Structure, Energetics, and Infrared Spectra of Weakly Bound HC2n+

Article pubs.acs.org/JPCA

Structure, Energetics, and Infrared Spectra of Weakly Bound HC2n+1N···HCl Complexes. A Theoretical Study Marcin Gronowski,*,† Robert Kołos,† and Joanna Sadlej*,‡ †

Institute of Physical Chemistry, Polish Academy of Sciences, 44/52 Kasprzak Street, 01-224 Warsaw, Poland Department of Chemistry, University of Warsaw, 1 Pasteur Street, 02-093 Warsaw, Poland

‡

S Supporting Information *

ABSTRACT: Three model systems, HCN···HCl, HC3N···HCl, and HC5N···HCl, have been investigated computationally with the use of the second-order Möller−Plesset (MP2) and the coupled cluster (with single and double excitations and noniterative inclusion of triples) methods. The global minima are linear hydrogen-bonded structures with HCl as a proton donor. Bent structures are proton-side complexes with HCl as an electron donor, while the bifurcated hydrogen bonds are predicted for tshape complexes. One of the most important findings in this paper is that, according to symmetry-adapted perturbation analysis, the induction-to-dispersion ratios are the biggest for linear complexes, and it is the most noticeable difference between linear, bent, and t-shape structures.

1. INTRODUCTION During the last years, it has been recognized that neutral− neutral reactions are about as important as ion−molecule reactions in the interstellar medium.1,2 This has prompted a great deal of experimental and theoretical studies on the neutral chemistry of the interstellar space. For reliable astrochemical modeling, there is a need to know not only the reaction rates but also the primary reaction products, their energy, and the dynamics of their formation. First steps to any chemical reaction rely on the molecular recognition phenomena, which profit from multiple contacts and which may be of weakly interacting nature. The information about this first step is most conveniently represented by an intermolecular potential energy surface (IPES), which quantifies forces between the interacting species. Therefore, knowledge of IPES is crucial not only for understanding the properties of molecular gases, liquids, and solids but also for the prediction of reaction channels. Interstellar chemistry generally deals with isolated molecules or collision complexes. One of the most interesting families of compounds is the cyanoacetylene group. It consists of unsaturated, conjugated species of diverse carbon chain lengths. Cyanoacetylene HC3N, isocyanoacetylen HCCNC, and an imine HNCCC were discovered in space.3,4 The neutral− neutral reaction C2H2 + CN is recognized as the main source of HC 3 N. Knowledge of the chemical bonding in these compounds comes mainly from the laboratory measurements in the microwave range,5,6 the vibrational matrix isolation IR spectroscopy,7−9 as well as quantum chemical calculations, the latter offering a complementary approach toward the structural and potential function information. Calculations are especially useful when the existence of different conformers is difficult to determine spectroscopically. The extensive investigations of the © 2012 American Chemical Society

members of the cyanoacetylene group and their isomers were performed by Botschwina et al.,10,11 Osamura et al.,12 and Kołos et al.13−17 The current list of interstellar molecules holds more than 100 entries (∼170); hydrogen chloride is one of them. Recently, solvation and ionization of HCl on/in ice have attracted considerable attention as important steps in the depletion of stratospheric ozone.18,19 Because both cyanoacetylene and hydrogen chloride exist in the interstellar space, the HC3N···HCl interactions are of potential importance for the understanding of the changes of rotational intensities due to inelastic collisions of these molecules, in the astrochemical context.20 Molecular complexes in which HCl interacts with a −CN group containing molecule are still a challenging problem for theory. It should be expected that the interaction between proton-donating and proton-accepting moieties leads to a mutual polarization of both subsystems. One of the most simple examples here is HCN···HCl. Hydrogen chloride can participate in a hydrogen bond either as a donor or acceptor of a proton. In the case of HCN, the vicinity of an electronegative atom strengthens the proton-donating ability. The HCN···HCl complex was first observed by Legon et al. in the gas phase21 and was studied at the MP2 level by Araujo and Ramos.22 A full four-dimensional IPES with rigid monomers, computed using the coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) method, was published by van der Avoird et al.23 The global minimum corresponds to the linear hydrogenReceived: January 24, 2012 Revised: May 17, 2012 Published: May 18, 2012 5665

dx.doi.org/10.1021/jp300778j | J. Phys. Chem. A 2012, 116, 5665−5673

The Journal of Physical Chemistry A

Article

bonding structure with HCl as a proton donor, while a secondary minimum is bent with HCN as a proton donor and HCl as a proton acceptor, the latter nearly perpendicular to the intermolecular axis. Continuing this line of research, here, we report on cyanoacetylenic species interacting with HCl, forming the hydrogen-bonding complexes. The aim of this paper is twofold, (i) to compute the characteristic points in the IPES and (ii) to achieve a better understanding of the nature of interactions within the complexes by analyzing the components of interaction energy, such as the electrostatic, exchange, induction, and dispersion contributions computed by symmetry-adapted perturbation theory (SAPT). It is clear that there is no single physical force that could be identified as responsible for hydrogen bonding. Therefore, our analysis will address the question to what extent do the components of the interaction energy change when the hydrogen bond becomes nonlinear in HC2n+1N···HCl. The remainder of this article is organized as follows. In section 2, we describe a brief account of computational details of the present study. In section 3, we present and discuss the results of calculations. Finally, a summary of our investigations is presented in section 4−, together with the conclusions.

2. METHOD OF CALCULATIONS 2.1. Optimization of the Geometry and Supermolecular Interaction Energies. The three first members of the cyanoacetylene group, HCN, HC3N, and HC5N, and their complexes with HCl were studied in this paper. These complexes can form linear (l), bent hydrogen-bonded (b), and t-type structures (c), as presented in Figure 1. The geometries of the complexes were fully optimized by means of Möller− Plesset (MP2) perturbation theory and the coupled cluster CCSD(T) methods for the linear complexes, with the aug-ccpVTZ basis set.24−27 The supermolecular BSSE-corrected interaction energy (the so-called binding energy, De) and the dissociation energy (the binding energy corrected by zero-point energy correction, ZPE, denoted as D0) were calculated for equilibrium geometries using the MP2 perturbation theory in the case of the l-, b-, and t-structures, and only for the lgeometry, the coupled cluster method CCSD(T) was used. The ZPE was calculated at the MP2 level at the harmonic approximation. Extrapolation to the complete basis set limit (CBS) is essential for the interaction and changes the stabilization energy significantly. The CBS extrapolation technique represents a very efficient method that yields accurate values of interaction energies without making extended (and expensive) calculations. The CCSD(T) level can be attained via extrapolation of SCF, MP2, and higher-order correlation energies toward the basis set limit. Each of the components mentioned is differently sensitive to the atomic orbital basis set. SCF calculations are easily carried out even for extended complexes, and for this term, as large of a basis set as possible is recommended (e.g., aug-ccpVQZ). The MP2 interaction energy is the slowest converging, and the lowest acceptable basis set for this extrapolation is augcc-pVQZ. The next term, ΔCCSD(T), is determined as the difference between CCSD(T) and MP2 interaction energies in a small basis set. The use of this term is possible as MP2 and CCSD(T) binding energies converge similarly with the basis set size. The generalization of the 1/X3 error law form, proposed by Helgaker and collaborators,28,29 was used throughout the study

Figure 1. Geometry of the analyzed complexes, l-type (a), b-type (b), and t-type (c), calculated at MP2/aug-cc-pVTZ with the CP-corrected geometry. Bond distances are in Å, and angles are in degrees.

EX = ECBS + A(X − k)−α

(1)

where ECBS is the CBS energy limit, X are the basis set cardinal numbers, and A, k, and α were treated as fit parameters. CBS approaches to interaction energies were used by (for example) Jankowski and Szalewicz30 and examined by Jeziorska et al.31 It was shown that (in case of a two-point extrapolation) different parameters should be used for different intermolecular distances or cardinal numbers X. We have done MP2-R12/ aug-cc-pVQZ calculations for HCN···HCl complexes to compare with different CBS approaches based on the aug-ccpVDZ, aug-cc-pVTZ, and aug-cc-pVQZ basis, (i) three-point extrapolation with α = 3, (ii) two-point extrapolation with α = 3 and k = 0, and (iii) two-point extrapolation with α = 3 and k = 1. We finally chose case (ii). 5666



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The full SAPT approach (named here SAPT) to the intermolecular interaction energy (equivalent to MP4) involves the calculation of the following terms:

Total energies were calculated by eq 2 HF MP2‐fc CCSD(T)‐full MP2‐fc E = Eaug + (Eaug ‐cc‐pVQZ + ECBS ‐cc‐CVDZ − Eaug‐cc‐pVDZ) MP2‐fc + 0.96 × ZPEaug ‐cc‐pVTZ

SAPT SAPT2 (1) (13) E int = E int + Eelst,resp + εexch (CCST)

(2)

(11) (12) (21) (22) − [Eexch + Eexch ] + Edisp + Edisp

where the subscripts denote the basis sets, superscripts the methods, and fc means frozen core. Optimization on the standard PES using medium-size basis sets leads sometimes to a wrong geometric structure; therefore, we performed the counterpoise-corrected (CP) surfaces calculations. The hydrogen-bonded structures of complexes correspond to minima on standard and CP potential energy surfaces (PESs). At each stationary point, the vibrational frequencies were computed at the same level of theory in order to confirm their nature on the PES. The absence of any imaginary frequency ensured that the optimized geometries were true minima. To check how the anharmonicity affects the frequencies of the modes, we have performed the anharmonic frequency calculations. The vibrational self-consistent field (VSCF) and its correlation-corrected variant (CC-VSCF) provide an effective way of obtaining vibrational results in an anharmonic approximation.32,33 However, we decided to use the perturbational treatment34 because of the size of the studied molecules. Geometry optimization and vibrational analysis (harmonic and anharmonic) were carried out with the Gaussian 09 program package.35 2.2. SAPT Calculations of the Interaction Energy. Despite being accurate on a given level of theory, total interaction energies lack information on physically meaningful energy contributions. In this study, we have employed the SAPT0, SAPT2, and SAPT approaches for the calculation of intermolecular interactions.36 At the SAPT0 level, the interaction energy is defined as follows:

In order to facilitate the discussion of the contribution of different terms to the total interaction energy, in this paper, we have arranged the terms in the following way:

=

SAPT0 E int

+

(12) Eelst,resp

+

(22) HF + tEexch −ind + δE int,resp

+

(12) Eexch

+

(10) (12) Eexch = Eexch + εexch

(7)

(20) (20) t (22) t (22) E ind = E ind,resp + Eexch −ind,resp + E ind + Eexch−ind

(8)

(20) (20) Edisp = Edisp + Eexch −disp

(9) (10)

3. RESULTS AND DISCUSSION 3.1. Structures and Supermolecular Interaction Energies. The supermolecular energetic results for the discussed complexes (see Figure 1) of the three cyanoacetylenes are presented in Table 1. First, we discuss the results of supermolecular calculations. Table 1. Binding Energy (De, kJ/mol), Dissociation Energy (D0, D0,CBS, kJ/mol), and Dipole Moment Values (μe, D) for Complexes Calculated with MP2/aug-cc-pVTZ

(3)

(11) Eexch

(6)

The analysis has been performed with the aug-cc-pVTZ basis set, which is large enough to provide a reliable estimatation of the electrostatic, induction, and exchange components. The dispersion term is underestimated by about 10−20% in this set. The interaction energy components were calculated by means of the above method implemented in the SAPT2008 program37 using DALTON software38 for integral calculations.

where E(10) elst is the classical (Coulombic) electrostatic energy, E(10) is the exchange term that results from the antisymmetrizaexch (20) tion (symmetry adaptation) of the wave function, Eind,resp (20) denotes the induction (with response) energy, Eexch−ind,resp is the second−order exchange−induction (with response) energy, (20) E(20) disp is the dispersion energy, and Eexch−disp denotes the exchange−dispersion energy. The agreement between SAPT0 and the supermolecular interaction energy is only qualitative because of the neglect of intramolecular correlation effects in all SAPT0 components.36 The interaction energy at the SAPT2 can be defined as SAPT0 plus some higher-order terms SAPT2 E int

(10) (12) Eelst = Eelst + Eelst,resp

SAPT2 HF E int = Eelst + Eexch + E ind + Edisp + δE int,resp

SAPT0 (10) (20) (20) (20) (10) E int = Eelst + Eexch + E ind,resp + Eexch −ind,resp + Edisp (20) + Eexch −disp

(5)

t (22) E ind

molecules

μe

HCN···HCl HC3N···HCl HC5N···HCl

5.5 6.7 7.7

HCN···HCl HC3N···HCl HC5N···HCl

3.9 4.9 5.7

HC3N···HCl HC5N-t1···HCl HC5N-t2···HCl

2.7 4.4 4.1

De (MP2) l-Complex −20.4 −20.6 −18.5 b-Complex −7.0 −7.7 −7.0 t-Complex −6.1 −6.3 −7.7

D0

D0,CBS (eq 2)

14.6 15.1 15.6

13.7 14.0 14.2

4.7 5.0 5.0

4.8 4.7 4.8

4.5 4.3 5.1

4.1 3.2 4.0

(4)

where the last term collects the contributions to the supermolecular Hartree−Fock energy beyond the second order of the intermolecular operator. The tE(22) ind is the part of (20) E(22) ind not included in Eind,resp. This level of theory may introduce about 10−20% error with respect to the exact interaction energies. In this approach, the correlative part of the interaction energy is equivalent to the supermolecular MP2 correlation energy.

The l-structures are more stable than bent b-structures for all three cyanides. Complexes l and b are hydrogen-bonded; l is a nitrogen-side structure with HCl as a proton donor (Figure 1a), while b-structures are proton-side complexes with HCl as an electron donor and with the HC2n+1N moiety acting as a proton acceptor (Figure 1b). Moreover, HC5N forms two t-type complexes with hydrogen bonds perpendicular to the molecular axis, where the HCl molecule is the proton donor to two C 5667



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Table 2. SAPT2 Interaction Energy and Its Composition (kJ/mol) for l-, b-, and t-Complexesa l-complex E(10) elst E(12) elst,resp E(10) exch E(11) exch E(12) exch E(20) ind,resp t (22) Eind t (22) Eex−ind (20) Eex−ind,resp E(20) disp (20) Eexch−disp HF δint,resp ESAPT2 int EMP2 int a

b-complex

t-complex

HCN

HC3N

HC5N

HCN

HC3N

HC5N

t-HC3N

t1-HC5N

t2-HC5N

−31.4 −0.7 33.5 0.7 2.7 −12.8 −0.9 0.4 6.1 −12.9 1.9 −5.9 −19.3 −20.6

−29.0 −0.8 30.3 0.6 2.8 −11.8 −0.9 0.4 5.4 −13.0 1.8 −5.3 −19.6 −20.8

−29.0 −1.0 30.8 0.6 2.9 −12.1 −0.9 0.4 5.5 −13.4 1.8 −5.5 −19.9 −21.1

−8.1 0.7 7.6 0.1 0.5 −3.6 0.04 −0.02 1.7 −4.6 0.4 −1.1 −6.4 −7.0

−8.0 0.6 8.8 0.08 0.7 −3.7 −0.01 0.0 1.9 −5.5 0.5 −1.2 −5.8 −6.6

−7.1 1.0 7.2 0.05 0.6 −3.1 −0.01 0.01 1.5 −5.1 0.5 −0.38 −5.9 −6.5

−7.0 0.7 8.6 0.3 0.1 −4.1 0.03 −0.03 3.1 −7.2 0.8 −0.8 −5.5 −6.1

−2.9 0.4 13.3 0.6 −0.3 −6.2 0.1 −0.05 3.5 −12.0 1.1 −2.1 −4.4 −6.4

−7.9 1.1 18.1 0.9 −0.9 −8.8 0.3 −0.2 5.6 −12.0 1.3 −3.1 −5.6 −7.8

Results of SAPT2/aug-cc-pVDZ//MP2/aug-cc-pVTZ calculations.

carried out in the aug-cc-pVDZ basis set (because of the system size) for the geometry of the systems previously optimized at MP2/aug-cc-pVTZ and CP-corrected levels. This basis is large enough to provide a reliable estimation of the energy terms. Corresponding results are presented in Table 2 and Figure 2.

atoms of the cyanoacetylenic chain (Figure 1c). An analogous tHC3N···HCl complex has also been found. The MP2 binding energy De (i.e., the interaction energy corrected for BSSE) of l-HCN···HCl is equal to −20.4 kJ/mol, the dipole moment is equal to 5.5 D, and R(N···H) is equal to 2.046 Å (the bond distance CP-corrected in MP2/aug-ccpVTZ). The hydrogen bonds R(N···H) in the l-structure of HC3N and HC5N are shorter (2.038 and 2.033 Å, respectively); the structures are characterized by similar binding energies (−20.6 and −18.5 kJ/mol, respectively). All b-structures have longer hydrogen bonds N···H, 2.718, 2.677, and 2.734 Å (CPcorrected distances), respectively, for HCH, HC3N, and HC5N complexes with HCl. Therefore, the binding energies for the above structures are much smaller (−7.0, −7.7, and −7.0 kJ/ mol, respectively). The values of De and D0 for the lHCN···HCl complex are close to the respective values obtained by van der Avoird et al. (18.72 and 13.05 kJ/mol23). Binding and dissociation energies for t-type complexes (t1,t2)HC5N···HCl and t-HC3N···HCl are quite close to those characterizing the respective b-type structures. The bifurcated hydrogen bonds predicted for the t-HC3N···HCl complex are much longer than H-bonds in respective l- and b-structures, while t1- and t2-HC5N···HCl complexes have much shorter Hbonds than those in corresponding b-structures. These structures are presented here for completeness, although they are less stable than l-structures. Finally, the values of the CBS limit are presented in the last column of Table 1. As observed previously, the MP2 has a tendency to overbind, while the correction for CCSD(T,full)/aug-cc-pCVDZ in eq 2 gives lower values; therefore, all values of D0,CBS, except for bcomplex HCN···HCl, are systematically a few % lower than those from the previous choice of basis set. We can conclude that the extrapolation from the aug-cc-pVTZ to the aug-ccpVQZ basis set is feasible even for relatively large complexes. The differences between intramolecular geometric parameters for the CP-corrected (shown in Figure 1) and standard optimized structures are small, yet the intermolecular distances differ significantly, and as expected, the CP correction leads to higher values. 3.2. Interaction Energy Components Derived with SAPT. The SAPT calculations have been performed for three types of structures (l, b, and t) and for each of the three molecules complexed with HCl. The SAPT2 calculations were

Figure 2. Bar graphs illustrating the SAPT2 results for the decomposition of the interaction energy into individual terms obtained for l-, b-, and t-structures with the aug-cc-pVDZ basis set. 5668



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subsection are based on results obtained with the basis set augcc-pVDZ as with this basis set, we could perform and uniformly interpret the SAPT2 calculations for the three complexes studied. The interaction energy decompositions for three HC2n+1N···HCl structures do not differ significantly. Obviously, the dominant attractive contribution originates in the electrostatic term E(10) elst . The ratio of the latter to the SAPT2 energy is larger for the linear HCN···HCl complex (1.63) than that for the other two (1.48 and 1.46). These attractive energies are compensated mainly by the first-order exchange interaction Eexch (higher than the electrostatic component) and also by the exchange−induction and exchange−dispersion terms. The second-order induction energy term E(20) ind reflects the electric polarization caused both by the charge of the electron cloud and by the nuclei charges. Consequently, in the traditional X−H···Y complex, the effect would be larger the more polar the X−H bond. These terms are attractive, and in the case of three l-complexes, the respective contributions to the total SAPT2 interaction energy are almost the same (their ratio being 0.36). The E(20) ind contribution is partly compensated (20) term, which constitutes for by the repulsive Eexch−ind,resp approximately half of the E(20) ind,resp absolute value in l-complexes. Another attraction effect comes from the dispersion term. This term, as is usual for hydrogen-bonded systems, constitutes ∼50% or more of the total interaction energy (the ratios of dispersion terms to the total SAPT2 energy are the same in three l-structures, 0.57). In a search for factors that would characterize possible differences/similarities exhibited in the properties of b-, l-, and t-systems, we focus on the dominant contributions. The hydrogen bond in b-complexes is formed between a proton and a chlorine atom, the latter acting as the donor of electrons; the interaction energy is smaller than that for the bonding of a proton to nitrogen in l-complexes. While for the l-complexes the ratios of electrostatic and exchange terms to the total SAPT2 energies (∼1.5−1.6; ∼1.7−1.9 respectively) are larger than those for b-complexes (∼1.1−1.2; ∼1.3−1.6, respectively), the ratio of the induction term to the total SAPT2 energy is almost the same in the case of both types of complexes (0.37 for l- and 0.32 for b-structures). Dispersion terms distinguish SPAT2 however both sets of complexes; the ratio Edisp,resp/Eint equals 0.60 for l-complexes, while for b-complexes, it is 0.65−0.85, that is, the dispersion term is more important in these structures than in l-ones. Finally, in the molecule− molecule interaction involving closed-shell species, the interplay between the induction and dispersion effects may be wellcharacterized by analyzing the ratio of these two contributions, Eind/Edisp. The greatest ratio should indicate a system

To provide a better estimate of different terms, we recomputed the decomposition in the aug-cc-pVTZ basis set for lHCN···HCl and l-HC3N···HCl; these results are presented in Table 3. The Supporting Information contains SI-Table 1 and SI-Table 2 with all calculated terms of SAPT2 and SAPT3 for several basis sets for comparison. Table 3. SAPT Interaction Energy and Its Composition (kJ/ mol) for Two l-Complexesa l-complex E(10) elst E(12) elst,resp E(13) elst,resp E(10) exch ε(1) exch(CCSD) E(20) ind,resp t (22) Eind t (22) Eex−ind (20) Eex−ind,resp E(20) disp E(21) disp E(22) disp (20) Eexch−disp HF δint,r ESPAT int

HCN

HC3N

−27.4 −0.2 1.1 25.4 2.5 −10.2 −0.4 0.2 4.7 −12.3 2.3 −2.5 1.7 −4.5 −19.5

−25.7 −0.3 1.1 23.6 2.4 −9.6 −0.4 0.2 4.3 −12.4 2.5 −2.6 1.7 −4.2 −19.4

a

Results of SAPT/aug-cc-pVTZ//CCSD(T)/aug-cc-pVTZ calculations.

Three aspects of the results on SAPT components of the interaction energy should be discussed. First, before analyzing the individual contributions to the intermolecular energy, we shall comment on the accuracy of the SAPT results. Second, we will address the question of how the interaction energy components change in the series of HCN, HC3N, and HC5N molecules interacting with HCl. Finally, it is interesting to conclude on whether the interaction-induced changes of the electronic structure and thus the components of the interaction energies depend on the geometry of the complexes. The SAPT2 estimates of the interaction energy are very close to the respective supermolecular MP2 and CCSD(T) interaction energies calculated with the same aug-cc-pVTZ basis set (Table 1). The l-complexes show a greater stability than the bent ones, in agreement with the supermolecular results. Let us now concentrate on the analysis of the decomposition of the interaction energies. The conclusions drawn in this

Table 4. Harmonic (ω, cm−1) and Anharmonic (ν, cm−1) Frequencies for HCN···HCl Calculated with Different Methods, Employing the aug-cc-pVTZ Basis Set for the CP-Uncorrected Geometrya ω 1σ 2σ 3σ 4π 5π 6σ 7π a

ν

B3LYP

MP2

CCSD(T)

3440 2769 2218 770 417 113 50

3454 2875 2040 727 435 126 56

3423 2878 2124 727 399 112 62

exp

39,42

100, 111

B3LYP

CCSD(T)

3309 2697 2186

3314 2798 2119 798 381 111 83

101

CCSD(T)23

exp 3310.327140,41 2779.096821

311.7 102.6 48.7

311.3996639

Comparison with experimental data and other theoretical results. 5669



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Table 5. Harmonic Frequencies (ω, cm−1) and Absolute IR Intensities (IIR, km/mol) for the HCN···HCl Complex Calculated with MP2/aug-cc-pVTZ for the CP-Corrected Geometrya

particularly favored by the induction effect. This ratio amounts to ∼0.6 for l- and only to ∼0.3 for b-structures (except HCN···HCl) for l-X···HCl. These data point to the most noticeable difference between l- and b-structures (easily identified in Figure 2). A different pattern characterizes the tstructures. Here, the Eind/Edisp values of 0.1 to 0.3 are similar to those predicted for b-complexes. However, the exchange effect outweighs the electrostatic one for t1 and t2-structures, and the dispersion effect is predominant. 3.3. Vibrational IR Spectra. Usually, the experimental identification of the basic unit HC2n+1N and of the complex HC2n+1N···HCl relied on the vibrational bands in FTIR spectra. There are no experimental data for the above-mentioned complexes. However, the precise frequencies of intermolecular vibrations extracted from the four-dimensional PES for the HCN···HCl complex were published by van der Avoird et al.23 Therefore, before presenting the results for all complexes, it is useful to discuss the results for the smallest one, where gasphase experimental data are available, in order to assess the performance of the theoretical methods used here. We summarized our results in four tables. Table 4 reports the harmonic and anharmonic vibrational frequencies for the smallest l-HCN···HCl complex calculated by different methods using the aug-cc-pVTZ basis set (with the CP-corrected geometry). The quoted indirect values are based on experimental data which, include anharmonicity effects and make use of very approximate formulas. Absorption bands at 2779.09 and 311.40 cm−1, found experimentally,21,39 were assigned to the H−Cl stretching and HCl libration modes, respectively. The downward shift expected with the introduction of anharmonicity is ∼3% at both the CCSD(T) and B3LYP levels. The HCl libration frequency is shifted by ∼5% at the CCSD(T) level, that is, more than the stretching mode, due to the large amplitude of the libration, giving rise to substantial anharmonic effects. The bend and librational modes of a linear complex are 2fold degenerate. The two vibrations with the highest wave numbers (of 3423 and 2124 cm−1 at the CCSD(T) harmonic approach) may be described as the stretching H−C and CN modes. These values shift slightly (to 3314 and 2119 cm−1, respectively) when anharmonicity is taken into account at the CCSD(T) and B3LYP levels. The anharmonic value of the stretching C−H mode is very close to the experimental value of 3310.33.40,41The intermolecular stretching mode is a largeamplitude motion; therefore, the harmonic approximation cannot be expected to give accurate results. It is generally of a quite low frequency and intensity, making its detection rather difficult. van der Avoird et al.23 derived the frequency of 102.6 cm−1 with an anharmonic approach, obtained from solving the vibrational problem on the 4D PES, while we obtained an anharmonic value equal to 111 cm−1. The difference between the CCSD(T) and B3LYP calculated frequencies (Table 4) is indeed encouraging, except the HCl stretching frequency. These results provide an estimate of the precision that we can expect when applying the B3LYP method in the study of other, similar complexes, where no experimental data are available for comparison. However, the HCl stretching mode is characterized by too low of a wavenumber within the anharmonic approach (2697 against the harmonic one of 2769 and the experimental value equal to 2779 cm−1). Tables 5−7 list the harmonic frequencies and IR intensity values calculated with MP2/aug-cc-pVTZ for l- and bcomplexes HCN···HCl, HC3N···HCl, and HC5N···HCl (with

symmetry 1σ 2σ 3σ 4π 5π 6σ 7π 1 A′ 2A′ 3A′ 4A′ 5A″ 5A′ 5A″ 6A′ 7A′

assignment

ωb

l-HCN···HCl H−C stretch. 3465 (−2) H−Cl stretch. 2885 (−160) CN stretch. 2040 (+18) HCN bend. 727 (+9) HCl librat. 414 HCN···HCl stretch. 120 HCN librat. 50 b-HCl···HCN H−C stretch. 3430 (−37) H−Cl stretch. 3029 (−15) CN stretch. 2020 (−2) HCN bend. 754 (+36) HCN bend. 743 (+26) HCl librat. 195 HCN···HCl stretch. 70 HCN and HCl librat. 61 HCN librat. 51

IIRc 93 (+20) 587 (+1077) 0.3 (+30) 68 (−6) 55 5 40 199 (+159) 62 (+24) 1 (+444) 28 (−33) 27 (−24) 33 1 27 24

a

In parentheses are the frequency and intensity changes of individual bands. bFrequency changes are given in cm−1. cPercent intensity changes calculated according to the formula [(Icomplex − Imonomer)/ Imonomer]·100.

CP-uncorrected geometry). The changes induced in the IR spectroscopic parameters of subunit molecules by the formation of hydrogen bond complexes are shown in parentheses. Let us discuss the intramolecular modes. Some of the vibrational modes of the monomers remain localized in HCl and in cyanoacetylenes. The harmonic stretching mode for HCl is equal to ν(H−Cl) = 3044 cm−1 on the MP2/aug-ccpVTZ approach and occurs at 2885, 2881, and 2877 cm−1 for lspecies (for HCN, HC3N, and HC5N complexes, respectively). Thus, with HCl acting as a proton donor, the red shift of HCl stretching increases (−160, −163, and −168 cm−1) for lstructures, with the growing length of the three nitriles considered. The frequency of this mode shifts by −64 and −41 cm−1 for t1- and t2-HC5N···HCl complexes. The shift to lower frequencies has generally been interpreted in terms of a lengthening of the H−Cl bond. Contrary to that, much smaller shifts, equal to −15, −11, and −10 cm−1, were noticed with HCl playing the role of an electron donor in b-complexes. The strong intensity enhancement of the HCl stretching mode for lstructures and a much smaller one for b-structures agree well with the earlier predictions on similar systems.39,42 In contrast to the HCl stretching mode, frequencies associated with the ν(CN) vibration within the studied complexes are changed little from their monomer values. The frequency analysis reveals the blue shifts of CN stretching modes in l-complexes in comparison to the respective monomers (+22, +8, and +1 for symmetric and +15 and +24 cm−1 for asymmetric modes), as is typical for a hydrogen bond involving nitrogen of the nitrile group. The blue shift of ν(CN) is proportional to predicted CN bond shortenings and is shown to decrease in the sequence from HCN to HC5N. More insight into the nature of these changes is provided with SAPT calculations. Due to the highest repulsive term of exchange energy (33.5 kJ/mol), the shortening of the CN distance and 5670



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Table 6. Harmonic Frequencies (ω, cm−1) and Absolute Intensities (IIR, km/mol) for the HC3N···HCl Complex Calculated with MP2/aug-cc-pVTZ for the CP-Corrected Geometrya symmetry 1σ 2σ 3σ 4σ 5σ 6π 7π 8π 9π 10σ 11π 1A′ 2A′ 3A′ 4A′ 5A′ 6A′ 7A″ 8A′ 9A″ 10A′ 11A″ 12 A′ 13A′ 14A″ 15A′

assignment

ωb

l-HC3N···HCl H−C stretch. 3469 (−3) H−Cl stretch. 2881 (−163) CN + CC stretch. 2226 (+7) CN + CC stretch. 2037 (+8) C−C stretch. 890 (+9) HCC bend. 668 (+8) CCCN bend. 498 (+3) HCl librat. 409 HC3N bend. 220 (−1) HC3N···HCl stretch 103 HC3N librat. 22 b-HCl···HC3N H−C stretch. 3440 (−32) H−Cl stretch. 3033 (−12) CN + CC stretch. 2216 (−3) CN + CC stretch. 2026 (+1) C−C stretch. 883 (+1) HCC bend. 700 (+41) HCC bend. 688 (+28) CCCN bend. 496 (+1) CCCN bend. 496 (+1) HC3N bend. 230 (+9) HC3N bend. 224 (+3) HCl librat. 165 HCl···HCN stretch. 67 HC3N librat. 23 HC3N, HCl librat. 16

Table 7. Harmonic Frequencies (ω, cm−1) and Absolute Intensities (IIR, km/mol) for the HC5N···HCl Complex Calculated with MP2/aug-cc-pVTZ for the CP-Corrected Geometrya

IIRc

symmetry

90 (+7) 789 (+1482) 25 (+258) 2 (−19) 0.4 (+21) 75 (−3) 10 (+68) 20 0.3 (−48) 5 3

1σ 2σ 3σ 4σ 5σ 6σ 7π 8σ 9π 10π 11π 12π 13π 14σ 15π

234 (+178) 62 (+24) 18 (+162) 9 (+260) 0.006 (−98) 27 (−29) 27 (−29) 3 (+6) 3 (+6) 3 (+935) 1 (+137) 32 0.2 4 4

1A′ 2A′ 3A′ 4A′ 5A′ 6A′ 7A″ 8A′ 9A″ 10A′ 11A″ 12A′ 13A′ 14A′ 15A″ 16A′ 17A″ 18A′ 19A′ 20A″ 21A′

a

Frequency and intensity changes of individual bands are given in parentheses. bFrequency changes are given in cm−1. cPercent intensity changes calculated according to the formula [(Icomplex − Imonomer)/ Imonomer]·100.

thus the increase of this mode frequency are the biggest for HCN···HCl. As expected, the IR intensities behave in the same way. The b-structure complexation of cyanoacetylenes breaks the symmetry, causing a splitting of the degenerate modes, corresponding to asymmetrical stretching and bending vibrations in an isolated molecule. When the CN group is not engaged in the intermolecular bond, as in the case of bstructures, asymmetric stretching is affected very little by the formation of complexes. Only small red shifts are noticed, contrary to the interaction with the nitrogen end of the nitryl molecules. This interaction, although less energetic, is characterized as being more due to dispersion forces than the one involved in the hydrogen bonding to nitrogen. The increase of the intensity is huge, which has been interpreted in terms of intermolecular polarization. The degenerate bending modes H−CH (718, 659, and 630 cm −1 for three cyanoacetylenes) are split into two components with higher frequencies, +40 and +25 cm−1, coupled to CC vibrational modes. Because of the difficulty in the detection of bands in the farIR region, calculations can play an important role in predicting this part of the spectrum. In Tables 5−7, we report the intermolecular hydrogen-bonding stretching bands, which are

assignment

ωb

l-HC5N···HCl H−C stretch. 3464 (−3) H−Cl stretch. 2877 (−168) CN + CC stretch. 2217 (+1) CN + CC stretch. 2146 (+7) CN + CC stretch. 2017 (+5) C−C stretch. 1180 (+6) HCC bend. 636 (+7) C−C stretch. 619 (+7) HC5N bend. 515 (+1) HC5N bend. 474 (+4) HCl librat. 410 HC5N bend. 256 (−1) HC5N librat. 109 (+2) HC5N···HCl stretch. 96 HC5N, HCl librat. 15 b-HCl···HC5N H−C stretch. 3436 (−31) H−Cl stretch. 3034 (−11) CN + CC stretch. 2214 (−2) CN + CC stretch. 2136 (−3) CN + CC stretch. 2009 (−3) C−C stretch. 1174 (0) HCC bend. 670 (+40) HCC bend. 658 (+28) C−C stretch. 613 (+1) HC5N bend. 514 (+0.5) HC5N bend. 514 (+0.4) HC5N bend. 472 (+1) HC5N bend. 471 (+0.8) CCC bend. 262 (+4) CCC bend. 259 (+2) HCl librat. 165 HC5N bend. 111 (+4) HC5N bend. 106 (−1) HCl···HC5N stretch. 55 HC5N, HCl librat. 18 HC5N, HCl librat. 14

IIRc 112 (+4) 998 (+1902) 124 (+150) 1 (−43) 1 (+70685) 1 (+2952) 75 (−2) 0.5 (+11) 4 (+114) 4 (+119) 42 8 (−42) 0.06 (−88) 6 0.2 274 (+154) 62 (+24) 71 (+44) 6 (+368) 2 (+103900) 0.1 (+255) 28 (−27) 28 (−27) 0.03 (−94) 1 (+45) 1 (+39) 1 (+16) 1 (+12) 6 (−15) 6 (−19) 31 0.5 (+100) 5 (+1662) 0.2 2 2

a

In parentheses are frequency and intensity changes of individual bands. bFrequency changes are given in cm−1. cPercent intensity changes calculated according to the formula [(Icomplex − Imonomer)/ Imonomer]·100.

generally of quite low frequency and intensity. Corresponding frequencies decrease in the order HCN, HC3N, HC5N (120, 103, 96 cm−1 for l-structures and 70, 67, and 55 cm−1 for bstructures). This is in line with the interaction energy values, although a mass effect could contribute to the changes too. The deviation between CCSD(T) anharmonic frequencies reported in Table 4 and those obtained from solving the vibration problem on a 4D PES are large, 381 versus 311.7, 111 versus 102.6, and 83 versus 48.7 cm−1.23 The intermolecular HCN libration band found experimentally at 41 cm−140 is presently predicted to occur at 50 cm−1. The description of low frequencies in our approach does not provide an appropriate reference for the motions within very shallow PESs. 5671



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4. CONCLUSIONS We have investigated the structural, energetic, and spectroscopic properties of HCN···HCl, HC 3 N···HCl, and HC5N···HCl complexes, interesting from the astrochemical point of view. Our results can be summarized as follows. (1) The equilibrium geometry of studied complexes corresponds to linear structures with a hydrogen bond involving the nitrogen atom of a nitrile and the HCl molecule as the donor. The hydrogen bond N···H is systematically shortened in this group from HCN to HC5N. The distance N···Cl computed for HCN···HCl is in agreement with experimental data coming from microwave measurements21 (3.333 calculated versus 3.4047 Å experimental) and other theoretical calculations.23 Our best estimates of the dissociation energy are 14.6, 15.1, and 15.6 kJ/mol (MP2/aug-cc-pVTZ), respectively, for HCl complexes with HCN, HC3N, and HC5N. Secondary hydrogen-bonding structures, with HCl playing the role of a proton acceptor, are characterized by bent geometries, with dissociation energies equal to 4.7, 5.0, and 5.0 kJ/mol, respectively, at the same level of theory. The t-shape complexes with bifurcated hydrogen bond interactions Cl−H···C have been found for HC3N···HCl and HC5N···HCl, with dissociation energies similar to those for b-structures. (2) SAPT calculations indicate that the bonding in l-type complexes is mainly governed by strong electrostatic and exchange terms; the latter slightly outweighs the former one, but large attractive induction and dispersion contributions lead to an attractive effect. The dispersion contribution is relatively more important for b-structures than that for linear ones and represents ∼70% of the total energy, while it amounts to as much as ∼120 or even 250% for t-structures. The induction-todispersion ratios are the highest for linear complexes. These data are the most noticeable difference between l-, b-, and tstructures. (3) Despite a fairly weak character of the hydrogen bond in HC2n+1N···HCl complexes, a blue shift (of +18 cm−1 for HCN···HCl, smaller for n = 1 and 2) and IR absorption intensity increase were found for the CN stretching mode. The spectrum of HCl is more strongly affected; a substantial red shift was found for the HCl stretch, much bigger for the linear than that for bent complexes. We have reliably reproduced all essential features of the IR spectra.

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ASSOCIATED CONTENT

* Supporting Information Tables containing SAPT calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (M.G.); [email protected]. edu.pl (J.S.). Notes

The authors declare no competing financial interest.

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REFERENCES

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ACKNOWLEDGMENTS

The computational part of this work was done using the computer cluster at the Computing Center of Faculty of Chemistry, Warsaw University. We acknowledge also the computer grant G31-13 at ICM, Warsaw University. 5672



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Structure, Energetics, and Infrared Spectra of Weakly Bound HC2n+

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