Isotope effects in ethylene–HX complexes (X=F, Cl or Br)

Journal of Molecular Structure (Theochem) 668 (2004) 41–45 www.elsevier.com/locate/theochem

Isotope effects in ethylene –HX complexes (X ¼ F, Cl or Br) Sean A.C. McDowell* Department of Biological and Chemical Sciences, University of the West Indies, Cave Hill Campus, P.O. Box 64, Bridgetown, Barbados Received 3 April 2003; accepted 6 October 2003

Abstract Ab initio calculations were performed at the MP2/6-311þþ G(2d,2p) level of theory to obtain optimized geometries, dipole moments, binding energies and harmonic vibrational frequencies for the symmetrical T-shaped structures of XH· · ·p bonded complexes involving ethylene (as the proton-acceptor) and the hydrogen halide molecules HF, HCl and HBr (as the proton donors). The relative stabilities of the D-containing isotopomers C2H4· · ·DX and C2H2HD· · ·HX were also determined from their zero-point energies. It was found that the Dbonded isotopomer (C2H4· · ·DX) was more thermodynamically stable than the H-bonded isotopomer (C2H2HD· · ·HX) for HF, HCl and HBrcontaining complexes, previous studies on the weakly bound T-shaped complexes C2H2· · ·HX also found that the D-bonded species was more stable than the H-bonded species. q 2004 Elsevier B.V. All rights reserved. Keywords: T-shaped complexes; Buckingham–Liu theory; Isotopomers; Zero-point-energy; Relative stability

1. Introduction A good understanding of the role of intermolecular forces is necessary in order to understand the structure, dynamics and reactivity of weakly bound assemblies of molecules. This has application to important phenomena in areas as diverse as chemistry, biochemistry, physics, surface science and low temperature spectroscopy. Small molecular clusters are especially attractive as prototype systems for both the theoretical and experimental study of intermolecular interactions because of their simplicity and size. For example, for systems of moderate size with a few atoms, high-level computations are now possible with a desktop PC. Intermolecular interactions may be conveniently divided into two types; van der Waals complexes and hydrogenbonded complexes. The weaker van der Waals interactions are generally governed by dispersion type interactions (e.g. in Ar· · ·Ar), whereas the stronger hydrogen-bonded interactions involve a partially positive proton and are dominated mainly by electrostatic forces (e.g. in H2O· · ·H2O). Hydrogen bonding is especially important in biological systems, for example, the structure of DNA is determined by these types of interactions. A number of * Fax: þ1-246-417-4325. E-mail address: [email protected] (S.A.C. McDowell). 0166-1280/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2003.10.015

useful contemporary reviews of hydrogen bonding may be found in the literature [1 – 3]. In the realm of chemical physics, complexes of the type B· · ·HX have been extensively studied, where B is a protonacceptor (containing a region of high electron density) and HX is a hydrogen halide (X ¼ F, Cl or Br). Interactions of the type XH· · ·p in T-shaped complexes are known to be important in the study of the early stages of an electrophilic addition to an unsaturated hydrocarbon [4]. In this present study, we examine the properties of the T-shaped complexes of the type C 2H 4· · ·HX (X ¼ F, Cl, Br), and is a continuation of previous work on the similar T-shaped C2H2· · ·HX complexes, in which the proton-donor molecule makes a H-bond with the midpoint of the acetylene triple bond [5]. There have been previous experimental and theoretical studies of C2H4· · ·HF [6 – 11] and C2H4· · ·HCl [9,12 – 23]. Flygare and coworkers established that C2H4· · ·HF [6] and C2H4· · ·HCl [12] both have T-shaped geometries using microwave spectroscopy. However, there are apparently no experimental or theoretical studies of hydrogen-bonded complexes of C2H4· · ·HBr reported in the literature, so this present study represents the first such study. In addition to the determination of equilibrium geometries, ab initio calculations are also useful in predicting changes in vibrational frequencies on complexation and can

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S.A.C. McDowell / Journal of Molecular Structure (Theochem) 668 (2004) 41–45

also be used to identify the most significant vibrational modes involved in certain aspects of intermolecular bonding. These calculations are now routinely possible with the use of powerful desktop PCs and efficient software packages, which are now readily available and also relatively cheap given their capabilities. The main focus of this paper is the study of the isotope effects on the relative stabilities of some H- and D-bonded isotopomers of C2H4· · ·HX (X ¼ F, Cl, Br), namely the complexes C2H4· · ·DX and C2H2HD· · ·HX. We also examine trends in these relative stabilities (as well as other properties) for ethylene – HF, ethylene – HCl and ethylene –HBr isotopomers. The relative stabilities of H-bonded and D-bonded species can be explained in terms of differences in zeropoint vibrational energy by using the theory of Buckingham and Liu [24]. Assuming that these species can be described by the same potential energy surface, then because of the large difference in mass between the H and D atom, the vibrational behaviour is quite different for the two cases. In the Buckingham – Liu theory (which is derived from perturbation theory), the hydrogen-bonded species is considered as if it were a linear triatomic molecule B· · ·H – X, with just three significant vibrational modes: the H –X stretching mode and the doubly degenerate Hbond bend. According to the theory, the energy difference between isomeric H-bonded and D-bonded dimers consists of the difference between two terms of opposite sign; namely, (i) the difference of the intermolecular bending vibration frequencies of the H- and D-bonds and (ii) onehalf of the difference of the frequency shifts of the H – X and D – X stretching vibration frequencies due to the effects of the H- and D-bond complexation [24]. The H – X stretching mode is stabilized (red-shifted) more than the D – X stretching mode by hydrogen bonding and this favours the H-bond strength over that of the Dbond. However, the larger amplitude of the bending motion in B· · ·H –X compared to the B· · ·D – X favours the D-bond, since the preferred configuration of the hydrogen bond is one in which the bond is as nearly linear as possible. This latter effect of bending is usually dominant, so in most cases the deuterium bond is stronger than the corresponding hydrogen bond. This has been confirmed by previous theoretical work on the linear complexes CO –C2H2 [25] and N2 – C2H2 [26] and from the spectroscopic studies of Legon and coworkers [27]. In this paper we report optimized geometries, binding energies and harmonic vibrational frequencies for the C2H4· · ·HX (X ¼ F, Cl, Br) series of T-shaped complexes obtained by ab initio molecular orbital calculations at the MP2/6-311þ þ G(2d,2p) level of theory. All calculations were carried out using the GAUSSIAN 98 suite of programs [28]. We compared the properties of the ethylene– HF, ethylene –HCl and ethylene –HBr species to identify any interesting trends. We also compared, where appropriate, the properties of this series of T-shaped complexes with

those of the previously studied acetylene –HX series. The ethylene –HX complexes, like acetylene – HX, are weakly bound molecules held together primarily by dipole – quadrupole and quadrupole – quadrupole intermolecular forces arising from permanent and induced multipole moments. The dispersion energy contribution to the binding energy is expected to be more significant in the ethylene complexes than in the acetylene complexes because of the extra hydrogen atoms in ethylene. As mentioned before, the main purpose of this work, however, is to determine whether the deuterium bond is stronger than the hydrogen bond in these types of nonlinear complexes, as it is for the linear complexes, and to see if the relative stabilities can be explained by the simple model of Buckingham and Liu. Normal mode analysis will be useful in the determination of the vibrational modes, which contribute significantly to the zero-point vibrational energies.

2. Results and discussion 2.1. Structural parameters Table 1 shows the geometrical parameters and Fig. 1 shows the optimized structure of the C2H4· · ·HX complexes. The H – X bondlength is the bond most affected by ˚ in all of complexation and is elongated by about 0.01 A the complexes. The CyC bond is only slightly perturbed and the C – H bondlengths are unaffected by complexation in all of the complexes. The intermolecular separation decreases in the order C2H4· · ·HF . C2H4· · ·HCl . C2H4· · ·HBr, which also reflects the order of the strength of the interaction (Table 2). It should be noted also that a slight distortion of the planarity of the C2H4 molecule occurs on complexation, causing the H atoms of the molecule to be repelled away from the HX proton; this distortion was also observed for the acetylene molecule in the acetylene – HX complexes [5].

Table 1 Optimized geometry and dipole moments ðmÞ for C2H4· · ·HX complexes (X ¼ F, Cl, Br) at the 6-311þ þG(2d,2p) level of theory Parameter

C2H4· · ·HF

C2H4· · ·HCl

C2H4· · ·HBr

˚) R(X– H) (A ˚) R(C–H) (A ˚) R(C–C) (A ˚) R(p· · ·H) (A /HCH (deg) /HCC (deg) m (Debye)

0.927 (0.009) 1.080 (0.0) 1.337 (0.003) 2.158 117.5 121.3 2.598 (1.873)

1.281 (0.010) 1.080 (0.0) 1.337 (0.003) 2.327 117.4 121.3 1.876 (1.183)

1.421 (0.009) 1.080 (0.0) 1.337 (0.003) 2.390 117.5 121.3 1.629 (0.921)

Refer to Fig. 1. R(p· · ·H) refers to the distance from the H atom of HX to the midpoint of the C2H4 double bond. The change in bondlength on complexation and the value for the dipole moment of the isolated HX molecule are shown in brackets in the appropriate columns.

S.A.C. McDowell / Journal of Molecular Structure (Theochem) 668 (2004) 41–45

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induced dipole moment values probably reflect the fact that the larger the hydrogen halide the greater the molecule is polarized by the partner ethylene molecule. 2.2. Binding energies

Fig. 1. The equilibrium structure of the C2H4· · ·HX complex (X ¼ F, Cl, Br). The H atoms are in a plane, which is perpendicular to the plane containing the C atoms and the HX molecule.

The dipole moments of the complexes shown in Table 1 result primarily from the polarization of the hydrogen halide molecule by the quadrupole moment of the ethylene molecule. The dipole moment decreases with increasing halogen size from 2.6 Debye for C2H4· · ·HF to 1.9 Debye for C2H4· · ·HCl to 1.6 Debye for C2H4· · ·HBr. The induced dipole moment is approximately given by Dm ¼ mðC2 H4 · · · HXÞ 2 mðHXÞ; and gives an indication of the charge reorganization in HX due to the electric field of the C2H4 molecule and/or intermolecular charge transfer. The induced dipole moment is calculated to be about 0.7 Debye in all three complexes, representing enhancements (over the isolated HX monomer value) of 39% (C2H4· · ·HF), 58% (C2H4· · ·HCl) and 77% (C2H4· · ·HBr). Our value of Dm ¼ 0:72 Debye for C2H4· · ·HF is in good agreement with the corresponding experimental value of 0.67 Debye obtained by Nelson et al. [7] using the molecular beam electric resonance technique. These Table 2 Binding energy ðDEÞ; BSSE corrected binding energy ðDEcorr Þ; zero-point energy (ZPE) corrected binding energy ðDE0 Þ in kJ mol21 for C2H4· · ·HX complexes (X ¼ F, Cl, Br) at the MP2/6-311þ þ G(2d,2p) level of theory Binding energy

C2H4· · ·HF

C2H4· · ·HCl

C2H4· · ·HBr

DE DEcorr DE0

20.6 13.3 17.3

15.2 10.3 11.9

13.1 9.2 10.6

The binding energies ðDEÞ shown in Table 2 were computed as the difference between the total energy of the complex and the sum of the energies of the isolated monomers. The binding energy was corrected for the basis set superposition error (BSSE) [29] by the counterpoise correction method of Boys and Bernardi [30]. The binding energy decreases from ethylene – HF to ethylene –HBr; this is probably due to the decreasing HX dipole moment as the halogen size increase and also probably reflects the dominance of the electrostatic dipole– quadrupole component of the intermolecular interaction. The BSSE correction reduces the binding energy by 35% (C2H4· · ·HF), 32% (C2H4· · ·HCl) and 30% (C2H4· · ·HBr), indicating that though the basis set used here is moderately large, the error due to the BSSE is not insignificant. This point was also mentioned in a previous study of the C2H4· · ·HCl dimer [23]. However, the zero-point energy (ZPE) correction reduces the interaction energy to a lesser extent; 16% for C2H4· · ·HF, 22% for C2H4· · ·HCl and 19% for C2H4· · ·HBr. We note that the binding energies for the ethylene –HX complexes are larger than the corresponding binding energies for the acetylene – HX complexes at the MP2 level from our previous study (though a larger basis set was used in that study). 2.3. Vibrational properties The harmonic vibrational frequencies and frequency shifts of monomer vibrational frequencies on complexation are shown in Table 3. Generally, the low frequency intermolecular vibrational frequencies decrease with increasing halogen size, also indicating the decreasing interaction strength. The most perturbed intramolecular mode is the H – X stretching mode. Our predicted redshift of 147 cm21 for the H –Cl stretch in C2H4· · ·HCl is larger than the value of 90 cm21 obtained by Carcabal et al. using a CCSD(T)/cc-pVTZ wavefunction. The other significant frequency shifts are for the CH2 out-of-plane bending vibrations (v7 and v8 ) of the C2H4 sub-unit, for which blueshifts of 15 and 18 cm21, respectively, were obtained. These values are in good agreement with the corresponding CCSD(T)/cc-pVTZ values of 13 cm21 ðv7 Þ and 16 cm21 ðv8 Þ obtained by Carcabal et al. [23]. Generally, we find a decrease in the frequency shifts in going from C2H4· · ·HF to C2H4· · ·HBr, which is a further indication of the strength of the interspecies interaction. The blueshifts obtained for the C2H4 bending modes (v7 ; v8 and v9 ) are also consistent with the fact that the ethylene sub-unit is found to be slightly distorted in

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S.A.C. McDowell / Journal of Molecular Structure (Theochem) 668 (2004) 41–45

Table 3 Harmonic vibrational frequencies of the C2H4· · ·HX (X ¼ F, Cl, Br) complexes obtained at the MP2/6-311þ þG(2d,2p) level of theory Normal mode

C2H4· · ·HF

C2H4· · ·HCl

C2H4· · ·HBr

v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12 v13 v14 v15 v16 v17 v18

102.8 118.5 141.6 479.0 535.1 834.4 (0.1) 928.5 (24) 996.7 (26) 1077.9 (9) 1245.2 (20.1) 1380.9 (22) 1493.5 (2) 1669.1 (28) 3172.8 (1) 3188.8 (22) 3265.4 (3) 3290.9 (2) 3949.8 (2216)

73.9 85.2 102.5 337.7 344.7 833.9 (20.4) 919.6 (15) 988.6 (18) 1074.5 (6) 1244.4 (21) 1380.4 (22) 1492.1 (0.3) 1670.0 (27) 3170.7 (21) 3187.4 (23) 3262.8 (1) 3288.7 (20.2) 2855.1 (2147)

63.5 80.7 81.0 229.0 303.4 834.6 (0.3) 915.6 (11) 986.8 (16) 1073.6 (5) 1244.8 (20.5) 1380.2 (22) 1491.9 (0.1) 1670.0 (27) 3168.0 (24) 3184.8 (26) 3259.8 (22) 3285.7 (23) 2593.9 (2118)

The vibrational frequency shift ðDvÞ is given in brackets, where Dv ¼ vcomplex 2 vmonomer : The intermolecular normal modes are v1 – v5 (v3 is the intermolecular stretching frequency), the intramolecular C2H4 normal modes are v6 – v17 ; and the HX normal mode is v18. All values are in cm21.

the complex, with the H atoms of ethylene on the side away from the HX sub-unit. The out-of-plane bending motion brings the H atoms of C2H4 close to the H atom of HX causing them to be repelled and increasing the frequency in the complex. This effect has also been observed in previous work on C2H2· · ·HX [5]. 2.4. Relative stabilities of isotopomers In Table 4 we compare the ZPE differences with respect to the monomer sub-units (DZPE) for the H- and D-bonded isotopomers of C2H4· · ·HX as a measure of the relative stability of these isotopomers (which are given explicitly in Table 5). The various vibrational modes contributing to the overall ZPE is also shown. Table 5 shows that for all

the complexes, the D-bonded complex is more stable than the H-bonded analogue, with the ZPE difference decreasing from the HF complex to the HBr complex. This is also the case for the acetylene – HX complexes [5]. The ZPE differences are 103 cm21 for the C2H4· · ·HF isotopomers, 68 cm21 for the C2H4· · ·HCl isotopomers and 52 cm21 for the C2H2· · ·HBr isotopomers. The true ZPEs of these isotopomers will be affected to some extent by anharmonicity. However, since we are only interested in the relative ZPEs of different arrangements of the same nuclei vibrating on a common potential energy surface, we expect anharmonic effects to cancel approximately and our calculated harmonic energy differences to give a reasonable measure of relative stabilities. The ab initio value for the intermolecular stretching frequency (about 140 cm21 for C2H4· · ·HF, 102 cm21 for C2H4· · ·HCl and 81 cm21 for C2H4· · ·HBr) is almost unchanged upon isotopic substitution of HX, showing that this motion (which involves motion of the whole HX subunit) is essentially decoupled from the higher frequency intramolecular H –X stretching vibration. The H – X stretching frequency is also unaffected by isotopic substitution in the ethylene sub-unit. The relative stabilities of the isotopomers of these Tshaped complexes can be readily understood by considering the Buckingham –Liu theory [24], which attributes the stabilities to the difference between the ZPEs associated with the intermolecular bending modes and the ZPE associated with the intramolecular vibrational shift of the HX monomer on complexation. Table 5 shows the contributions to the ZPEs from the intermolecular bending modes, as well as the contributions from the vibrational shifts of the HX and DX monomers on formation of the appropriate complexes. It is clear from the results given in Table 5 that the full ab initio values for the relative stabilities of the H- and Dbonded isotopomers of all the complexes are in excellent agreement with the predictions of the Buckingham –Liu theory, as was the case for the H-bonded and D-bonded isotopomers of linear complexes like CO· · ·C2H2 and

Table 4 Ab initio zero-point vibrational energies for the H- and D-bonded isotopomers of the C2H4· · ·HX complexes (X ¼ F, Cl, Br) at the MP2/6-311þ þG(2d,2p) level of theory Physical property

C2H2HD· · ·HF

C2H4· · ·DF

C2H2HD· · ·HCl

C2H4· · ·DCl

C2H2HD· · ·HBr

C2H4· · ·DBr

P vintermol bend 1219.2 952.8 829.2 650.7 665.1 525.8 vintermol stretch 141.1 139.6 102.0 101.9 81.0 80.9 P v (C2H4) 21,194.4 22,542.9 21,164.5 22,512.4 21,147.5 22,495.2 v (HX) 3949.8 2864.5 2855.1 2048.2 2593.9 1846.8 ZPE 13,252.2 13,249.9 12,475.4 12,656.7 12,243.8 12,474.4 D(ZPE) 599.4 495.9 404.3 336.3 317.8 265.1 P P vintermol bend represents the sum of the intermolecular bending frequencies, vintermol stretch represents the intermolecular stretching frequency, v (C2H4) represents the sum of the intramolecular C2H4 (or C2H2HD) vibrational frequencies and v (HX) represents the HX (or DX) stretching frequency. ZPE is the P total zero-point vibrational energy for the complex (i.e. ZPE ¼ 1=2 vi ; i ¼ 1 – 18) and D(ZPE) is the zero-point vibrational energy of the complex with respect to the monomer sub-units, i.e. D(ZPE) ¼ ZPE(C2H4· · ·HX) 2 ZPE(C2H4) 2 ZPE(HX).

S.A.C. McDowell / Journal of Molecular Structure (Theochem) 668 (2004) 41–45 Table 5 Relative stabilities of the H- and D-bonded isotopomers of the C2H4· · ·HX complexes (X ¼ F, Cl, Br), given by the ab initio zero-point energy differences at the MP2/6-311þþ G(2d,2p) level of theory, compared with the Buckingham–Liu theory [18] Physical parameter

C2H4· · ·HF isotopomers

C2H4· · ·HCl isotopomers

C2H4· · ·HBr isotopomers

HX shift DX shift Dshift Dbend Relative stability (Relative stability)BL

2216.0 2155.7 230.2 133.2 103.0 103.5

2147.1 2104.8 221.2 89.2 68.0 68.0

2118.2 283.8 217.2 69.6 52.4 52.6

[4] [5] [6] [7] [8] [9] [10]

HX shift (DX shift) represents the complexation induced stretching frequency shift, i.e. HX shift ¼ vðC2 H2 HD· · ·HXÞ 2 vðHXÞ; DX shift ¼ vðC2 H4 · · ·DXÞ 2 vðDXÞ: Dshift ¼ 1=2ðHX shift 2 DX shiftÞ: Dbend is onehalf of the difference between the total intermolecular bending frequencies of the H-bonded isotopomer and the D-bonded isotopomer, P P i.e. Dbend ¼ 1=2{ vintermol bend ðC2 H2 HD· · ·HXÞ 2 vintermol bend ðC2 H4 · · · DXÞ}: Relative stability ¼ D(ZPE)(C2H2HD· · ·HX) 2 D(ZPE)(C2H4· · ·DX) defines the relative stability of the isotopomers, with the zero-point vibrational energy (D(ZPE)) values taken from Table 4. These values are compared with the prediction from the Buckingham–Liu theory, which is ðRelative stabilityÞBL ¼ Dshift þ Dbend : All quantities are in cm21.

N 2· · ·C2 H2 [25,26], and T-shaped complexes like C2H2· · ·HX [5]. In conclusion, we have optimized the C2H4· · ·HX series of dimers to T-shaped geometries with binding energies decreasing in the order C2 H4 · · ·HF . C2 H4 · · ·HCl . C2 H4 · · ·HBr as the size of the hydrogen halide (and interspecies separation) increases. We also found that the D-bonded species are more thermodynamically stable than the corresponding H-bonded analogues, with the differences in their ZPEs decreasing in the same order as the binding energies. The full ab initio calculations of the relative stabilities can be explained by the simple model of Buckingham and Liu, which is in excellent agreement with the full ab initio results.

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