OH substituent for each of the two ring puckering conformations. On the contrary, (S)-1-indanol in DMSO has numerous hydrogen-bonded conformations with ∼80% arising from ring puckering that results in the pseudoequatorial substituent and ∼20% from the pseudoaxial substituent. The QC-predicted spectra for the minimum energy geometry optimized conformers of (S)-1-methylindan, (R)-1-methylindan-1-d, (R)-1-aminoindan, and (S)-1-indanol in CCl4 and (S)-1-indanol/DMSO-d6 complex are found to be in excellent agreement with corresponding experimental VA and VCD spectra. The methods to correct overestimated VA and VCD intensities for the ∼1420 cm–1 band of 1-indanol in CCl4, without negatively influencing other regions of spectra, however, remain to be identified.

Methods

Conformational Analysis and QC-Predicted Spectra

For all molecules studied here, an initial conformational search was conducted using CONFLEX,[38] unless otherwise stated. Final optimizations were carried out using B3LYP functional[31−33] and 6-311++G(2d,2p) basis set,[34] as implemented in the Gaussian program,[44] followed by QC prediction of VA and VCD at the same level. VCD spectra were obtained using magnetic field perturbation theory,[17−19] as implemented in the Gaussian 09 program.[44] The QC-predicted spectral intensities were Boltzmann population-weighted using Gibbs free energies and spectra simulated using Lorentzian band profiles with 10 cm–1 band width. For all four indan molecules considered, calculations were done for the (S) configuration. Since experimental spectra were reported for the (R)-enantiomers of 1-methylindan-1-d and 1-aminoindan, the corresponding calculated VCD spectra were multiplied by −1 for comparison to the experimental spectra. The comparisons between experimental and QC-predicted spectra and similarity analysis were carried out using CDSpecTech.[28,29] SSO plots were also generated using CDSpecTech.

Spectral Similarity Overlap (SSO) Plots

SSO was calculated using the Sim function suggested by Shen et al.[45] The Sim function is given as[35]In eq , h(x) represents the experimental spectrum as a function of the running index for x-axis values; subscript XXX represents the type of spectrum (XXX = VA, VCD, VDF); f(σ:x) represents the simulated predicted spectrum obtained after scaling the predicted transition frequencies/wavelengths with a scale factor σ; SimXXX(σ) represents the numerical measure of SSO between experimental and predicted spectra as a function of σ, for the type of spectrum XXX; the integrals run over the spectral region of interest. The display of SimXXX(σ) as a function of σ is referred to as the SSO plot.[27,29] For similarity analysis, VA, VCD, and VDF spectra are normalized individually using square root of the sum of squared intensities.

The range for SimVCD, as well as SimVDF, values is −1 to +1. A value of +1 indicates perfect agreement of experimental spectra with predicted spectra of correct AC. A value of −1 indicates perfect agreement of experimental spectra with predicted spectra of AC, opposite to that used for calculations. The range for SimVA values is 0–1 and does not relay information on the AC.

We have previously advocated that the analysis of VCD spectra, without accompanying absorption spectra, is not appropriate. Furthermore, although separate evaluations of QC predictions of VA and VCD spectral intensities may appear satisfactory, the VDF (ratio of VCD to VA) spectra are more challenging for QC predictions. For this purpose, we have advocated the quantitative analysis of experimental and predicted VDF spectra to verify the agreement between them.[27−29,46−48] The agreement between experimental and predicted spectra is quantified using maximum SimVA, SimVCD, and SimVDF values in SSO plots. While SimVA value comes out to be generally high and not very discriminatory, SimVCD and SimVDF values provide good measures of quantitative agreement between experiment and QC predictions of VCD and VA. Achieving a SimVCD value of +0.4 or higher is recommended for an acceptable agreement between experimental and calculated spectra for assigning the correct molecular structures.[35] Approximately the same value of SimVDF is also recommended.

VDF has the advantage that it is not influenced by errors in concentration and path length, when both VA and VCD spectra are measured simultaneously for the same sample and using the same instrument. The influence of baseline off-sets and of VCD magnitude calibration error is suppressed during the calculation of SimVDF by normalizing the intensities in VDF spectra. This process can only take care of the situation where the experimental baseline offset is constant as a function of the wavenumber and experimental VCD magnitudes are off by a constant as a function of the wavenumber. If the VCD baseline is not horizontal, then VDF will not appear normal and cannot be used. That is why, it is important to have a good reliable experimental VCD spectrum before proceeding to calculate VDF.

Two considerations are taken into account in calculating VDF spectra: (a) baseline tolerance for absorption spectra and (b) reliability criterion for experimental VDF signals, which we previously referred to as the robustness criterion based on experimental ΔA/A values. Baseline tolerance for absorption spectra helps remove the amplification of noise in the regions where absorbance is nearly zero and the associated VCD signal is only noise. The choice for absorption baseline tolerance influences only small regions of spectra for the molecules considered (for example, the region around 1400 cm–1 for 1-aminoindan). The choice for reliability criterion for experimental VDF signals can vary from instrument to instrument and for individual research groups. In the past, we have been using 40 ppm (i.e., ΔA/A = 4 × 10–5) as the threshold for reliability, in which case spectral regions with VDF less than 40 ppm are blanked out, giving the appearance of spectral discontinuities in VDF spectra. To avoid the appearance of such unpleasant spectral discontinuities, the VDF spectral analysis presented in this manuscript did not impose any reliability criterion for experimental VDF signals. For the interested readers, VDF spectra with 40 ppm reliability criterion are presented in the Supporting Information. The SimVDF values, in general, did not change significantly with and without reliability criterion (compare Table and Table S1 in the SI). For 1-indanol in CCl4, SimVDF has improved when the reliability criterion is not imposed.

Experimental Spectra

The experimental spectra of (S)-1-methylindan, (R)-1-methylindan-1-d, and (R)-1-aminoindan were reported previously[16] where all spectra were recorded for neat liquids in absorbance units, but y-axis values cannot be discerned with sufficient quantitative accuracy. The spectra for (S)-1-indanol in CCl4 and in DMSO-d6 solvents were reported by Zehnacker et al.,[30] where y-axis values were not available. These literature experimental VA and VCD spectra were digitized using WebPlotDigitizer[49] and normalized for carrying out similarity analyses. The excessive level of absorbance in some spectral regions restricted the analysis of experimental VCD spectra to the following regions: 925–1320 cm–1 for 1-methylindan; 920–1345 cm–1 for methylindan-1-d; 950–1450 cm–1 for 1-aminoindan; 900–1700 cm–1 for 1-indanol in CCl4; and 1100–1700 cm–1 in DMSO-d6. The y-axes values in the displayed VA and VCD spectra are those of predicted spectra in molar extinction units; VDF spectral intensities are presented as ppm. The experimental spectral intensities were scaled to be on the same scale as those for predicted spectra.