DFT study of vibrational circular dichroism spectra of D-lactic acid–water complexes

Abstract

This paper presents a discussion of the interaction energies, conformations, vibrational absorption (VA, harmonic and anharmonic) and vibrational circular dichroism (VCD) spectra for conformers of monomeric chiral D(−)-lactic acid and their complexes with water at the DFT(B3LYP)/aug-cc-pVDZ and DFT(B3LYP)/aug-cc-pVTZ levels. A detailed analysis has been performed principally for the two most stable complexes with water, differing by lactic acid conformation. The VCD spectra were found to be sensitive to conformational changes of both free and complexed molecules, and to be especially useful for discriminating between different chiral forms of intermolecular hydrogen bonding complexes. In particular, we show that the VCD modes of an achiral water molecule after complex formation acquire significant rotational strengths whose signs change in line with the geometry of the complex. Using the theoretical prediction, we demonstrate that the VCD technique can be used as a powerful tool for structural investigation of intermolecular interactions of chiral molecules and can yield information complementary to data obtained through other molecular spectroscopy methods.

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I. Introduction

Small biomolecules have received a lot of attention because of their relative simplicity. They are also suited to theoretical treatment by methods based on first principles. The joint analysis of experimental methods such as Raman, vibrational absorption (VA), and vibrational circular dichroism (VCD) spectroscopies, as well as theoretical treatments, plays an important role in providing insight into the processes that take place in proteins and peptides. It has been known for a long time that water interactions play a vital structural role in proteins and peptides.¹ Arguably, to reach a better understanding of the crucial role of water molecules in modifying the arrangement of biomolecules, one needs to investigate hydration phenomena at the quantum mechanical level.

VCD is an attractive technique, since the VCD spectrum provides a unique fingerprint information for a chiral molecule. It requires the molecule to have at least one chiral center (element), which allows the molecule to exhibit chirality and optical activity. The VCD spectra of chiral molecules are of interest from both a theoretical and biophysical standpoint. Each VCD band reports information regarding the molecular structure and the coupling of particular vibrational modes in the chiral molecules. Thus, the VCD spectrum is a subtle, stereospecific effect associated with the interaction of a chiral molecule with light. Although the intensity scale of the VCD spectra is approximately four orders of magnitude smaller than the scale for the parent VA (IR) spectra, nowadays advances in laser technology enables one to collect spectra of biologically interesting molecules and to reveal sensitive structural and stereochemical details of molecules in an aqueous environment.²

The ab initio calculations of VCD spectra prove a difficult and time-consuming computational task. In order to predict a VCD spectrum, it is necessary to evaluate the vibrational electric and magnetic dipole transition moments. Moreover, as so frequently occurs in the case of calculations of properties involving magnetic dipole operators, there arises a question of the origin-dependence of the results. As a consequence, most ab initio studies of the VCD effect focused on medium-sized molecules exhibiting optical activity.³ Theoretical prediction of the IR absorption and VCD spectra within the harmonic approximation requires calculations of harmonic frequencies and dipole and rotational strengths. These quantities, in turn, demand calculation of the molecular Hessian, harmonic force field (HFF), atomic polar tensors (APT), and atomic axial tensors (AAT).^4–6

Several recent developments have enhanced the efficiency of calculations of VCD spectra involving the application of density functional theory (DFT) methods. Recently, DFT has been accepted by the ab initio quantum chemistry community as a cost-effective approach to computations of molecular structures and spectra (vibrational and NMR) of molecules of chemical interest. Many studies have shown that vibrational frequencies calculated by DFT methods are more reliable than those obtained at MP2 level.^7,8

For VCD spectra calculations, the implementation of direct analytical derivative methods for calculating HFFs, APTs, and AATs⁹ is of most importance. Incorporation of gauge invariant atomic orbitals (GIAO) into the calculation of AATs makes it possible to predict the VCD spectra using the DFT method. It was shown that the spectra predicted using the DFT hybrid functional methods were of greater accuracy than those produced by the HF and MCSCF calculations.^10,11

Numerous experimental and theoretical studies were devoted to proving the advantage of engaging the VCD spectra in determinations of conformational structure shaped by intramolecular hydrogen bonding.¹² However, the subject of the influence of intermolecular H-bonds was undertaken in relatively few papers, where geometrical arrangement of the H-bond partners was shown to be determinable based on the VCD spectra.^13–16 Our current interest in the VCD spectra is provoked by the potential use of the VCD technique in this way.

This paper aims to explore the role of VCD spectra in determining the intermolecular H-bond geometry of the complex of D-lactic acid with a water molecule. Lactic acid belongs to the group of α-hydroxyacids and is one of the simplest chiral molecules usually chosen as a model for studying biological systems exhibiting organic acid-type bonding. In eukaryotic cells, lactic acid is produced as a result of glucose anaerobic metabolism. It is also the main metabolic product of lactic acid bacteria. The molecule displays a quasi-planar HOC–COOH molecular skeleton with the oxygen atom of the aliphatic hydroxyl groups beside the C=O group in the crystal structure.¹⁷ The acidic hydroxyl group is involved in intermolecular H-bonding as a proton donor to the aliphatic hydroxyl group of a neighboring molecule, while the aliphatic hydroxyl group also participates in a bifurcated intramolecular H-bond, in which the aliphatic hydroxyl and acid carbonyl oxygen atoms of a symmetry-related molecule participate as acceptors. The microwave spectrum analysis of lactic acid in the gaseous phase shows that a conformation with a H-bond from the α-hydroxyl group to the carbonyl oxygen is the most stable form of the molecule.¹⁸ The Raman spectra of lactic acid have been collected in aqueous solution,^19,20 where the lactic acid is shown to be dissociated.

Lactic acid was studied theoretically by Pecul et al.²¹ at the SCF and MP2/aug-cc-pVDZ levels. However, only two low energy minima on the potential energy surface (PES) were discussed in their work. Recently, an analysis of argon and xenon matrix-isolation FT-IR spectra at 9 K has been published and supported with a systematic search for the possible minima on the PES, using the DFT(B3LYP)/6-311++G(d,p) and MP2/6-31G(d,p) calculations.²² That very experiment was the first to show the existence of three low energy conformers of lactic acid.

To the best of our knowledge, no experimental VCD spectra of the lactic acid optical isomers are available in the literature. A comparison of theoretical predictions and experimental spectra would be difficult even if more experimental data were available, because lactic acid may be present in most solvents in the form of dimers (and/or complexes with the solvent). However, according to the authors of ref. 22, “water doping of the matrix allowed the identification of spectral features ascribable to weakly bound complexes of lactic acid with water”. In the FT-IR spectra the isolated lactic acid monomers (three conformers) and weakly bonded lactic 1 : 1 acid⋯water complexes were detected.²² These findings yielded us an additional argument to study the complexes theoretically.

The lactic acid molecule (Scheme 1) has four sites potentially amenable to forming H-bonds with water, i.e., the proton donor carboxylic OH group, alcoholic COH group, proton acceptor carboxylic C=O group and alcoholic oxygen atom. The H-bond of water with the whole –COOH group seems to be of particular importance, as both the water molecule and the –COOH group simultaneously play proton donor and proton acceptor roles. All these possibilities turn the hydration of a lactic acid molecule into an interesting subject to be investigated by theoretical means. The interaction with water is expected to affect the conformational stability of the lactic acid molecule; hence characterization of the complexes with water seems to be important for understanding the dissociation process as well as for acquiring other valuable information on the properties of the H-bonding of this molecule.

Scheme 1

As far as we are aware, with the exception of the study of Borba et al.,²² the lactic acid–water complex has not been observed in spectroscopic experiments or considered in theoretical studies. In this study we analyze the conformational stability of 1 : 1 H-bonded complexes formed between lactic acid and water. Thus, the first aim of this paper is to study possible structures and the infrared spectra of stable hydrated complexes. The second priority of this paper is to obtain some insight into the influence of the molecular conformation and presence of intermolecular H-bonds on the VCD spectra using lactic acid as a model system. We hope that the analysis of the influence of molecular conformation on the VCD spectra will contribute to the development of VCD spectroscopy as a tool for structural investigations of biologically active compounds. We wish to utilize this feature in our computational research.

II. Computational details

All of the calculations were performed using DFT with the B3LYP hybrid functional, which includes Becke’s gradient exchange correction and the Lee, Yang and Parr correlation functionals,²³ combined with the aug-cc-pVDZ and aug-cc-pVTZ basis sets. The relevance of DFT for VCD calculations has been widely accepted, see for example refs. 4 and 24. The Dunning’s basis sets are known to adequately describe H-bonded systems.²⁵ Our work was comprised of two key stages: the first involved geometry and energy calculations of lactic acid and its complexes with water molecules; the second focused on calculations of IR frequencies, intensities, and VCD spectra of the monomers and complexes. It is well known that the geometries of monomers in a complex differ slightly from their optimal isolated geometries. Therefore, ab initio calculations of the interaction, binding and dissociation energies require a fairly meticulous approach. The interaction energies (ΔE_int) of the complexes have been obtained as the difference of the total energy between the complex and isolated monomers. Then, we corrected the computed interaction energy for the basis set superposition error (BSSE) using the technique prescribed by Boys and Bernardi.²⁶ To compute the binding energy D_e, the interaction energy has to be corrected for the so-called deformation energies,²⁷ that is, the energy needed to deform the monomers from their optimal equilibrium geometries so that they can assume their geometries in a complex. Finally, dissociation energies D₀ were obtained from the binding energies by applying the correction for the zero-point vibrational motion (ΔE_ZPE), an estimate based on harmonic frequencies. Hence, we report both D_e and D₀ energies. Calculations of the harmonic VA and VCD spectra were computed using the DFT HFFs, APTs, and AATs calculated by direct analytical methods implemented within the Gaussian98 program.^28a The anharmonic VA spectra were calculated using the Gaussian 03 suite of programs.^28b The AATs are calculated by means of the GIAO basis set. Accordingly, AATs are gauge-independent, and yield origin-independent rotational strengths. The vibrational modes have been analyzed using the potential energy distribution (PED) analysis implemented in the VEDA program.²⁹ The harmonic frequencies were scaled down to approximately account for various systematic errors in the theoretical approach.³⁰ Finally, the effect of anharmonicity was investigated by calculating anharmonic frequencies.

III. Results and discussion

A. Geometries, energies, vibrational frequencies, and VCD spectra of the D-lactic acid monomers

The lactic acid molecule has three axes around which free rotations are possible. As a result, quite a number of local minima might occur. However, due to the possibility of intramolecular H-bond formation, some of them are much more stabilized than the others. The three low energy structures of lactic acid (I, II, III, Fig. 1), out of the four studied here at the B3LYP/aug-cc-pVDZ and B3LYP/aug-cc-pVTZ levels (Table 1), are stabilized solely by intramolecular H-bonds.

Fig. 1 Considered conformers of D-lactic acid.

Table 1 Relative binding D_e, dissociation D₀, and Gibbs free energies ΔG₂₉₈ (p = 1 atm, T = 298.15 K) and dipole moments (μ) for various conformations of lactic acid calculated using the B3LYP functional and two basis sets

		aug-cc-pVDZ				aug-cc-pVTZ
Conformer	D e(X–I)/kJ mol^−1^a	D 0(X–I)/kJ mol^−1^a	ΔG298/kJ mol^−1	μ/D	D e(X–I)kJ mol^−1^a	D 0(X–I)kJ mol^−1^a	ΔG298/kJ mol^−1	μ/D
a D(X–I) = D(X)–D(I)
I	0	0	0	2.383	0	0	0	2.370
II	8.79	8.70	8.12	1.616	9.29	9.25	8.28	1.519
III	10.63	10.46	10.04	4.928	10.75	10.33	9.46	4.888
IV	19.37	18.74	18.07	3.278	20.08	18.95	17.74	3.258

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According to the methods used in this work, conformer I is predicted to be the most stable, with the energy differences with conformers II, III, and IV being 9.25, 10.33, and 18.95 kJ mol⁻¹, respectively. The DFT(B3LYP)/aug-cc-pVDZ method used throughout this study is fairly sophisticated for monomers, and it yields relative stabilization and Gibbs free energies concordant with those obtained using the DFT(B3LYP)/aug-cc-pVTZ level (Table 1). Moreover, these results are in good agreement with the recently published DFT and MP2 results.²² For example, at the MP2/ 6-31++G(d,p) level the energies of the conformers GskC, AaT, and AsC (here denoted as II, III, and IV), in relation to the energy of the ScC conformer (I in our notation), equal 6.5, 11.4, and 18.5 kJ mol⁻¹, respectively.²²

Conformer I (Fig. 1) is stabilized by the intramolecular H-bond between the H12 proton of the alcohol O6–H12 group and the O4 oxygen atom of the carbonyl C3=O4 group. It is defined by the following dihedral angles: O4=C3–O5–H11, C3–C2–O6–H12, and C2–C3–O5–H11, which are equal to ca. 0.0, 0.2 and 179.5°, respectively. This conformer, with an almost planar structure of the five-membered intramolecular H-bond ring and a relatively short intramolecular H-bond H12⋯O4 distance (2.093 Å), is the global PES minimum. The second most stable conformer, II, (Fig. 1) is fixed by an O6–H12(alcohol)⋯O5–H11(carboxyl) intramolecular H-bond, where the O5 oxygen atom of the carboxylic OH group acts as a proton acceptor. For conformer II, the above-mentioned dihedrals equal −0.2, 46.0, and −177.3°, respectively. Thus, these two conformers differ in their rotation around the C2–C3 axis. In the third conformer, III, (Fig. 1), an intramolecular H-bond is formed between O5–H11(carboxylic)⋯O6–H12(alcoholic) groups, where (as opposed to conformation I) the carboxylic C=O and alcoholic O–H groups are in the energetically less favorable trans configuration and the alcoholic oxygen atom acts as a proton acceptor. In this case, the dihedrals equal 179.0, −164.4, and −1.7°, respectively. The fourth conformer considered here, IV, is quite high in energy (Fig. 1, Table 1), and is not stabilized by an intramolecular H-bond. As may be seen in ref. 22, the remaining conformers of lactic acid are even higher in energy and are not studied in this paper. As one may expect from energy differences between the first three conformers, all of them were identified in a most impressive experimental study of the lactic acid Ar and Xe low temperature matrix IR spectra.²²

Each of the three conformers has an intramolecular H-bond. In two of them, I and II, the alcoholic proton is involved in the intramolecular H-bond as a proton donor, while in the conformer III, the oxygen atom of the alcoholic group acts as a proton acceptor. That is, the O–H bond in the conformer III is much shorter (0.964 Å) than its counterpart in conformers I and II (0.971 and 0.966 Å, respectively). Unlike in the above-described cases, the carboxylic OH group is a proton donor only in the conformer III, and therefore the group exhibits the greatest O5–H11 distance of 0.975 Å, whereas in conformers I and II the analogous distances equal 0.971 Å. Enlargement of the basis set from aug-cc-pVDZ to aug-cc-pVTZ did not change the results significantly.

The vibrational frequencies are discussed solely for conformers I and II. All 30 IR active fundamental vibrations are considered and interpreted. The frequencies of the most important modes: stretching ν(OH_C), ν(OH_A), ν(C=O), ν(C–H), ν(C–O), bending and out-of plane were found to be close to the other calculated values, and to the data found in experimental literature.²² This may serve as evidence that the calculated frequencies of monomeric lactic acid described in this paper constitute reliable reference data for calculations of frequency shifts in H-bonding complexes with water molecules.

The coordinate definitions for the analysis of the vibrational spectra of the lactic acid are presented in Table 2. Tables 3 and 4 contain the interpretation of the calculated IR frequencies, VA intensities, and VCD spectra for conformers I and II.

Table 2 The internal coordinate definitions for the PED analysis of the vibrational spectra of lactic acid interacting with a H₂O molecule (Ia and IIa) and of the monomers (I and II )

Number	Mode description	Name	Monomer
Modes: ν-stretching, β-bending, τ-torsion, δ-out-of-plane bending, σ-hb stretching, λ-libration Indices: W-water, A-alcoholic, C-carboxylic, hb-H-bonded, free-not H-bonded, s-symmetric, a-asymmetric, S-skeleton, butt-butterfly, MI, MII-monomers I, II.
1	R(O13–H15)	ν(OHW,free)
2	R(O6–H12)	ν(OHA)
3	R(O13–H14)	ν(OHW,hb)
4	R(O5–H11)	ν(OHC)
5	R(C1–H7) − R(C1–H9)	ν ^a(CH3)1
6	R(C1–H8) − R(C1–H9)	ν ^a(CH3)2
7	R(C1–H7) + R(C1–H8) + R(C1–H9)	ν ^s(CH3)
8	R(C2–H10)	ν(C*H)
9	R(C3–O4)	ν(C=O)
10	A(H14–O13–H15)	β(H2O)
11	A(H7–C1–H9) − A(H8–C1–H9)	β ^a(CH3)
12	A(H7–C1–H8) − A(H7–C1–H9) − A(C3–O5–H11)	β(CH + OH)1
12MI, MII	A(H7–C1–H8) − A(H8–C1–H9)		β(CH)1
13	A(H7–C1–H8) + A(H10–C2–C3) + A(C3–O5–H11) − A(C2–O6–H12)	β(CH + OH)2
13MI, MII	A(H10–C2–C6) + A(C3–O5–H11) + A(C2–O6–H12)		β(CH + OH)2
14	A(H7–C1–H8) − A(H10–C2–C3) + A(C3–O5–H11) + A(C2–O6–H12)	β(CH + OH)3
14MI	A(H7–C1–H8) − A(H10–C2–C3) − A(C3–O5–H11) + A(C2–O6–H12)		β(CH + OH)3
14MII	A(H7–C1–H9) + A(H10–C2–C3) − A(C2–O6–H12)		β(CH + OH)3
15	A(H7–C1–H8) + A(H7–C1–H9) + A(H8–C1–H9)	β ^s(CH3)
16	D(H10–C1–C3–C2)	τ(C*H)
17	A(H10–C2–C3) + A(H12–O6–C2)	β(C*H + OHA)
18; 18MII	R(C3–O5)	ν(C–O)
18MI	R(C3–O5) + R(C2–O6)		ν ^s(C–O)
19; 19MII	R(C1–C2) − R(C2–O6)	ν(C*O)
19MI	R(C3–O5) − R(C2–O6)		ν ^a(C–O)
20	D(H8–C2–C3–C1) − D(H9–C2–O6–C1)	τ(CH3)
21	A(C2–C1–H9) − A(C3–C2–H10)	β(C*H)
22	R(C1–C2) − R(C2–C3) − R(C3–O5)	ν(S)1
23	D(H11–O5–C3–C2) + D(H14–O13–H11–O5)	δ(OHC)
23MI, MII	D(H11–O5–C3–C2)		δ(OHC)
24	R(C1–C2) + R(C2–C3) + R(C3–O5)	ν(S)2
25	D(C2–O4–O5–C3)	τ(OC=O)
26	A(H11–O13–H14) + A(H14–O4–C3)	β(OHW⋯O)
27	A(O4–C3–O5)	β(OC=O)
28	Ia A(C2–C3–O5)
	IIa A(C2–C3–O5) − A(C3–C2–O6)	β(CC–OC)
29	A(C1–C2–O6)	β(CC–OA)
30	D(H11–O13–H14–O4) + D(H12–O6–C2–C3)	λ(H2O + OHA)
30MI	D(H12–O6–C2–C3)		δ(OHA)
31	Ia A(C2–C3–O4) + A(C3–C2–O6)
	IIa A(C1–C2–O3) + A(C2–C3–O5)	β(O=CC–OA)
32	Ia D(H11–O13–H14–O4) − D(H12–O6–C2–C3)	λ(H2O–OHA)
	IIa D(H12–O6–C2–C3)	δ(OHA)
33	A(C1–C2–C3)	β(CCC)
34	D(H15–O13–H14–O4)	δ(OHW,free)
35	D(H7–C1–C2–C3) + D(H8–C1–C2–C3) + D(H9–C1–C2–C3)	λ(CH3)
36	R(H11–O13)	σ(OHC⋯O)
37	R(O4–H14) − R(H11–O13)	σ(OHW⋯O)
38	Ia D(H14–O4–C3–C2) + D(C1–C2–C3–O4)
	IIa D(H14–O4–C3–C2)	τ(butt)1
39	Ia D(H14–O4–C3–C2) − D(C1–C2–C3–O4)
	IIa D(C1–C2–C3–O4)	τ(butt)2
39MI, MII	D(C1–C2–C3–O4)		τ(butt)

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Table 3 The B3LYP/aug-cc-pVDZ calculated IR frequencies and intensities, VCD rotational strengths R_i of the Ia complex of D-lactic acid⋯water, and of D-lactic acid conformer I

Complex Ia						Monomer I
ν harm cm^−1	ν scal ^a cm^−1	ν anharm cm^−1	I IR km mol^−1	R i 10^−44 esu^2 cm^2	PED %	ν harm cm^−1	ν scal ^a cm^−1	ν anharm cm^−1	I IR km mol^−1	R i 10^−44 esu^2 cm^2	PED %
a ν scal = 0.955 νcalc + 29.6
3863	3719	3679	101.5	−28.90	95 ν(OHW,free)
3719	3581	3526	83.6	13.56	100 ν(OHA)	3719	3581	3533	86.0	16.3	100 ν(OHA)
3635	3501	3444	295.1	10.17	92 ν(OHW,hb)
3312	3192	3108	805.3	1.89	95 ν(OHC)	3738	3599	3540	73.0	−2.2	100 ν(OHC)
3137	3025	2980	14.3	−1.90	94 ν^a(CH3)1	3136	3024	2982	12.6	−3.7	96 ν^a(CH3)1
3126	3015	2967	18.9	4.11	92 ν^a(CH3)2	3127	3016	2970	18.4	3.8	95 ν^a(CH3)2
3046	2938	2863	14.7	−0.98	99 ν^s(CH3)	3047	2939	2923	13.3	−0.9	99 ν^s(CH3)
2996	2891	2846	25.2	−23.22	99 ν(C*H)	3002	2896	2844	24.3	−22.3	99 ν(C*H)
1744	1695	1716	260.9	49.19	74 ν(C=O)	1790	1739	1758	300.4	0.8	82 ν(C=O)
1607	1564	1558	131.9	−134.74	89 β(H2O)
1489	1452	1440	13.1	13.22	65 β(CH + OH)2 + 17 ν(C–O)	1330	1300	1312	74.2	44.2	57 β(CH + OH)2
1470	1433	1441	7.44	6.61	77 β^a(CH3) – 13 τ(CH3)	1469	1432	1432	8.3	6.3	83 β^a(CH3) −10 τ(CH3)
1454	1418	1414	1.35	−16.21	74 β(CH + OH)1	1476	1439	1437	2.7	2.4	71 β(CH)1
1397	1364	1344	24.4	−13.36	70 β(CH + OH)3	1424	1389	1371	5.1	−25.6	56 β(CH + OH)3
1384	1351	1353	5.7	22.44	83 β^s(CH3)	1386	1353	1515	9.4	11.3	87 β^s(CH3)
1336	1305	1296	6.2	−19.96	71 τ(C*H)	1335	1304	1301	15.6	−37.3	60 τ(C*H)
1287	1259	1246	259.2	133.21	30 β(C*H + OHA) + 31 ν(C–O)	1187	1163	1148	41.2	17.7	36 ν^s(C–O) −10 β(CH + OH)2
1249	1222	1221	17.1	−35.57	54 β(C*H + OHA)–16 ν(C–O)	1261	1234	1235	42.2	70.7	75 β(C*H + OHA)
1155	1133	1130	128.5	13.70	42 ν(C*O) − 14 τ(CH3) + 11 β(C*H)	1139	1117	1106	262.9	18.3	50 ν^a(C–O) − 11 β(CH + OH)3 − 12 τ(CH3)
1104	1084	1073	26.6	−29.02	16 ν(C*O) + 34 τ(CH3) − 13 ν(S)1	1103	1083	1073	39.4	−41.6	35 τ(CH3) −20 ν(S)1 − 16 ν(S)2
1044	1027	1023	36.1	35.66	21 ν(C*O) − 45 β(C*H)	1042	1025	1020	38.5	34.3	49 β(C*H) + 20 ν(S)1
935	922	910	2.3	4.29	17 τ(CH3) − 13 β(C*H) + 47 ν(S)1	931	919	908	1.3	10.5	28 ν(S)1 − 10 ν^s(C–O)
917	905	839	106.8	−7.19	85 δ(OHC)	579	582	551	54.3	83.1	69 δ(OHC)
823	815	806	20.1	−17.16	45 ν(S)2	805	798	792	23.2	−12.4	33 ν(S)2 + 13 τ(OC=O)
744	740	732	6.3	−3.43	36 τ(OC=O) − 21β(OC=O) − 12 β(CCC)	735	731	721	39.4	−12.5	38 τ(OC=O) − 22 ν(S)2 − 12 β(OC=O)
628	629	612	25.1	17.67	12 ν(C*O) + 14 τ(OC=O) + 43 β(OC=O)	632	633	615	42.6	−74.9	43 β(OC=O) + 12 ν^s(C–O) + 23 δ(OHC)
614	616	491	179.8	−16.06	74 β(OHW⋯O)
515	521	504	10.0	0.09	12 ν(S)2 + 44 β(CC–OC) + 13 β(CC–OA)	494	501	486	13.6	−4.7	40 β(CC–OC) + 18 β(CC–OA)
422	433	410	8.5	6.50	60 β(CC–OA)	408	419	393	15.6	1.7	51 β(CC–OA) + 10δ(OHA)
376	389	337	81.7	−184.31	49 λ(H2O + OHA) − 10 β(O=CC–OA)
360	373	330	32.8	114.25	62 λ(H2O–OHA)	353	367	268	48.9	−20.6	63 δ(OHA) − 11 β(CCC)
309	325	297	61.8	55.91	14 λ(H2O + OHA) + 40 β(O=CC–OA) − 10 λ(H2O–OHA)	298	314	254	28.4	13.2	41 β(O=CC–OA) + 21 δ(OHA)
276	293	261	69.9	18.00	36 β(CCC) − 15 σ(OHC⋯O)	243	261	237	0.7	8.6	43 β(CCC) + 10 τ(OC=O) + 11 β(CC–OC) − 13 λ(CH3)
245	264	288	73.7	38.02	64 δ(OHW,free)
215	235	259	3.6	31.83	88 λ(CH3)	218	238	202	0.5	−11.4	82 λ(CH3)
185	206	168	5.0	2.31	68 σ(OHC⋯O)
133	157	106	17.7	12.01	75 σ(OHW⋯O)
67	93	79	1.7	−5.47	74 τ(butt)1 − 10 λ(H2O + OHA)
50	77	65	6.3	−9.68	74 τ(butt)2	51	78	39	2.6	0.1	84 τ(butt)

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Table 4 The B3LYP/aug-cc-pVDZ calculated IR frequencies, IR intensities, VCD rotational strengths R_i of the IIa complex of D-lactic acid⋯water, and of D-lactic acid conformer II

Complex 2a						Monomer 2
ν harm cm^−1	ν scal ^a cm^−1	ν anharm cm^−1	I IR km mol^−1	R i 10^−44 esu^2 cm^2	PED %	ν harm cm^−1	ν scal ^a cm^−1	ν anharm cm^−1	I IR km mol^−1	R i 10^−44 esu^2 cm^2	PED %
a ν scal = 0.955 νcalc + 29.6
3862	3718	3675	97.8	−29.66	96 ν(OHW,free)
3803	3661	3617	52.0	11.89	100 ν(OHA)	3813	3671	3618	51.1	10.3	100 ν(OHA)
3603	3470	3403	364.5	−25.05	92 ν(OHW,hb)
3293	3174	3080	810.9	60.20	95 ν(OHC)	3744	3605	3547	73.8	0.6	100 ν(OHC)
3148	3036	2992	10.3	−2.28	93 ν^a(CH3)1	3149	3037	2991	10.2	−2.9	93 ν^a(CH3)1
3132	3021	2970	17.6	3.02	93 ν^a(CH3)2	3133	3022	2975	16.2	1.2	93 ν^a(CH3)2
3055	2947	2928	13.9	0.87	98 ν^s(CH3)	3057	2949	2931	10.2	0.9	99 ν^s(CH3)
2955	2852	2816	34.3	−9.01	99 ν(C*H)	2961	2857	2821	34.0	−8.0	99 ν(C*H)
1764	1714	1734	226.9	53.02	75 ν(C=O) + 10 β(CH + OH)2	1816	1764	1791	269.7	1.9	83 ν(C=O)
1610	1567	1560	115.3	−109.75	89 β(H2O)
1474	1437	1476	2.2	2.30	71 β^a(CH3) − 11 τ(CH3)	1462	1426	1432	9.6	14.0	67 β^a(CH3) + 18 β(CH)1 − 10 β(CH + OH)3
1464	1428	1421	13.5	10.07	79 β(CH + OH)1 + 10 β^a(CH3)	1473	1436	1437	0.7	−1.02	65 β(CH)1 − 10β^a(CH3) + 12τ(CH3)
1446	1411	1391	14.7	21.49	59 β(CH + OH)2 + 12 ν(C–O)	1314	1284	1262	19.5	3.2	56 β(CH + OH)2 − 16 β(C*H + OHA)
1409	1375	1375	29.5	−26.49	44 β(CH + OH)3 − 22 β^s(CH3)	1411	1377	1364	17.1	−21.7	47 β(CH + OH)3 + 18β^s(CH3)
1382	1349	1346	48.2	−38.79	69 β^s(CH3) + 18 β(CH + OH)3	1382	1349	1348	41.5	−37.8	74 β^s(CH3)
1329	1300	1297	27.0	−16.19	58 τ(C*H) + 11 β(C*H + OHA)	1352	1321	1325	17.6	−25.0	44 τ(C*H) + 10 β^s(CH3)
1274	1246	1242	53.4	108.73	63 β(C*H + OHA) − 14 τ(C*H) + 13 τ(CH3)	1274	1246	1241	64.6	94.3	50 β(C*H + OHA) + 14 τ(CH3) − 23β(CH)1
1261	1234	1224	231.0	−69.81	53 ν(C–O) + 12 β(CH + OH)3 − 11 β(CH + OH)2	1157	1135	1117	229.7	−75.2	43 ν(C–O) − 17β(CH + OH)2 − 11β(CH + OH)3
1156	1134	1124	60.8	−25.63	49 ν(C*O) − 16 β(C*H)	1149	1127	1118	57.9	−35.9	49 ν(C*O) + 17 β(C*H)
1092	1072	1067	19.2	−16.22	41 τ(CH3) − 12 β(C*H + OHA) − 13 ν(S)1	1084	1065	1057	44.6	−7.2	40 τ(CH3) − 11 ν(S)1 − 12β(CH + OH)3
1042	1025	1021	49.0	55.24	44 β(C*H) + 21 ν(C*O) + 16 ν(S)1	1042	1025	1018	54.6	72.4	42 β(C*H) + 16 ν(S)1 − 20 τ(C*H)
931	919	895	40.9	−0.81	31 ν(S)1 + 25 δ(OHC) + 13 τ(CH3)	921	909	902	7.7	−9.5	43 ν(S)1 + 16β(C*H + OHA)
926	914	858	70.7	−9.73	60 δ(OHC) − 15 ν(S)1	614	616	588	91.5	59.6	75 δ(OHC) − 13β(OC=O)
824	816	810	9.8	−14.07	37 ν(S)2 − 13 τ(OC=O) + 12 β(OC=O)	810	803	795	7.5	27.2	26 τ(OC=O) − 27ν(S)2
743	739	733	11.1	26.07	33 τ(OC=O) − 24 β(OC=O) + 15 β(CC–OC)	726	723	717	31.9	−56.1	26 τ(OC=O) + 27ν(S)2 + 22 β(OC=O)
647	647	526	197.0	−14.94	73 β(OHW⋯O)
573	577	568	22.7	−20.36	36 β(OC=O) − 13 τ(OC=O) − 23 ν(S)2	535	541	525	32.5	−21.6	33 β(OC=O) − 22τ(OC=O) + 12δ(OHC)
517	523	514	16.6	−15.78	45 β(CC–OC) + 11 ν(C*O) + 13 β(O=CC–OA)	503	510	499	13.0	4.2	39 β(O=CC–OA) − 18 β(CCC) − 13β(CCC) + 16 ν(C*O)
429	439	423	6.3	−13.28	73 β(CC–OA)	412	423	407	8.9	−15.6	69 β(CC–OA)
384	396	309	68.0	−109.13	61 λ(H2O + OHA) + 14 δ(OHW,free)
357	371	337	31.4	94.34	11 τ(OC=O) − 33 β(O=CC–OA) − 16 β(CCC)	338	352	312	50.0	−6.7	38δ(OHA) + 16τ(OC=O) − 13 β(CC–OC) − 12 β(O=CC–OA)
304	320	252	94.2	75.60	79 λ(H2O–OHA)
288	305	249	95.1	16.33	39 β(CCC) + 12 β(O=CC–OA) + 12 δ(OHW,free) + 17 σ(OHW⋯O)	245	264	235	4.7	−22.4	40 β(CC–OC) − 37 β(CCC)
262	280	163	65.7	40.62	12 λ(H2O + OHA) − 11 β(CCC) + 61 δ(OHW,free)	313	329	276	71.3	54.2	49 δ(OHA) + 22 β(CCC)
213	233	138	0.5	−16.68	89 λ(CH3)	205	225	157	3.2	−11.5	94 λ(CH3)
185	206	160	3.8	−2.92	74 σ(OHC⋯O)
136	159	114	19.6	22.73	69 σ(OHW⋯O) − 15 β(CCC)
68	95	60	1.9	0.96	86 τ(butt)1
44	72	29	2.2	0.89	93 τ(butt)2	42	67	36	2.8	−4.4	92 τ(butt)

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The high frequency stretching modes (Tables 3 and 4) constitute the most localized vibrations. As far as the other vibrations are concerned, except in a few cases, they are the combinations of different bending and stretching modes (Tables 3 and 4). There are several differences between the IR spectra of monomers I and II. Firstly, the ν(OH_A) band in conformer I is predictably located at wavenumbers ca. 90 cm⁻¹ lower than that of conformer II. This is due to the higher strength of the OH_A⋯O=C intramolecular H-bond in I than the OH_A⋯OH_C intramolecular H-bond in conformer II. The band intensity is much higher in conformer I than in II as well. Secondly, the ν(C*H) band position differs in the two spectra by ca. 40 cm⁻¹, at 2986 cm⁻¹ for Ivs. 2857 cm⁻¹ for II. Such a difference in this region of the spectra is quite meaningful. Thirdly, the location of the ν(C=O) band is also significant: in I, where the C=O group is H-bonded, it is shifted 25 cm⁻¹ towards lower wavenumbers than in the conformer II, where such a H-bond is absent.

The main differences between the VCD spectra of the two conformers are illustrated in Table 5 and Fig. S1 of the ESI.† The VCD effect is greater for the medium frequency bending vibrations than for the high frequency stretching ones. The bending β(C*H + OH_A) mode of the H10–C2–C3 moiety, including the chirality center at the C*2 atom, displays a relatively high optical activity R_i (70.7 and 94.3 × 10⁻⁴⁴ esu² cm², for conformer I and II, respectively). A similar characteristic is observed for the second C*H bending mode, denoted as β(C*H), which is not as localized as the previous one (Tables 3 and 4). For this mode, R_i is positive and equals 34.3 and 72.4 × 10⁻⁴⁴ esu² cm² for conformers I and II, respectively. The medium frequency region also contains the ν^a(C–O) stretching vibrations mode of the C2–O6 moiety, at 1117 (conformer I) and 1135 cm⁻¹ (conformer II), which is one of the most intense bands in the IR spectra and has opposite signs in the VCD spectra, 18.3 and −75.2 × 10⁻⁴⁴ esu² cm² for conformers I and II, respectively. It is remarkable that in the former case the O6-H group is engaged in the H-bond with the carbonyl group, namely O6-H12⋯O4=C3, and the ν(C2–O6) mode couples to ν(C3–O5) one, whereas in the latter the O5–H11 moiety acts as H-bond acceptor and the ν(C2–O6) local mode is not coupled (Tables 3 and 4). For the two conformers, the out-of-plane bending δ(OH_C) mode absorbs near 600 cm⁻¹. The band has a relatively high rotational strength R_i: 83.1 and 59.6 × 10⁻⁴⁴ esu² cm² for conformers I and II, respectively. In the low frequency region, a bending vibration with an important β(CCC) mode contribution has a positive R_i value for conformer I (8.6 × 10⁻⁴⁴ esu² cm²), while this is negative and quite significant for conformer II (−22.4 × 10⁻⁴⁴ esu² cm²).

Table 5 Comparison between the B3LYP/aug-cc-pVDZ calculated IR frequencies and intensities, and VCD rotational strengths of conformers I and II of D-lactic acid, upper and lower line, respectively

ν harm/cm^−1	ν scal/cm^−1	ν anharm/cm^−1	I IR/km mol^−1	R i/× 10^−44esu^2cm^2	PED(%)
1261	1234	1235	42.2	70.7	75 β(C*H + OHA)
1274	1246	1241	64.6	94.3	50 β(C*H + OHA) + 14 τ(CH3) − 23β(CH)1
1139	1117	1106	262.9	18.3	50 ν^a(C–O) − 11 β(CH + OH)3 − 12 τ(CH3)
1157	1135	1117	229.7	−75.2	43 ν(C–O) − 17β(CH + OH)2 − 11β(CH + OH)3
1042	1025	1020	38.5	34.3	49 β(C*H) + 20 ν(S)1
1042	1025	1018	54.6	72.4	42 β(C*H) + 16 ν(S)1 − 20 τ(C*H)
579	582	551	54.3	83.1	69 δ(OHC)
614	616	588	91.5	59.6	75 δ(OHC) − 13β(OC=O)
242	261	237	0.7	8.6	43 β(CCC) + 10 τ(OC=O) + 11 β(CC–OC) − 13 λ(CH3)
245	264	235	4.7	−22.4	40 β(CC–OC) − 37 β(CCC)
218	238	202	0.5	−11.4	82 λ(CH3)
205	225	157	3.2	−11.5	94 λ(CH3)

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Summarizing, the VCD spectra change quite remarkably when the D-lactic acid molecule assumes different conformations.

B. Geometries and energies of lactic acid⋯water complexes

The first stage of the study on the spectroscopic consequences of the H-bond interaction between the lactic acid and water molecules dealt with geometry and energies of the 1 : 1 complexes. Fig. 2 shows complex geometries for lactic acid, and conformers I and II, with a water molecule. Table 6 summarizes the theoretically calculated binding D_e and dissociation D₀, as well as relative Gibbs energies for all of these structures.

Fig. 2 Considered forms of D-lactic acid complexes with a water molecule.

Table 6 The B3LYP/aug-cc-pVDZ and B3LYP/aug-cc-pVTZ calculated binding D_e, dissociation D₀ and relative Gibbs free ΔG₂₉₈ energies of the studied water complexes with conformers I and II of lactic acid

Complex	ΔEint/kJ mol^−1	ΔEint+BSSE/kJ mol^−1	D e/kJ mol^−1	ΔEdef/kJ mol^−1	D 0/kJ mol^−1	ΔG298/kJ mol^−1
ΔE = int uncorrected interaction energy, ΔE = int+BSSE interaction energy counterpoise corrected, ΔE = def deformation energy.
aug-cc pVDZ
Ia	−40.88	−41.84	−38.91	2.93	−31.34	0
Ib	−21.38	−26.28	−19.41	6.96	−13.60	12.35
Ic	−21.25	−19.75	−19.08	0.67	−13.72	11.44
Id	−10.29	−8.87	−8.20	0.67	−5.10	17.01
IIa	−41.92	−43.56	−40.00	3.56	−32.22	7.65
IIb	−21.00	−22.55	−18.70	3.81	−11.05	27.89
IIc	−19.83	−18.58	−18.03	0.54	−12.72	18.92
IId	−19.04	−8.87	−16.99	−8.12	−12.09	18.89
aug-cc-pVTZ
Ia	−40.63	−41.92	−41.17	1.76	−30.42	0
IIa	−41.17	−44.27	−39.71	4.56	−29.92	7.44

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Any of the lactic acid conformers could possibly form four complexes with a water molecule. Indeed, water could act as an electron donor to both carboxylic and alcoholic OH groups in structures Ia and IIa, and Ib and IIb, respectively. Moreover, the water molecule could act as a proton donor to the oxygen atom of both alcoholic oxygen and carboxylic oxygen OH atoms as in structures Ic and Id, respectively. Formally, a linear water OH⋯O=C is also possible, however, this supposed form converges to a cyclic H-bond as, for example, in Ia.

Structures Ia and IIa are the most stable, yet Ia remains the most populated (Table 6). Not including the intramolecular H-bond, the two complex forms exhibit two intermolecular H-bonds between the carboxylic O5–H11 group and O13 atom of water, and between the carbonylic O4 atom and water H14–O13 moiety. In this way a 6-membered H-bonded cycle is formed. Note that an analogous water complex with conformer III cannot exist because the carboxylic OH group is in a trans position and a cyclic H-bond with the COOH group cannot form.

The calculated energies at the B3LYP level, carried out with the two basis sets aug-cc-pVDZ and aug-cc-pVTZ for Ia and IIa, are given in Table 6. The binding energies of the two most stable complexes do not differ substantially, and equal −38.91 and −40.00 kJ mol⁻¹ for Ia and IIa, respectively. Moreover, an extension of the basis set to aug-cc-pVTZ changes the binding energies to a fairly insignificant extent, i.e. to −41.17 and −39.71 kJ mol⁻¹ (Table 6), respectively.

The intermolecular H-bond between the alcoholic OH_A group, acting as a proton donor, and the water oxygen atom, acting as an acceptor, together with the water OH group donating the proton to either the carboxylic O4 (Ib) or O5 (IIb) atom, give rise to formation of a cyclic 7-membered H-bond system stabilizing the structures Ib and IIb with energies much lower than those of Ia and IIa (−19.41 and −18.70 kJ mol⁻¹ for Ib and IIb, respectively). This is probably due to weaker H-bonds between the alcoholic hydroxyl group with water in Ib and IIb compared to those of the carboxyl OH group in Ia and IIa, and a weaker stabilization of the 7-membered H-bond ring in Ib and IIb than the 6-membered H-bonded ring in Ia and IIa.

Complexes of type c, Ic and IIc, in which a water molecule is the proton donor to the oxygen atom of alcoholic group, also form structures less stable than those of type a. They display binding energies of −19.08 and −18.03 kJ mol⁻¹ for Ic and IIc, respectively. In the two type d structures, the water molecule plays the role of proton donor, but in Id it is donated to the oxygen atom of the carboxylic O–H group, while in IId it is donated to the oxygen atom of the carboxylic C=O group. The binding energies of Id and IId are the lowest in the series studied, i.e., −8.20 and −16.99 kJ mol⁻¹, for Id and IId, respectively, while the ΔG₂₉₈ values are much closer (17.01 and 18.89 kJ mol⁻¹, respectively), but this indicates that the d-type complexes would hardly be observable in the mixture of complexes (Table 6).

To investigate the role of basis set effects on binding energy between lactic acid and a single water molecule in more detail, let us turn to Table 6, in which the results of the binding energy obtained with the two basis sets are listed. The numbers shown are corrected for the BSSE effect. As expected, basis set sensitivity exists, but is small, and as the basis set is enlarged, the role of the BSSE decreases. Also, the binding energy values for the complexes calculated at the B3LYP/aug-cc-pVDZ and B3LYP/aug-cc-pVTZ levels are convincing proof that the former level is quite suitable for the purpose of studying H-bonding.

To analyze the influence of intermolecular interactions on the lactic acid molecule, let us comment in more detail on the changes to selected geometrical parameters (Table 7). The alcoholic O6–H12 distance is almost insensitive to the side on which water molecule approaches the acid. For three complexes, Ia, Ic and Id, this is connected with the intramolecular H-bond O6–H12⋯O4, which stabilizes the geometry of this moiety, whereas for Ib the distance is slightly greater, which means that the intermolecular interaction with water exerts a slightly stronger influence than the intramolecular H-bond does. Similarly, the carboxylic O5–H11 distance is constant, except in structure Ia where it is elongated by the intermolecular H-bond (Fig. 2). The changes in the C3=O4 distance are in line with the changes in binding energy. The intramolecular H12⋯O4 distance reveals that in the case of Ib, water constrains any significant change in the intramolecular H-bond O6–H12⋯O4 geometry. In the complexes of conformer II, it is interesting to note that the O6–H12 distance is far shorter than for conformer I. This is due to a change in the type of intramolecular H-bond from O6–H12⋯O4=C3 to O6–H12⋯O5(H). As shown below, all of the above-mentioned changes are reflected even more in the vibrational spectra.

Table 7 Comparison of the selected distances in lactic acid complexes with a water molecule, calculated at the B3LYP/aug-cc-pVDZ level

Complex	r(O6–H12)/Å	r(O5–H11)/Å	r(C3=O4)/Å	r(H12⋯O4)/Å	r(H11,12⋯O13)/Å	r(On⋯H14)/Å
a H11⋯O13. b H12⋯O13. c H14⋯O4. d H14⋯O6. e H14⋯O5.
Ia	0.971	0.993	1.227	2.070	1.757^a	2.008^c
Ib	0.974	0.971	1.216	2.496	1.924^b	1.947^c
Ic	0.972	0.972	1.214	2.074		1.931^d
Id	0.970	0.972	1.211	2.126		2.103^e
				r(H12⋯O5)/Å
IIa	0.966	0.994	1.222	2.170	1.748^a	1.971^c
IIb	0.977	0.971	1.207	2.670	1.908^b	1.987^e
IIc	0.967	0.971	1.208	2.188		1.937^d
IId	0.965	0.972	1.215	2.274		1.942^c

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C. The IR and VCD spectra of D-lactic acid⋯water complexes

In comparison to the spectra of I, nine new bands appear in those of Ia (Table 3, Fig. S2 in the ESI†). Obviously, three of them are water absorption bands at 3719, 3501, and 1564 cm⁻¹, the ν(OH_W,free), ν(OH_W,hb), and β(H₂O), respectively, which are quite intense in the IR spectra. Two of them, ν(OH_W,free) and β(H₂O), have significant VCD intensities too, −29 and −135 × 10⁻⁴⁴ esu² cm², respectively. Furthermore, another new band, β(OH_W⋯O) at 616 cm⁻¹, has very remarkable IR intensity of 180 km mol⁻¹, as well as a non-negligible R_i value equalling −16 × 10⁻⁴⁴ esu² cm². Moreover, the band at 390 cm⁻¹, with a significant contribution of the λ(H₂O + OH_A) mode, has a large VCD intensity equal to −185 × 10⁻⁴⁴ esu² cm².

As expected,³¹ the most conspicuous change in the IR spectra of I after formation of complex Ia is a shift of the ν(OH_C) band towards lower frequency by ca. 400 cm⁻¹ and a simultaneous, ca. tenfold, increase of the band intensity. The ν(C=O) band undergoes a relatively small, yet significant, shift towards lower frequency, ca. 40 cm⁻¹, and a small intensity decrease of no essential significance. There are three bands in the bending vibrations region that are shifted considerably: firstly, the β(CH + OH)₂ band is shifted from 1300 to ca. 1450 cm⁻¹; secondly, the ν^S(C–O) band which changes its form from symmetric ν(C2–O6) + ν(C3–O5) to uncoupled ν(C3–O5), and shifts from 1165 to 1260 cm⁻¹; and finally, the δ(OH_C), which shifts as much as 325 cm⁻¹ towards higher frequency from 580 to 905 cm⁻¹.

In our previous paper^14a we have shown that after complex formation with a chiral molecule, an achiral molecule becomes active in the VCD spectra. This is also the case for the system studied in this paper. An achiral water molecule exhibits the VCD absorptions of the ν(OH_W,free), ν(OH_W,hb), and β(H₂O) modes at 3719, 3501, and 1564 cm⁻¹, respectively. Moreover, although the rotational strengths of the two stretching modes of water are of average value, −29 and 10 × 10⁻⁴⁴ esu² cm², the strength of the bending vibration mode is one of the most intense in the VCD spectrum of the Ia complex, i.e., it equals −135 × 10⁻⁴⁴ esu² cm² (Table 3). Furthermore, the intramolecular H-bond bending vibration band β(OH_W⋯O), water librations λ(H₂O + OH_A), and out-of-plane bending δ(OH_W,free) vibration of water come into view and absorb at 616, 389, and 264 cm⁻¹ with rotational strengths in the VCD spectrum of ca. −16, −184 and 38 × 10⁻⁴⁴ esu² cm², respectively. It is worth noting that the λ(H₂O + OH_A) librations are of greater magnitude, yet they are placed in the beginning of the far-IR region, and therefore have lesser value as an indicator of the complex. Thus, the new VCD bands appear in quite specific regions, they are fairly appreciable, and none of the bands of water that are not H-bonded to the chiral molecule manifest themselves in the VCD spectrum.

After complexation the R_i of the ν(C=O) band increases from 1.0 to 50 × 10⁻⁴⁴ esu² cm², but the ν(OH_C) VCD band changes negligibly (Table 3). The out-of-plane bending δ(OH_C) vibration VCD band changes remarkably in its magnitude as well as in sign alteration, from 83 to −7 × 10⁻⁴⁴ esu² cm², for I and Ia, respectively. Surprisingly, this is also the case for the out-of-plane bending δ(OH_A) vibration of the OH_A engaged in the intramolecular H-bond.

The Ia complex formation induces several changes in the bending vibration region between 1470 and 1170 cm⁻¹, however the modes are difficult to interpret since the PED contributions of the particular local modes are small and we will not go into the interpretational details.

The differences between the IR spectra of II and IIa are fairly analogous to those for conformer I (Table 4). In comparison with II, the new bands in the VCD spectrum of IIa originating from water exhibit important VCD intensities: −30, −25, −110, −15, and 76 × 10⁻⁴⁴ esu² cm², for the ν(OH_W,free), ν(OH_W,hb), β(H₂O), β(OH_W⋯O), and λ(H₂O–OH_A) bands, respectively. Also, as before, the ν(C=O) of negligible intensity in the spectrum of conformer II becomes quite considerable in the VCD spectrum of IIa. In contrast to the VCD spectrum of Ia, the ν(OH_C) in IIa is increased 100-times when compared to that of II. A change can be seen for the δ(OH_C) VCD band rotational strength, too; it equals ca. 60 × 10⁻⁴⁴ esu² cm² for II while it is ca. −10 × 10⁻⁴⁴ esu² cm² for IIa.

Below, we shall comment on the differences in the VCD spectra of Ia and IIa (Table 8, Fig. S3 in the ESI).† Firstly, and most importantly, dissimilarity between the VCD spectra gives the rotational strength of the ν(OH_W,hb) band a different sign: 10 vs. −25 × 10⁻⁴⁴ esu² cm² for Ia and IIa, respectively, which also differs with respect to the position of maxima by ca. 30 cm⁻¹, yet their IR intensities are fairly similar. Next, the ν(OH_C) band is almost absent in the VCD spectra of Ia, whereas it is quite prominent for IIa (2 vs. 60 × 10⁻⁴⁴ esu² cm²). It is worth recording the fact that the large IR intensity of this mode is a paramount feature of H-bond formation in the mid-IR region, which does not provide a basis for differentiation between the Ia and IIa complexes. In this context, the ν(OH_W,hb) and ν(OH_C) VCD bands yield a very important distinction between the two similar complex structures.

Table 8 Comparison between the B3LYP/aug-cc-pVDZ calculated IR frequencies and intensities, and VCD rotational strengths of conformers Ia and IIa of D-lactic acid interacting with a water molecule, upper and lower line, respectively

ν harm/cm^−1	ν scal/cm^−1	ν anharm/cm^−1	I IR/km mol^−1	R i/× 10^−44 esu^2 cm^2	PED(%)
3635	3501	3444	295.1	10.2	92 ν(OHW,hb)
3603	3470	3403	364.5	−25.1	92 ν(OHW,hb)
3312	3192	3108	805.3	1.9	95 ν(OHC)
3293	3174	3080	810.9	60.2	95 ν(OHC)
2996	2891	2846	25.2	−23.22	99 ν(C*H)
2955	2852	2816	34.3	−9.01	99 ν(C*H)
1607	1564	1558	131.9	−134.7	89 β(H2O)
1610	1567	1560	115.3	−109.8	89 β(H2O)
1454	1418	1414	1.4	−16.2	74 β(CH + OH)1
1464	1428	1421	13.5	10.1	79 β(CH + OH)1 + 10 β^a(CH3)
1384	1351	1353	5.7	22.4	83 β^s(CH3)
1382	1349	1346	48.2	−38.8	69 β^s(CH3) + 18 β(CH + OH)3
1287	1259	1246	259.2	133.21	30 β(C*H + OHA) + 31 ν(C–O)
1274	1246	1242	53.4	108.73	63 β(C*H + OHA) − 14 τ(C*H) + 13 τ(CH3)
1155	1133	1130	128.5	13.7	42 ν(C*O) − 14 τ(CH3) + 11 β(C*H)
1156	1134	1124	60.8	−25.6	49 ν(C*O) − 16 β(C*H)
628	629	612	25.1	17.7	43 β(OC=O) + 14 τ(OC=O) + 12 ν(C*O)
573	577	568	22.7	−20.4	36 β(OC=O) − 13 τ(OC=O) − 23 ν(S)2
422	433	410	8.5	6.5	60 β(CC–OA)
429	439	423	6.3	−13.3	73 β(CC–OA)
376	389	337	81.7	−184.3	49 λ(H2O + OHA) − 10 β(O=CC–OA)
384	396	309	68.0	-109.1	61 λ(H2O + OHA) + 14 δ(OHW,free)
360	373	330	32.8	114.3	62 λ(H2O–OHA)
304	320	252	94.2	75.6	79 λ(H2O–OHA)
215	235	259	3.6	31.8	88 λ(CH3)
213	233	138	0.5	−16.7	89 λ(CH3)

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The separation of the ν(C*H) bands in the spectra of the two complexes, Ia and IIa, seems to be important for complex identification when they form a mixture. Although they display similar characteristics in terms of IR intensity, and magnitude and sign of VCD rotational strength, they are separated by as much as 40 cm⁻¹ at a very specific lower limit of the ν(CH) vibrations’ region. The VCD intense β(H₂O) band is comparable for the two complexes. In fact, the same holds true for the water libration VCD λ(H₂O + OH_A) band, whereas the other libration, λ(H₂O–OH_A), has similar VCD intensities for Ia and IIa. Indeed, the position of λ(H₂O–OH_A) in the two spectra differs by as much as 50 cm⁻¹. This difference would be important for discriminating between the complexes, providing that the bands would not be positioned in the far-IR range (Table 8). An inspection of two kinds of vibrational spectra, IR and VCD, in the region near 1250 cm⁻¹ also possibly allows one to determine whether the complex mixture is composed of two complexes or not. Indeed, in the IR spectrum at 1260 cm⁻¹, the band corresponding to the β(C*H + OH_A) mode of Ia has an intensity five times higher in magnitude than that of IIa, positioned at 1245 cm⁻¹. On the other hand, in the VCD spectrum these two bands have similar rotational strengths, i.e. 133 and 109 × 10⁻⁴⁴ esu² cm², for Ia and IIa, respectively.

The successful discrimination based on the VCD spectra between the two structures is most likely when bands in the two spectra have opposite signs, are intense, and are positioned at (at least slightly) different wavenumbers. If they satisfy the first two conditions, but they are not positioned at different places, they may compensate each other partially or even annihilate each other. Presumably, this would be the case for the β^s(CH₃), ν(C*O), and λ(CH₃) VCD bands, whose maxima differ by ca. 2 cm⁻¹. Also, for the β(CC–O_A) VCD bands of Ia and IIa, which exhibit weak VCD absorptions but different signs (7 (Ia) vs. −13 × 10⁻⁴⁴ esu² cm² (IIa)), the band maxima are separated by only 6 cm⁻¹ (Table 8) and it depends on the band halfwidths as to whether they may mutually compensate each other or not. This is why only two additional bands are fairly good markers for complex discrimination, namely β(CH + OH)₁ and β(OC=O). Although they are not intense, they differ in sign; and for the Ia and IIa complexes the difference in band location of the former equals ca. 10 cm⁻¹ (the β(CH) bands are fairly narrow) whereas for the latter it equals 50 cm⁻¹.

This paper aimed to address the important question of how to relate the characteristic pattern of the VCD spectra to the intermolecular H-bonding present in the studied system. One may conclude, based on investigations of the formation of H-bonded systems, that the O–H⋯O=C H-bond formation results in a significant increase of the ν(C=O) rotational strength (Ia and IIa, Tables 3, 4, and 8). In case of the Ib system, where the alcoholic OH_A moiety of the D-lactic acid is a proton donor in the intermolecular H-bond with water, there is a tenfold increase of VCD intensity. Moreover, when the water molecules form a cyclic H-bonded ring, as in Ia and IIa as well as Ib, the bending β(H₂O) mode is one of the most intense bands in the VCD spectrum (and in our particular systems bears a negative sign). On the other hand, when the H-bond is not cyclic, as in Ic and Id, the rotational strength of the β(H₂O) band is rather small and either positive (Id) or negative (Ic) (Table 9).

Table 9 Juxtaposition of the selected mode parameters of the IR and VCD spectra of different complexes of D-lactic acid conformer I with a single water molecule

System	Mode	ν harm/cm^−1	I IR/km mol^−1	R i/ × 10^−44 esu^2 cm^2
I	ν(OHA)	3719	86.0	16.3
	ν(OHC)	3738	73.0	−2.2
	ν(C*H)	3002	24.3	−22.3
	ν(C=O)	1790	300.4	0.8
Ia	ν(OHA)	3719	83.6	13.57
	ν(OHC)	3312	805.3	1.89
	ν(C*H)	2996	25.2	−23.22
	ν(C=O)	1744	261	49.19
Ib	ν(OHA)	3628	256.9	116.4
	ν(OHC)	3738	68.2	−6.4
	ν(C*H)	2959	38.1	−30.0
	ν(C=O)	1778	361.4	18.5
Ic	ν(OHA)	3702	58.9	7.3
	ν(OHC)	3736	77.4	−1.7
	ν(C*H)	3043	10.6	−23.3
	ν(C=O)	1789	292.8	3.5
Id	ν(OHA)	3734	54.6	20.4
	ν(OHC)	3733	97.7	−1.0
	ν(C*H)	3047	17.7	5.1
	ν(C=O)	1799	306.8	−5.4
Ia	ν(OHfree)	3863	101.5	−28.9
	ν(OHHB)	3635	295	10.2
	β(HOH)	1607	132	−134.7
Ib	ν(OHfree)	3878	104.3	−39.2
	ν(OHHB)	3689	431.8	−87.9
	β(HOH)	1617	87.1	−47.4
Ic	ν(OHfree)	3878	95.8	−10.9
	ν(OHHB)	3668	408.7	−5.0
	β(HOH)	1643	58.9	−14.7
Id	ν ^a(OH)	3888	127.2	18.9
	ν ^s(OH)	3760	88.2	−4.0
	β(HOH)	1627	73.9	21.3

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Finally, let us comment on the anharmonic frequencies calculated for the two most stable conformers of the monomers and complexes (Tables 3 and 4). The high frequency anharmonic stretchings are red-shifted ca. 150–200 cm⁻¹, in comparison to harmonic wavenumbers, and the extent of their shift is greater than that in the case of the scaled values. Below 1800 cm⁻¹, the anharmonic frequencies fluctuate around the appropriate scaled values. For example, in comparison to scaled values, the anharmonic ν(C=O) frequency is ca. 20 cm⁻¹ blue-shifted in both monomers and complexes, whereas for instance the δ(OH_C) is significantly red-shifted (especially in complexes). For numerous modes the difference between the scaled and anharmonic data is negligible (Tables 3 and 4).

IV. Conclusions

In this paper we have presented the results of DFT(B3LYP)/aug-cc-pVDZ calculations of vibrational optical activity spectra for 1 : 1 complexes of chiral D-lactic acid with a water molecule. The main conclusions can be summarized as follows:

1. The calculations predicted the conformer (I) stabilized by a C–OH_A⋯O=C intramolecular H-bond to be the most stable form. The second stable form (II), higher in energy by ca. 9.2 kJ mol⁻¹, is also stabilized by the intramolecular C–OH_A⋯OH_C H-bond. Subsequently, more conformers were found, but they were ruled out of further considerations.

2. For each of the conformers I and II, interacting with a water molecule, four stable minima have been found and studied. The complexes with a cyclic intermolecular H-bond between the carboxylic group of the acid and water (Ia and IIa) proved most stable, playing both a proton donor and proton acceptor role. The binding energies of the two most stable complexes do not differ substantially, with values of −38.9 and −40.0 kJ mol⁻¹, for Ia and IIa, respectively. The Gibbs free energy of the Ia complex is ca. 7.5 kJ mol⁻¹ lower than that of the IIa complex, and thus the former is predicted to be much more populated in a mixture of these two complexes.

VA spectroscopy discriminates between lactic acid conformers Ia and IIa, on the basis of frequency shifts for ν(OH_A), ν(C*H), and ν(C=O) where the OH_A hydroxyl group is a proton donor to an intramolecular H-bond.

The calculated VCD spectra change when the interacting molecules of D-lactic acid⋯water assume different configurations. First, after forming a complex with the D-lactic acid molecule, the VCD modes of the achiral water molecule acquire significant rotational strengths, whose signs change in parallel with the geometry of the complex. Second, several VCD bands enable unequivocal differentiation between conformer structures, which may give new insight into the interpretation of vibrational spectra of complex mixtures. As well as for VCD bands such as ν(OH_W,hb) and ν(OH_C), which highlight the differences between patterns in the VA and VCD spectra and in this way help interpretation, there are modes like, for example, β(CH + OH)₁ and β(OC=O) which change their signs upon a change in the complex structure. Third, the stretching vibration ν(C=O) VCD band has a small rotational strength for a monomeric form of D-lactic acid, whereas it turns quite intense when the carbonyl group is engaged in an intramolecular H-bond. In conclusion, the VCD spectra of intramolecularly interacting molecules can be used as a powerful tool for the structural investigation of intermolecular interactions of chiral molecules, and can yield information complementary to data obtained from other molecular spectroscopy techniques.

Acknowledgements

This work was supported by KBN Grant No. 3 T09A 088 28. The computational Grant G19-4 from the Interdisciplinary Center of Mathematical and Computer Modeling (ICM) at Warsaw University is gratefully acknowledged.

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Footnote

† Electronic supplementary information (ESI) available: Optimised geometries and a graphical comparison of the calculated VCD spectra. See DOI: 10.1039/b509351a

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