Anharmonic Calculation of the Structure, Vibrational Frequencies and

Article pubs.acs.org/JPCA

Anharmonic Calculation of the Structure, Vibrational Frequencies and Intensities of the NH3···trans-HONO Complex Valentin P. Bulychev, Marina V. Buturlimova, and Konstantin G. Tokhadze* Physical Faculty, St. Petersburg State University, Peterhof, St. Petersburg, 198504 Russian Federation ABSTRACT: The equilibrium geometry of the NH3···transHONO complex and the harmonic vibrational frequencies and intensities are calculated in the MP2/aug-cc-pVTZ approximation with the basis set superposition error taken into account. Effects of anharmonic interactions on spectroscopic parameters are studied by solving vibrational Schrödinger equations in 1−4 dimensions using the variational method. Anharmonic vibrational equations are formulated in the space of normal coordinates of the complex. Detailed analysis is performed for the H-bond stretching vibration and internal vibrations of the trans-HONO isomer in the complex. The intermode anharmonicity and anharmonic coupling between two, three, and four vibrational modes are studied on the basis of correct ab initio potential energy surfaces calculated in the above approximation. The combinations of normal modes of the complex most strongly coupled to one another are examined. The calculated frequencies and intensities of vibrational bands are compared with the experimental data on the NH3···trans-HONO complex in an argon matrix and results of earlier calculations of monomeric HONO. In this calculation the strong resonance between the first excited state of the OH stretching vibration and the doubly excited state of the NOH bending vibration of trans-HONO isomer in the complex is thoroughly studied by solving vibrational equations in two and four dimensions.

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INTRODUCTION Nitrous acid (HONO) plays an important role in atmospheric chemistry. There is a general agreement that HONO is a source of the hydroxyl radical (OH), which is a key species in the photochemical cycles responsible for the generation of tropospheric ozone.1 Nitrous acid is one of the simplest systems that possess different stable isomers. For these reasons the HONO molecule has been the object of extensive experimental2−9 and theoretical10−13 studies. The trans−cis isomerization of HONO was studied in nitrogen matrixes.2 It has been shown that the isomerization was caused by photons with energies in the 3650−3200 cm−1 range. The authors estimated the height of the potential barrier to isomerization and proposed an isomerization mechanism involving an efficient energy transfer between vibrational modes. The complete assignment of the fundamental vibrational transitions of both conformers was made on the basis of the gas-phase absorption spectra.3 Six fundamentals of the cis and three of the trans isomers were identified from infrared spectra of cis and trans-HONO in an Ar matrix.4 The equilibrium structures and dipole moment values were derived for both isomers from the microwave spectra of isotopic species of cis and trans nitrous acid. The frequencies for fundamental transitions, some overtones and combination bands of the cis and trans forms of HONO, as well as rovibrational parameters of the conformers, were obtained from the Fourier transform absorption spectra recorded at high resolution.5−7 To our knowledge, the reliable data on these quantities were obtained only for the ν3 and ν4 bands of trans-HONO and the ν4 band of cis-HONO.8,9 © 2013 American Chemical Society

A vast literature has been devoted to calculating the properties of nitrous acid. Most of the theoretical papers report the equilibrium geometry, relative stability of isomers, and harmonic frequencies.10,11 A fully coupled six-dimensional dynamics calculation was performed on this molecule.12 In this study the frequencies and intensities were correctly obtained for many fundamental and some overtone bands using the potential energy and dipole moment surfaces computed by the density-functional theory method. Vibrational characteristics of trans- and cis- isomers of nitrous acid were obtained in the variational anharmonic calculation.13 This study revealed the presence of a significant interaction between the O−H stretching vibration, the HON bending vibration, and the OH torsional vibration in both isomers of HONO and the resonance interaction between the (ν3, ν6) and (ν3−1, ν6 + 2) states of cis-HONO. Many investigations were also devoted to complexes formed by HONO with other compounds. The infrared matrix isolation technique was used to study the complexes of nitrous acid with the following important atmospheric species: N2 and CO,14 CH4,15,16 SiH4 and GeH4,16 C6H6,17 CS2 and CO2,18 H2O,19 NO2,20 SO2,21 HF,22 HCl,22,23 C2H4,24 and oxygen bases (acetone and ethers).25,26 In these studies the objectives were the equilibrium geometry of complexes, the frequency and intensity shifts upon complexation, and the isotope effects. Some of these experimental studies were supplemented with Received: July 3, 2013 Revised: August 14, 2013 Published: August 14, 2013 9093

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calculations of vibrational characteristics, mainly, in the harmonic approximation. However, there are few publications devoted to the strong hydrogen-bonded HONO···NH 3 complex. The kinetics and thermochemistry of the reversible gas phase reaction were studied27 between ammonia and HONO, H3N + HONO → H3N···HONO. The authors also reported the results of ab initio MP2/6-31+G(d,p) calculations on the thermochemistry of the H3N···HONO complex, which was found to form a fairly strong hydrogen bond with the binding energy of 49.4 kJ mol−1. The absorption spectra of the H3N···HONO complexes containing the cis and trans isomers of HONO were recorded in an argon matrix.28 The equilibrium configurations and the harmonic fundamental transition frequencies and intensities were calculated in the MP2/631+G(d,p) approximation with the basis set superposition error (BSSE) taken into account by the counterpoise method. Values of 40.13 and 36.39 kJ mol−1 for the binding energies of complexes formed by trans-HONO and cis-HONO, respectively, were obtained with a wider basis set 6-311+G(2d,2p). The authors of this work identified five HONO vibrations and one NH3 bending vibration for the NH3···trans-HONO complex. The fundamental frequencies of the O−H stretching vibration and the HON in-plane bending vibration in this complex are, respectively, red-shifted by about 800 cm−1 and blue-shifted by about 190 cm−1 relative to the corresponding bands of trans-HONO monomer. Doublet structures were observed in the O−H stretch regions of the trans-HONO monomer at 3568.5 and 3572.6 cm−1 and the NH3···transHONO complex at 2737.5 and 2765.2 cm−1. The former doublet was convincingly assigned to the matrix site effect, while it was assumed that the doublet in the spectrum of the complex could result from both the site effect and a resonance between the first excited O−H stretching state and the second excited HON bending state. The purpose of this paper is to report a nonempirical quantum-mechanical calculation of the equilibrium structure and vibrational spectroscopic characteristics of the strongly bound H3N···HONO heterodimer formed by the trans-isomer of nitrous acid with ammonia. The frequencies and intensities of absorption bands are derived from anharmonic variational solutions of vibrational Schrö dinger equations with the potential energy surfaces (PESs) computed in the same approximation that was used in calculations of free HONO isomers.13 This fact will facilitate comparison of parameters calculated for free trans-HONO molecules and the NH3···transHONO complex. The results predicted for the complex by the calculation will be compared with the experimental findings.28 One of the objectives is to resolve the problem of the origin of the doublet observed in argon matrixes in the region of the O− H stretching fundamental of the NH3···trans-HONO complex.28 The vibrationally averaged values of r(OH) and R(N··· O) will also be evaluated by averaging over the ground state and several important excited states of the complex.

Figure 1. The equilibrium geometry of the NH3···trans-HONO complex.

atoms of NH3 lie in the symmetry plane. The most important geometrical parameters of the calculated configuration are presented in Table 1. Table 1. Optimized Structural Parameters of the NH3···transHONO Complex Distances (Å) r(H1−O1)

r(O1−N1)

r(N1O2)

0.9993

1.3770

r(N2···O1)

H1O1N1

O1N1O2

N2H1O1

H2N2H1

H3N2H1

H2H3N2H1

102.09

111.92

175.82

106.61

114.26

122.70

1.1931 2.7815 Angles (deg)

r(N2−H2)

r(N2−H3)

1.0133

1.0127

These structural parameters are in good agreement with the values obtained earlier.28 Comparison with the parameters calculated for the trans-HONO monomer13 shows that r(H1− O1) and r(N1O2) increase upon complexation by 0.031 and 0.016 Å, respectively, but r(O1−N1) decreases by 0.046 Å. Both angles of trans-HONO are slightly increased. With the electronic energies computed for NH3 and trans-HONO in the same approximation, we obtained, in agreement with the calculation,28 a value of 43.34 kJ mol−1 for the binding energy. For the NH3···trans-HONO complex in the equilibrium configuration, the dipole moment value is 5.159 D, and the rotational constants are 30.387, 2.726, and 2.535 GHz. Harmonic frequencies and intensities for vibrational transitions of the NH3···trans-HONO complex computed using GAUSSIAN 0329 are summarized in Table 2. For comparison, the frequencies and intensities computed for the trans-HONO monomer are shown in parentheses. One can see in Table 2 that the frequencies of all fundamental transitions of trans-HONO, except for the N1O2 and H1−O1 stretching modes, appreciably increase upon complexation. The changes in the stretching frequencies of trans-HONO upon complexation are in agreement with the changes in the corresponding bond lengths (Table 1). The frequency of torsional OH vibration strongly increases because of the hydrogen bonding with the ammonia molecule. The decrease in the H1−O1 frequency upon complexation is as large as 598 cm−1. The relative changes in transition intensities are, as a rule, more

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METHOD OF CALCULATION The equilibrium geometry of the NH3···trans-HONO complex, the harmonic transition frequencies and intensities, as well as the PESs, were calculated in the MP2/aug-cc-pVTZ approximation using the GAUSSIAN 03 package of codes29 with the BSSE correction taken into account. The equilibrium nuclear configuration of this complex is shown in Figure 1. This configuration possesses the symmetry properties of the Cs point group. All atoms of HONO, the N atom and one of the H 9094

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Table 2. Harmonic Frequencies (cm−1) and Intensities (km mol−1) for the Fundamental Transitions of the NH3···trans-HONO Complex

a

assignment

frequency

intensity

assignment

frequency

intensity

H-bond twist. H-bond bend. H-bond bend. H-bond stretch. H-bond bend. H-bond bend. O1N1O2 bend. O1−N1 stretch. O1−H1 tors.

37 75 139 230 308 357 718 (614)a 926 (819)a 1035 (577)a

0.2 3.9 0.5 30 19 24 42 (194)a 342 (161)a 76 (99)a

NH3 bend. H1O1N1 bend. N1O2 stretch. NH3 bend. NH3 bend. H1−O1 stretch. NH3 stretch. NH3 stretch. NH3 stretch.

1126 1467 (1291)a 1637 (1658)a 1668 1671 3176 (3774)a 3499 3638 3643

155 215 (175)a 44 (107)a 17 23 1560 (91)a 0.6 24 23

Values of transition frequencies and intensities for the free trans-HONO isomer13 are shown for comparison in parentheses.

Table 3. Fundamental Frequencies (cm−1) and Intensities (km mol−1) of Modes νk Obtained from 1D Anharmonic Equations and the Frequency Shifts (cm−1) Due to Interactions in Pairs (ν1,νk) mode νk

1D frequency

1D intensity

ν1(2D) − ν1(1D)

νk(2D) − νk(1D)

ν1(O−H) ν2(NO) ν3(NOH) ν4(N−O) ν5(ONO) ν6(OH tors) ν7(H-bond str)

2867 1638 1477 909 716 1105 225

1827 81 291 301 29 102 26

0 −0.5 −64.2 −0.8 −6.5 −1.6 −99.9

0 3.1 −23.5 6.4 −3.4 −90.5 11.4

Results of 1D and 2D Anharmonic Calculations. At the first stage, we solved 1D anharmonic equations for seven considered vibrations of the NH3···trans-HONO complex. Values of vibrational transition frequencies and absolute intensities derived from these solutions are presented in Table 3 (columns 2 and 3). As one might expect, the anharmonic frequency values for stretching modes, except for the vibration of the strong NO bond, are appreciably smaller than the harmonic values. These 1D anharmonic values are in better agreement with the experimental findings.28 It is worth noting that the anharmonic frequency of the OH torsional vibration is significantly higher than the harmonic value. The same effect was observed earlier13 in the calculations of both HONO isomers. As for the anharmonic intensity values, they are, as a rule, higher than the harmonic values. Of interest are the elongations of the bond length r(OH) in HONO and the H-bond length R(N···O) because of 1D anharmonic vibrations: the values of these distances averaged over the ground state of the corresponding 1D vibration are 1.0002 and 2.7985 Å, respectively. Comparison with the equilibrium bond lengths (Table 1) shows that these bonds become longer, respectively, by 0.0009 and 0.0175 Å because of the anharmonic zero-point vibration. We solved 2D vibrational equations for all pairs (qk, qj) using ab initio PESs V(qk, qj). As an example, Figure 2 shows the plot of potential energy V calculated for the 2D system (ν1, ν6) as a function of variables ξ1 and ξ6. One can see that for positive ξ1, that is, for r(OH) shorter than re(OH), the potential energy has two minima in ξ6 (torsional motion of OH), and, consequently, the trans-HONO subunit is no longer planar. It follows from solutions of 2D problems that the spectroscopic parameters of the ν2(NO), ν4(N−O), and ν5(ONO) bands are only weakly perturbed by the pairwise anharmonic interactions. The other four modes are sufficiently strongly coupled with one another (see Table 3). The changes in the 1D frequency value of the ν1(O−H) band caused by the interaction with a νk vibration are

significant than the relative changes in frequencies. The increase in the H1−O1 intensity by a factor of 17 is most drastic. Anharmonic calculations with the inclusion of intramode anharmonic effects and coupling between different vibrational degrees of freedom were performed for the modes of NH3··· trans-HONO assigned to the HONO subunit and the H-bond stretching mode. In these calculations we used the massweighted normal coordinates qi of the complex as the vibrational coordinates. It was shown13 that this choice of vibrational coordinates allowed the frequencies and intensities of HONO molecules to be obtained with good accuracy. We considered the vibrational Schrödinger equations in one−four dimensions (1D−4D). The region of variation of each variable qi was chosen sufficiently wide so that it was possible to describe the ground state and a number of excited vibrational states. The vibrational energy values and wave functions were obtained by the variational method from solutions of secular equations. The wave functions were expanded in harmonicoscillator eigenfunctions χk(ξi) of a dimensionless argument ξi = qi(ωi/ℏ)1/2, where ωi is the cyclic frequency of a harmonic oscillator and ℏ is the Planck constant. For the multidimensional problems, the basis functions were chosen in the form of products of one-dimensional functions. The PESs necessary in the variational method were computed by the MP2 method used above to determine the equilibrium nuclear configuration. The surfaces of dipole moment components required for evaluating the transition intensities were calculated in the selfconsistent field approximation. Test calculations showed that such calculation of the dipole moment increases the transition intensities by several percent as compared to the MP2 calculations. Other mathematical and computational details of the adopted procedures have been reported earlier.13 In what follows we will omit subscripts of atoms entering the complex since this omission will not cause any confusion. 9095

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MP2/aug-cc-pVTZ approximation with allowance for the BSSE correction at points corresponding to roots of the Hermite polynomial H11(ξk) for each variable. The dipole moment components were computed on the same grid of points of the 4D space. The total number of variational basis functions was equal to 10 000. To reduce the dimension of the 4D Hamiltonian matrix, we expanded the 4D wave functions not in products of four initial 1D basic functions but in products of 2D anharmonic eigenfunctions φk(ξ1, ξ6) and ψk(ξ3, ξ7) obtained for subsystems (ν1, ν6) and (ν3, ν7). 10

φk (ξ1 , ξ6) =

∑

Akμν χμ(1) (ξ1) χν(2) (ξ6)

μ,ν=1 10

Figure 2. Potential energy V (ξ1,ξ6) calculated for the 2D system (ν1, ν6).

ψn(ξ3 , ξ7) =

∑

Bnμν χμ(3) (ξ3) χν(4) (ξ7)

μ,ν=1

presented in column 4 of Table 3, and the analogous changes in the 1D frequency value of the νk band caused by its interaction with the ν1 vibration are shown in column 5 of Table 3. The pairwise interactions of the ν1 mode with all other modes lower the ν1 frequency. The largest decrease of ν1 is caused by the ν7 vibration. The last fact agrees with the larger average value of r(OH) (1.0287 Å), the shorter average value of R(N···O) (2.76428 Å), and the higher value of the ν7 frequency in the 2D vibrational system (ν1, ν7) as compared to the corresponding 1D values. In a certain sense the hydrogen bonding becomes stronger if the O−H and H-bond stretching vibrations can occur simultaneously. In contrast, the coupling of the ν7 mode to the torsional motion of OH (ν6) or to the HON bending vibration (ν3) weakens the hydrogen bond. In these 2D systems the ground-state average value of R(N···O) is equal to 2.8134 and 2.8033 Å, respectively. The ν6 vibration experiences the largest frequency shift due to the coupling to the ν1 vibration (−90.5 cm−1); however, this effect is smaller than in the isolated trans-HONO (−230 cm−1).13 Note that in the system (ν1, ν3) the second excited state is a mixture of the doubly excited ν3 state and the singly excited ν1 state with weights 0.7 and 0.3, respectively. The third excited state of this system is a mixture of the same excited states with weights of 0.3 and 0.7. This is indicative of a considerable (ν1/2ν3) resonance. The resonance is possible because the 1D values of the ν1 fundamental and 2ν3 overtone are very close (2867 and 2962 cm−1). On the whole the data of Table 3 suggest that vibrations ν1, ν3, ν6, and ν7 have to be considered simultaneously, which requires a calculation of V(q1, q3, q6, q7) and solution of a 4D Schrödinger equation. Results of 3D and 4D Anharmonic Calculations. A number of 3D problems were solved for different combinations of vibrations ν1, ν3, ν6, and ν7. These solutions confirmed that the trends observed above in the changes of spectroscopic parameters caused by intermode interactions are regular and consistent. For example, the variational solution of the Schrödinger equation for system (ν3, ν6, ν7) predicts the following values of frequencies (cm−1) (and intensities (km mol−1)): 1478 (292) for ν3, 2963 (0.3) for 2ν3, 1091 (102) for ν6, and 216 (26) for ν7. Note that the 2ν3 overtone transition has a frequency close to the 1D ν1 frequency and a very low intensity. In our case the most accurate description of vibrational parameters of trans-HONO in the complex can be obtained by solving the 4D Schrödinger equation in the space of the coordinates ξ1, ξ3, ξ6, and ξ7. The 4D PES was calculated in the

70

Φj(ξ1 , ξ6 , ξ3 , ξ7) =

∑

Cjkn φk (ξ1 , ξ6) ψn(ξ3 , ξ7)

k ,n=1

We used the 70 lowest energy solutions for each 2D vibrational subsystem. In this case, the number of basis functions for 4D wave functions is 4900. The frequencies and absolute intensities for the transitions most interesting to us of the NH3···trans-HONO complex derived from the variational solution of the 4D Schrödinger equation are presented in Table 4. Of these results the Table 4. Frequencies (cm−1) and Absolute Intensities (km mol−1) for Transitions from the Ground State to Excited Vibrational States of the 4D System (ν1, ν3, ν6, ν7) and the Values of r(OH) and R(N···O) (Å) Averaged over the Excited States excited state

frequency

intensity

r(OH)

R(N···O)

(0,0,0,1) (0,0,1,0) (0,1,0,0) (0,0,2,0) (0,2,0,0) (1,0,0,0)

226 1001 1448 1926 2806 2923

34 98 287 86 954 314

1.0225 1.0200 1.0243 1.0188 1.0478 1.0568

2.8153 2.8181 2.7945 2.8488 2.7812 2.7574

calculated values of frequency and intensity for the ν3 transition are in very good agreement with the experimental findings.28 In view of the theoretical value of 1001 cm−1 predicted for the ν6 band, it is natural to assume that in identifying the experimental data28 it would be better to assign this band not to a diffuse absorption at about 1230 cm−1, but to one of the bands observed near 1000 cm−1. The 4D calculation confirmed the mixing of wave functions of the singly excited state of the ν1 mode and the doubly excited state of the ν3 mode, which was predicted above by the 2D calculation. The mixing of wave functions of different states can be interpreted in terms of a resonance between the states of subsystems obtained in a lower approximation. In this case the decisive parameter that determines the resonance strength is the matrix element of potential energy between the wave functions of resonating states. If the wave functions of resonating (unperturbed) states of the 4D system are represented, for example, by products of wave functions of the ground and excited states of subsystems (ν1, ν6) and (ν3, ν7), the resonance matrix element has a significant value of 66 cm−1. Other possible representations of 9096

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Figure 3. Dependence of the wave functions of the first (a) and second (b) components of the resonance doublet at 2806 and 2923 cm−1, respectively, on the dimensionless coordinates ξ1 and ξ3.

1−4 dimensions using accurate ab initio PESs. Comparison of 1D results with the values obtained by considering 2D and 3D vibrational systems showed the sensitivity of parameters of a particular mode to intermode anharmonic interactions. The parameters associated with the ν1, ν3, ν6, and ν7 vibrations were obtained by solving the corresponding 4D equation. The calculated results are compared with the experimental values for NH3···trans-HONO in an argon matrix28 and the values calculated earlier13 for free trans-HONO. The theoretical anharmonic values of fundamental transition frequencies obtained for the ν2, ν3, ν4, and ν5 vibrations are in good agreement with the experimental data.28 The calculation suggests that the ν6 torsional band tentatively assigned in the experiment28 to a diffuse band at 1230 cm−1 should be assigned to one of the absorption bands observed near 1000 cm−1. The calculation confirms the appearance of a doublet in the region of the ν1 fundamental as a result of a strong ν1/2ν3 resonance. A certain discrepancy between the theoretical and experimental positions of doublet components can be attributed to the influence of the Ar matrix on the resonating states. Of interest are the ground-state averaged values of r(OH) and R(N···O) evaluated for different 1D and 2D subsystems and these distances averaged over the ground state and several excited states of the 4D system (ν1, ν3, ν6, ν7).

wave functions of unperturbed states yield virtually the same value of the matrix element. Two transitions from the ground state to the states resulting from the resonance lie at 2806 and 2923 cm−1. The high-frequency component of the resonance has a somewhat larger weight of the ν1 wave function, while the low-frequency component can be assigned to the 2ν3 state. Thus, the calculation correctly predicts the appearance of the doublet experimentally observed28 near 2750 cm−1. Distinctions between the theoretical position and intensity of components and the corresponding experimental values may be explained not only by some inaccuracies of the calculation, but also by a significant influence of the matrix surroundings on the frequency and intensity of vibrational bands of the impurity. It can be noted here, for example, that the argon matrix strongly affects the HCl stretching vibration and its resonance with the overtone of the NH3 symmetric bending mode in the NH3··· HCl complex,30 as compared to very weak perturbation by the Ne matrix. The nature of the states resulting from the (ν1/2ν3) resonance is clearly seen in Figures 3a and 3b, where 2D cuts of the 4D wave functions of these states are shown in the (ξ1, ξ3) plane. One can see that these plots are very similar and almost coincide to within reflection at zero value of ξ1, that is, the equilibrium value of r(OH). Note that positive values of ξ1 correspond to shortening of r(OH). From the viewpoint of dynamical changes in the structural parameters of the NH3···trans-HONO complex associated with its vibrations, of interest are the values of r(OH) and R(N···O) averaged over the ground state and some excited states of the complex (Table 4). The last two upper states in Table 4 result from the ν1(OH)/2ν3(HON) resonance. One can see in Table 4 that the changes in vibrationally averaged values of r(OH) and R(N···O) on excitation of the modes relative to the 4D ground-state averaged values 1.0238 and 2.7840 Å are consistent with the nature of each vibration considered.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by the Russian Foundation for Basic Research, Grant no. 12-03-00215.

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CONCLUSIONS The equilibrium geometry and the harmonic vibrational frequencies and intensities of the strong hydrogen-bonded NH3···trans-HONO complex were calculated in the MP2/augcc-pVTZ approximation with the BSSE correction taken into account. Anharmonic values of frequencies and absolute intensities were obtained for six vibrations of trans-HONO in the complex and the H-bond stretching vibration. The anharmonic electro-optical parameters were derived from variational solutions of vibrational Schrödinger equations in

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REFERENCES

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dx.doi.org/10.1021/jp406569y | J. Phys. Chem. A 2013, 117, 9093−9098