Theoretical study of the structures, stability and vibrational spectra of the nitrous acid complexes with CH4

Spectrochimica Acta Part A 60 (2004) 2163–2170

Theoretical study of the structures, stability and vibrational spectra of the nitrous acid complexes with CH4 Yordanka Dimitrova∗ Institute of Organic Chemistry, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., 1113 Sofia, Bulgaria Received 18 August 2003; accepted 10 October 2003

Abstract The structures, stability and vibrational spectra of the binary complexes CH4 · · · HONO-trans and CH4 · · · HONO-cis have been investigated using ab initio calculations at the SCF and MP2 levels with 6-311++G(d,p) basis set and B3LYP calculations with 6-31G(d,p) and 6-31+G(d,p) basis sets. Full geometry optimization was made for the complexes studied. It was established that the complex CH4 · · · HONO-trans is more stable by 0.41 kcal mol−1 than the complex CH4 · · · HONO-cis. The accuracy of the ab initio calculations have been estimated by comparison between the predicted values of the vibrational characteristics (vibrational frequencies and infrared intensities) and the available experimental data. It was established, that the methods, used in this study are well adapted to the problem under examination. The predicted values with the B3LYP calculations are very near to the results, obtained with 6-311++G(d,p)/MP2. The changes in the vibrational characteristics of methane and trans-, cis-nitrous acid upon formation of the hydrogen bond show that the complexes CH4 · · · HONO-trans and CH4 · · · HONO-cis have geometry in which the OH group interacts with a methane molecule forming a single hydrogen bond. This fact is confirmed by relatively strong perturbation of the OH stretching vibration to lower frequencies and an increase of the infrared intensity of this vibration up to three times upon hydrogen bonding. © 2003 Elsevier B.V. All rights reserved. Keywords: Ab initio and DFT calculations; Structure; Vibrational spectra; Methane–nitrous acid complexes

1. Introduction Nitrous acid plays an important role in atmospheric chemistry and is one of the smallest molecules which exhibits a cis–trans conformational equilibrium. The clarification of the structure and stability of the hydrogen-bonded complexes of nitrous acid with various atmospheric bases is very important for atmospheric chemistry. Bearing in mind that the direct measurements of the rates and mechanisms of heterogeneous reactions on surfaces or in liquid droplets are hard to carry out under the conditions of the Antarctic stratosphere, the computer simulations of such reactions are very useful for the clarification of the structure and stability of the hydrogen-bonded complexes important for atmospheric chemistry [1–10]. The complexes CH4 · · · HX (X = Cl, F, CN) are a new and interesting class of hydrogen-bonded systems. The experimental and theoretical studies of the CH4 · · · HX ∗

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complexes [11–15] indicate that methane acts as a proton acceptor in these systems which is a quite interesting result for understanding the nature of the hydrogen bonding. In the previous study [16], the results of infrared matrix isolation studies of the CH4 · · · HONO2 system have been reported. The analysis of the spectral characteristics show that a weak complex of well-defined structure is formed between methane and nitric acid molecules. In our previous studies, the structure [17], stability [18] and vibrational spectrum [19] have been studied by ab initio calculations at the SCF and MP2 levels with different basis sets and DFT calculations. It was established that in the complex CH4 · · · HONO2 nitric acid acts as a proton donor forming a weak hydrogen bond with methane molecule. This fact is confirmed by relatively strong perturbation of the OH stretching vibration to lower frequencies, whereas the NOH in plane bending vibration and HONO torsion vibration are shifted to higher frequencies. The review [20] summarized the theoretical studies of structures, stability and vibrational spectra of various hydrogen-bonded complexes of nitric acid. It was

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Y. Dimitrova / Spectrochimica Acta Part A 60 (2004) 2163–2170

established that the studied hydrogen-bonded nitric acid complexes can order (in decreasing order of stability) as follows:

6

H 8

H

5

H3 N · · · HONO2 > (HONO2 )2 > NO2 · · · HONO2

2.1. Structures and stability The first step in the study was to establish the most stable structures of the complexes between CH4 and HONO (trans and cis) by ab initio calculations at SCF and MP2 levels with 6-311++G/d,p) basis set and B3LYP calculations with 6-31G(d,p) and 6-31+G(d,p) basis sets using the GAUSSIAN 98 series of programs [27]. Full geometry optimization has been performed for the complexes studied. Our aim was to select the most stable structures for the complexes CH4 · · · HONO-trans (1A) and CH4 · · · HONO-cis (1B). In Fig. 1 and Table 1 are shown the structures, optimum values of the total energy and optimized structural parameters for the hydrogen-bonded complexes 1A and 1B. As can be seen from the results of the Etot in Table 1, the complex CH4 · · · HONO-trans (1A) is more stable than the CH4 · · · HONO-cis (1B). The calculated structural parameters for the monomers (HONO-trans, HONO-cis and CH4 ) are compare with the corresponding parameters for the complexes 1A and 1B. The changes in the structural parameters from monomers to complexes are defined. It is seen that the bond lengths and angles for the binary complexes 1A and 1B are slightly perturbed from their values in the monomers. The more sensitive to the complexation are the structural parameters of HONO-trans. The N2 O3 bond is shorter upon

4 3

O H7

> CH4 · · · HONO2 .

2. Results and discussion

9

H

2.581

> OC · · · HONO2 > CO · · · HONO2 > N2 · · · HONO2 Weakly bound molecular dimers have been extensively investigated in the gas phase by radiofrequency, microwave, and high-resolution infrared spectroscopy [21]. The matrix infrared spectra provide very common information about the hydrogen bonding and structure of such systems [22]. The infrared matrix isolation studies on the complexes of nitrous acid with important atmospheric species: N2 , CO [23], NH3 [24] and CH4 , C2 H2 [25] have been reported. The interaction between nitrous acid and atmospheric species is of potential interest in connection with atmospheric modeling. Nitrous acid is unstable in the gas phase and occurs in complex equilibrium with the product of its decomposition [26]. The object of the present study are the binary complexes CH4 · · · HONO-trans (1A) and CH4 · · · HONO-cis (1B). The ab initio calculations at SCF and MP2 levels with 6-311++G/d,p) basis set and B3LYP calculations with 6-31G(d,p) and 6-31+G(d,p) basis sets have been performed in order to established the most stable structures of the complexes and the changes in the vibrational characteristics from free monomers to complexes.

H

C

2

111.0

N

O1

(1A) H8 H

5

7

C 2.686 4

6

H H

9

1

H

O

113.6 3

O

2

N

(1B) Fig. 1. Optimized structures with the B3LYP/6-31+G(d,p) calculations and atomic numbering for the hydrogen-bonded complexes: CH4 · · · HONO-trans (1A) and CH4 · · · HONO-cis (1B).

formation of the hydrogen bond with 0.0051 Å, while the bond O3 H4 is lengthened in the complex with 0.0021 Å. The corresponding changes for the HONO-cis are smaller. In order to investigate the charge rearrangement of the monomers (HONO-trans, HONO-cis and CH4 ) upon hydrogen bonding, the atomic charges (qi ) for the monomers and for the complexes 1A and 1B have been calculated with the B3LYP/6-31+G(d,p) calculations, using the Mulliken population analyses. The changes in the atomic charges (qi ) from monomers to complexes have been estimated. The data are shown in Table 2. The results in Table 2 show that the negativity of the atoms O3 and C5 increases significantly in the complexes, while the negativity of the N2 increases at a lower rate. As can be seen as a result of the hydrogen bonding the atoms O3 , C5 and N2 act as an acceptor of electric charge and the hydrogen atoms (H4 , H6 , H7 , H8 and H9 ) release positive charges. The charge rearrangement upon hydrogen bonding for HONO-trans is more significant than for HONO-cis. The dissociation energy (uncorrected and BSSE-corrected) was calculated by ab initio and B3LYP calculations. In Table 3 are shown the dissociation energies at SCF and MP2 levels with 6-311++G(d,p) basis set and density functional B3LYP/6-31G(d,p) calculations. As can be seen from the results in Table 3, the BSSE correction at the MP2 level is larger in comparison with the corresponding values at the SCF level. As a result, the corrected values of the dissociation energy at the MP2 at SCF level at the same basis set are very near.

Y. Dimitrova / Spectrochimica Acta Part A 60 (2004) 2163–2170

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Table 1 Optimized geometries for free and complexed HONO and CH4 molecules, obtained from B3LYP/6-31+G(d,p) calculations Parameter

trans-HONO Monomera

cis-HONO Complexa

∆

Monomera

Complexa

∆

lengthb

Bond r(O1 N2 ) r(N2 O3 ) r(O3 H4 ) r(H4 · · · C5 ) r(C5 H6 ) r(C5 H7 ) r(C5 H8 ) r(C5 H9 )

1.1787 1.4266 0.9724 – 1.0928 1.0928 1.0928 1.0928

Anglec O3 N2 O 1 H4 O3 N2 H6 C5 · · · H4 H6 C5 H8 H7 C5 H8 H6 C5 H9 H7 C5 H9

110.89 103.08 – 109.47 109.47 109.47 109.47

b c d e f

111.02 103.13 84.05 108.71 108.74 110.21 110.22

−205.71501d –40.20916f

Etot (a.u.) a

1.1781 1.4215 0.9745 2.5805 1.0937 1.0936 1.0923 1.0937

−246.24218 –

−0.0006 –0.0051 0.0021 – 0.0009 0.0008 −0.0005 0.0009

1.1901 1.3869 0.9839

1.1905 1.3860 0.9846 2.6859 1.0934 1.0936 1.0925 1.0934

– 1.0928 1.0928 1.0928 1.0928

0.13 0.05

113.52 106.64 – 109.47 109.47 109.47 109.47

– −0.76 −0.73 0.74 0.75

−205.71428e −40.20916

– –

113.56 106.94 83.66 108.86 108.77 109.99 110.16 −246.24120 –

0.0004 −0.0009 0.0007 – 0.0006 0.0008 −0.0003 0.0006 0.04 0.30 – −0.61 −0.70 0.52 0.69 – –

See Fig. 1 for numbering of atoms. In angstrom. In degrees. Etot for trans-HONO. Etot for cis-HONO. Etot for CH4 .

Table 2 Mulliken charges (qi ) for free and complexed HONO (trans and cis) and CH4 obtained from B3LYP/6-31+G(d.p) calculations No.a

Atom

1 2 3 4 5 6 7 8 9

O N O H C H H H H a b

trans-HONO

cis-HONO

Monomer

Complex

qi

0.0020 −0.1375 −0.2163 0.3518 −0.6102 0.1526 0.1526 0.1526 0.1526

0.0068 −0.1411 −0.2287 0.3607 −0.6496 0.1594 0.1620 0.1711 0.1595

0.0048 −0.0025 −0.0124 0.0089 −0.0394 0.0068 0.0094 0.0185 0.0069

b

Monomer

Complex

qi

−0.0556 −0.1320 −0.1473 0.3349 −0.6102 0.1526 0.1526 0.1526 0.1526

−0.0588 −0.1321 −0.1498 0.3430 −0.6491 0.1590 0.1602 0.1684 0.1591

−0.0032 −0.0001 −0.0025 0.0081 −0.0389 0.0064 0.0076 0.0158 0.0065

See Fig. 1 for numbering of atoms. complex qi = qi − qimonomer .

Table 3 Dissociation energies E (uncorrected and corrected), basis set superposition error (BSSE) and MP2 correlation contribution to the dissociation energy δE(MP2) in kcal/mol for the hydrogen-bonded complexes between CH4 and HONO-trans and HONO-cis, shown in Fig. 1A and B Basis set

Complex

E (uncorr)

BSSE

E (corr)

δE(MP2)

R(C5 . . . H4 )

B3LYP/6-31G(d,p)

1A (trans) 1B (cis)

−1.0897 −1.0606

0.3670 0.7432

−0.7228 −0.3173

– –

2.4928 2.6042

SCF/6-311++G(d,p)

1A (trans) 1B (cis)

−0.4947 −0.3863

0.0118 0.0835

−0.4829 −0.3028

– –

2.8442 3.0564

MP2/6-311++G(d,p)

1A (trans) 1B (cis)

−1.2842 −1.2294

0.4559 0.8213

−0.8283 −0.4081

−0.7895 −0.8431

2.5095 2.6002

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Y. Dimitrova / Spectrochimica Acta Part A 60 (2004) 2163–2170

As can be seen in Table 3, the ab initio calculations at MP2 level and B3LYP calculations predict that the trans-CH4 · · · HONO complex (1A) is more stable by 0.41 kcal mol−1 than the cis-CH4 · · · HONO complex. The MP2 correlation contribution to the dissociation energy δE(MP2) for the trans complex (1A) is 52% from the uncorrected dissociation energy while for the cis complex (1B) is 69%. It can be noted in our previous studies [20], the MP2 correlation contribution to the dissociation energy δE(MP2) is very important in order to receive a real estimation of the stability of the complexes. 2.2. Vibrational spectra The prediction of the vibrational characteristics (vibrational frequencies and infrared intensities) of the

hydrogen-bonded systems by ab initio calculations at different levels [28–35] has become widely employed in order to elucidate the influence of the hydrogen bonding on the vibrational spectra of the monomers forming a complex. In the hydrogen-bonded system, the geometrical symmetry of the monomers often changes under perturbation [36]. The vibrational mixing, derived by a perturbation approach, is the counterpart of the orbital mixing. The vibrational frequencies and infrared intensities for free monomers (HONO-trans, HONO-cis and CH4 ) and for the binary complexes 1A and 1B (see Fig. 1) have been predicted by ab initio calculations at the SCF and MP2 levels with the 6-311++G(d,p) basis set and B3LYP calculations (see Tables 4–6). The first step in the study is to predict the vibrational characteristics (vibrational frequencies and infrared intensities)

Table 4 Experimental and calculated vibrational characteristics (ν in cm−1 , A in km mol−1 ) for trans-HONO, cis-HONO and CH4 Mode

Approximate description (PED)a

trans-HONO ν1 100ν(O–H) ν2

89ν(N=O)

ν3

85δ(NOH) + 11ν(N=O)

ν4

49δ(NOH) + 42ν(N–O)c

ν5 ν6

60ν(N–O) + 40δ(ONO)d 100τ(HONO)

cis-HONO ν1 100ν(O–H)

Experimentalb

SCF/6-311++G(d,p)

MP2/6-311++G(d,p)

B3LYP/6-31+G(d,p)

B3LYP/6-31G(d,p)

ν

ν/scale fac.

A

ν/scale fac.

ν/scale fac.

ν/scale fac.

4134/0.8642 0.8632 2025/0.8341 0.8334 1492/0.8484 0.8471 1081/0.7404 0.7369

145.2

3811/0.9374 0.9364 1672/1.0102 1.0096 1294/0.9782 0.9767 826/0.9690 0.9644

794/0.7666 582/0.9440 0.9419

24.5 139.2

616/0.9882 565/0.9724 0.9703

176.7 116.4

628/0.9693 586/0.9375 0.9355

118.4 118.1

631/0.9647 595/0.9234 0.9214

83.0 105.8

3961/0.8615 0.8610 1969/0.8299 0.8292 1509 1144/0.7457 0.7432 782 706/0.9042

71.1

37.5

119.0 22.9

3575/0.9545 0.9540 1726/0.9467 0.9460 1349 922/0.9253 0.9221 736 648/0.9852

15.2

121.9 46.8

3575/0.9545 0.9540 1714/0.9533 0.9526 1332 897/0.9511 0.9478 698 639/0.9991

26.3

14.7 152.6

3552/0.9607 0.9602 1545/1.0576 1.0568 1306 898/0.95 0.9468 706 647/1.0231

41.3 41.6 41.9 0.4 0 0 12.0 12.2 11.8

3219/0.9807 3209/0.9838 3199/0.9869 3071/0.9854 1572/1.0070 1572/1.0070 1366/1.0007 1364/1.0022 1363/1.0029

20.5 20.7 20.8 0.1 0 0 14.5 14.6 14.3

3149/1.0025 3149/1.0025 3149/1.0025 3036/0.9967 1564/1.0122 1564/1.0122 1348/1.0141 1348/1.0141 1348/1.0141

25.5 25.5 25.5 0 0 0 19.3 19.3 19.3

3162/0.9984 3162/0.9984 3162/0.9984 3046/0.9934 1579/1.0025 1579/1.0025 1356/1.0081 1356/1.0081 1356/1.0081

A

3572.6 3568.5 1689.1 1688.0 1265.8 1263.9 800.4 796.6 608.7 549.4 548.2

ν2

77ν(N=O) + 17δ(NOH)

ν3 ν4

71δ(NOH) + 23ν(N=O) 41δ(ONO) + 47ν(N–O)e

ν5 ν6

100τ(HONO)f 53ν(N–O) + 36δ(ONO)g

3412.4 3410.7 1634.0 1632.8 – 853.1 850.2 – 638.4

CH4 ν7 ν8 ν9 ν10 ν11 ν12 ν13 ν14 ν15

96ν(C–H) 86ν(C–H) 96ν(C–H) 100ν(C–H) 81δ(HCH) + 11τ(HCHH) 63δ(HCH) + 28τ(HCHH) 65δ(HCH) + 24τ(HCHH) 73τ(HCHH) + 27δ(HCH) 53τ(HCHH) + 25δ(HCH)

3157 3157 3157 3026 1583 1583 1367 1367 1367

a b c d e f g

s

s

s

s

67 67 67 0 0 0 33 33 33

3261/0.9681 3251/0.9711 3241/0.9741 3148/0.9613 1667/0.9496 1667/0.9496 1455/0.9395 1453/0.9408 1452/0.9415

188.3 260.9 255.0

264.3 9.4 379.9

A 94.0 107.8 189.6 177.7

126.4 7.1 376.3

3749/0.9530 0.9519 1783/0.9473 0.9467 1297/0.9760 0.9738 831/0.9632 0.9586

PEDs elements lower than 10% are not included. PEDs elements obtained with MP2/6–311++G(d,p) are given. Ref. [24] for trans-HONO and cis-HONO; [38,39] forCH4 . PEDs for trans-HONO. 86ν(N–O). 80δ(ONO). PEDs with SCF/6-311++G(d,p) for cis-HONO. 82ν(N–O). 73δ(ONO) + 20ν(N=O). 100τ(HONO).

A 80.9 178.7 188.4 159.0

216.0 6.5 325.6

3756/0.9512 0.9501 1792/0.9426 0.9420 1308/0.9677 0.9663 862/0.9285 0.9241

A 57.3 135.4 187.5 144.2

171.5 5.8 264.8 108.9 14.9 25.3 25.3 25.3 0 0 0 14.1 14.1 14.1

Table 5 Experimental and calculated vibrational characteristics (ν in cm−1 , A in km mol−1 ) for the hydrogen-bonded complex CH4 · · · HONO-trans Mode

a b c d e f g h i j k l

Experimentalb

SCF/6-311++G(d,p)

MP2/6-311++G(d,p)

B3LYP/6-31+G(d,p)

B3LYP/6-31G(d,p)

ν/ν

ν/c νscal

A/d A

ν/c νscal

A/d A

ν/c νscal

A/d A

ν/c νscal

A/d A

100ν(O–H) 82ν(C–H) 99ν(C–H) 100ν(C–H) 100ν(C–H) 88ν(N=O) 56δ(HCH) + 35τ(HCHH) 55τ(HCHH) + 38δ(HCH) 73τ(HC · · · HO) + 16 δ(HC · · · H)e 69τ(HC · · · HO) + 20δ(HC · · · H)f 98δ(HC · · · H) 82δ(NOH)g 46δ(ONO) + 45ν(N–O)h 56ν(N–O) + 44 δ(ONO)i 100τ(HONO) 62τ(HC · · · HO) 62τ(HC · · · HO) + 38δ(HC · · · H) 98ν(C · · · H)j 60τ(C · · · HON) + 15δ(HC · · · H)k 78δ(C · · · HO) 87δ(HC · · · H)l

3547.2/−25.4

4163/−12.1 3274/12.6 3252/0.97 3237/−3.9 3147/−0.96 2022/−2.5 1672/4.75 1671/3.8 1492/0.0 1460/6.6 1458/2.8 1455/0.0 1085/2.96 802/6.1 584/1.9 107 92 74 50 21 18

215.7/70.5 33.8/−7.5 33.8/−7.8 35.5/−6.4 4.3/3.9 206.6/18.3 0.3/0.3 0.2/0.2 236.2/−24.7 14.2/2.0 16.9/4.9 24.4/12.4 262.4/7.4 19.0/−5.5 118.1/−21.1 0.0 0.0 0.1 1.5 1.5 16.2

3827/−15.0 3224/4.9 3206/−2.9 3192/−6.9 3068/−3.0 1664/−8.1 1579/7.1 1572/0.0 1367/3.0 1366/2.0 1363/3.0 1294/0.0 836/9.6 636/19.8 585/19.5 103 90 83 49 40 28

210.1/116.1 16.6/−3.9 13.0/−7.7 13.6/−7.2 3.0/2.9 115.2/7.4 0.5/0.5 0.4/0.4 15.0/0.4 14.1/0.5 20.1/8.1 189.4/0.2 208.9/31.2 155.6/−22.1 91.3/−25.1 0.0 7.1 1.2 5.8 1.3 0.1

3730/−18.1 3151/2.0 3142/−7.0 3141/−8.0 3030/−6.0 1778/−4.7 1569/5.1 1569/5.1 1354/6.1 1354/6.0 1345/−3.0 1306/8.3 838/6.7 637/8.7 607/19.7 86 78 71 50 29 34

196.4/115.5 20.1/−4.2 17.7/−5.7 18.7/−7 2.9/2 191.6/22.8 0.4/0.3 0.4/1.6 20.6/3.6 15.8/−3.5 23.7/−8.5 192.4/4.0 182.8/23.8 108.0/−10.4 92.2/−94.6 0.0 0.4 1.1 0.6 1.8 12.0

3744/−11.4 3164/2.0 3155/−7.0 3188/26.0 3038/−7.9 1787/−4.7 1582/3.0 1580/1.0 1363/7.1 1359/3.0 1352/−4.0 1319/10.6 871/8.3 642/10.6 604/8.3 116 98 91 56 27 24

160.5/103.2 16.8/−8.5 16.2/−9.1 19.8/−5.5 3.0/3 148.9/13.5 0.3/0.3 0.3/0.3 15.3/1.2 11.4/−2.5 35.1/21.0 188.9/1.4 163.2/19.0 69.8/−13.2 81.7/−24.1 0.3 0.2 1.8 0.9 2.1 10.2

PEDs elements lower than 10% are not included. PEDs elements obtained with MP2/6-311++G(d,p) are given. Ref. [25]. complex νscal = ki (νi − νimonomer ), where ki is a scale factor. complex Ai = Ai − Amonomer . i Different PEDs obtained with the SCF/6-311++G(d,p) is: 85δ(NOH). Different PEDs obtained with the SCF/6-311++G(d,p) is: 92τ(HC · · · HO). Different PEDs obtained with the SCF/6-311++G(d,p) is: 96δ(HC · · · H). Different PEDs obtained with the SCF/6-311++G(d,p) is: 86ν(N–O) + 11δ(ONO). Different PEDs obtained with the SCF/6-311++G(d,p) is: 80δ(ONO) + 15ν(N–O). Different PEDs obtained with the SCF/6-311++G(d,p) is: 91δ(HC · · · H). Different PEDs obtained with the SCF/6-311++G(d,p) is: 96ν(C · · · H). Different PEDs obtained with the SCF/6-311++G(d,p) is: 50τ(C · · · HON) + 22τ(HC · · · HO).

Y. Dimitrova / Spectrochimica Acta Part A 60 (2004) 2163–2170

ν1 ν2 ν3 ν4 ν5 ν6 ν7 ν8 ν9 ν10 ν11 ν12 ν13 ν14 ν15 ν16 ν17 ν18 ν19 ν20 ν21

Approximate description (PED)a

2167

2168

Table 6 Experimental and calculated vibrational characteristics (ν in cm−1 , A in km mol−1 ) for the hydrogen-bonded complex CH4 · · · HONO-cis Mode

a b c d e f g h i j k l

100ν(O–H) 80ν(C–H) 96ν(C–H) 100ν(C–H) 100ν(C–H) 85ν(N=O) 52δ(HCH) + 40τ(HCHH) 51τ(HCHH) + 42δ(HCH) 48τ(HC · · · HO) + 40δ(HC · · · H)e 82τ(HC · · · HO) 78δ(HC · · · H) 70δ(NOH)f 56ν(N–O) + 34δ(ONO) 100τ(HONO)g 52δ(ONO) + 46ν(N–O)h 80δ(HC · · · H) 93τ(HC · · · HO) 60τ(C · · · HON)i 92ν(C · · · H)j 68δ(C · · · HO)k 65τ(HC · · · HO)l

Experimentalb

SCF/6-311++G(d,p)

MP2/6-311++G(d,p)

B3LYP/6-31+G(d,p)

B3LYP/6-31G(d,p)

ν/c ν

ν/c νscal

A/d A

ν/c νscal

A/d A

ν/c νscal

A/d A

ν/c νscal

A/d A

3397.5/−14.9

4014/45.6 3270/8.7 3249/−2.0 3235/−5.8 3145/−4.9 1966/−2.5 1671/3.8 1670/12.8 1514/5.0 1457/3.8 1456/3.8 1456/3.8 1146/1.5 791/9.0 704/1.8 132 107 88 51 27 20

106.5/35.4 35.8/−5.5 36.6/−5.0 34.5/−7.4 2.9/2.5 249.9/−14.4 0.1/0.1 0.6/0.6 10.7/1.3 13.6/1.4 17.1/5.3 14.4/2.6 379.9/0.0 15.7/1.0 135.0/−17.6 0.0 0.0 0.1 1.3 0.0 12.4

3518/−32.7 3210/8.8 3195/−13.8 3190/−8.9 3059/−10.8 1549/−2.0 1578/6.0 1570/2.0 1367/1.0 1364/0.0 1363/0.0 1331/25.0 920/20.9 643/23.0 653/6.0 124 118 98 70 47 15

98.0/60.5 13.6/−6.9 14.0/−6.7 19.2/−1.6 1.4/1.3 135.9/9.5 2.8/2.8 2.9/2.9 19.2/4.7 15.5/0.9 14.9/0.6 21.2/14.1 401.6/25.3 96.6/−25.3 33.0/−13.8 0.2 2.5 1.2 0.4 0.8 8.8

3563/−11.5 3150/1.0 3144/−5.0 3143/−6.0 3032/−4.0 1712/−1.8 1568/4.0 1568/4.0 1354/6.0 1353/5.0 1348/0.0 1334/2.0 900/2.8 711/13.0 641/2.0 80 76 62 56 46 32

80.2/53.9 21.3/−4.2 19.8/−5.7 18.60/−7.0 2.0/2.0 201.5/−14.5 0.3/0.3 1.6/1.6 22.9/3.6 20.5/1.2 20.8/1.5 33.2/25.7 320.2/−5.4 96.9/−22.1 23.5/0.6 0.1 2.0 0.8 1.7 0.9 9.7

3573/−9.5 3162/0 3156/−6.0 3152/−10.0 3039/−5.0 1720/−5.7 1581/2.0 1581/2.0 1362/6.0 1361/5.0 1356/0.0 1351/2.0 928/5.5 744/12.0 653/4.9 132 99 70 51 42 30

70.9/55.7 18.6/−6.7 14.6/−10.7 21.2/−4.1 1.3/1.3 151.1/−20.4 2.3/2.3 0.2/0.2 15.0/0.9 13.5/0.6 17.6/3.5 22.9/17.1 249.5/−15.3 90.3/−18.6 13.8/−1.1 0.1 0.1 0.2 2.6 2.8 8.9

PEDs elements lower than 10% are not included. PEDs elements obtained with MP2/6-311++G(d,p) are given. Ref. [25]. complex νscal = ki (νi − νimonomer ), where ki is a scale factor. complex Ai = Ai − AMonomer . i Different PEDs obtained with the SCF/6-311++G(d,p) is: 80δ(NOH). Different PEDs obtained with the SCF/6-311++G(d,p) is: 56τ(HC · · · HO) + 38δ(HC · · · H). Different PEDs obtained with the SCF/6-311++G(d,p) is: 73δ(ONO) + 18ν(N–O). Different PEDs obtained with the SCF/6-311++G(d,p) is: 99τ(HONO). Different PEDs obtained with the SCF/6-311++G(d,p) is: 52δ(HC · · · H) + 45τ(HC · · · HO). Different PEDs obtained with the SCF/6-311++G(d,p) is: 37ν(C · · · H) + 18δ(C · · · HO). Different PEDs obtained with the SCF/6-311++G(d,p) is: 63ν(C · · · H). Different PEDs obtained with the SCF/6-311++G(d,p) is: 65τ(C · · · HON) +30τ(HC · · · HO).

Y. Dimitrova / Spectrochimica Acta Part A 60 (2004) 2163–2170

ν1 ν2 ν3 ν4 ν5 ν6 ν7 ν8 ν9 ν10 ν11 ν12 ν13 ν14 ν15 ν16 ν17 ν18 ν19 ν20 ν21

Approximate description (PED)a

Y. Dimitrova / Spectrochimica Acta Part A 60 (2004) 2163–2170

for free monomers (HONO-trans, HONO-cis and CH4 ). The predicted values of the vibrational frequencies and infrared intensities are compared with the available experimental data (see Table 4). The aim is to established the accuracy of the calculations used in the study and to define the ‘optimal’ exp scale factors for each vibration from the ratio νi /νicalc . The concept of the ‘optimal’ scale factor has been proposed by Destexhe et al. [37] in order to obtained an estimation of the anharmonicity of the modes in H-bonded H2 O with pyridine. This procedure could only be applied for modes which are experimentally accessible in the spectral region. In the present study the ‘optimal’ scale factors for the stretching and bending vibrations of the monomers are shown in Table 4. The calculated vibrational frequencies and infrared intensities for the monomers (HONO-trans, HONO-cis and CH4 ) are presented in Table 4 together with the available experimental data. In Table 4 is included a detailed description of the normal modes of the monomers based on the potential energy distribution (PED) obtained from MP2/6-311++G(d,p) calculations. As can be seen from the results in Table 4, the calculated vibrational frequencies at the MP2 level are in better agreement with the experimental data, than the frequencies calculated at the SCF level. The predicted values with B3LYP calculations are very near to the results, obtained with MP2/6-311++G(d,p). It was important to investigate the accuracy of the ab initio calculations at the SCF and MP2 levels and B3LYP calculations for the prediction of the infrared intensities. The comparison between the predicted values of the infrared intensities for the vibrations of the monomers with the available experimental data show that the calculations used in this study give a satisfactory description for the infrared intensities of the stretching and deformation vibrations. The second step in the study was to predict the vibrational frequencies and infrared intensities for the hydrogen-bonded complexes CH4 · · · HONO-trans (1A) and CH4 · · · HONO-cis (1B) and to estimate the changes in the vibrational characteristics arising from the hydrogen bonding. The predicted vibrational characteristics and PED’s elements for the complexes 1A and 1B are shown in Tables 5 and 6. The potential energy distribution (PED), obtained from MP2/6-311++G(d,p) calculations is used for a description of the normal modes. The predicted vibrational characteristics and PED’s elements for the complexes studied are shown in Tables 5 and 6. Different PED’s elements obtained with the SCF method are indicated in the end of the second column of Tables 5 and 6. As can be seen from the results for approximate description (PED) presented in Table 4, most of the intramolecular vibrations of the dimers can be correlated with normal modes of the monomers, described in Table 4. The hydrogen bonding leads to the changes in the percentage contributions (PED’s elements) of localized modes to each normal mode in the monomers. In addition, there are six more intermolecular

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vibrations (see Tables 5 and 6, modes ν16 –ν21 ), which arise from the complexation between nitrous acid and CH4 : the stretching C · · · H vibration, the torsional vibrations and in plane bending vibrations. The predicted values of the stretching C · · · H vibration for the complex CH4 · · · HONO-trans (see Table 5) are in the range: 74–91 cm−1 , with weak infrared intensity. The deformation intermolecular vibrations (ν16 , ν17 , ν19 , ν20 , and ν21 ) are predicted in the range: 18–116 cm−1 . For the complex CH4 · · · HONO-cis, the predicted values of the stretching C · · · H vibration (see Table 6) are in the range: 51–70 cm−1 . The torsional (ν17 , ν18 and ν21 ) and in plane bending vibrations (ν16 and ν21 ) are predicted in the range: 15–132 cm−1 . The next aim in the study is to estimate the changes in the vibrational characteristics (vibrational frequencies and infrared intensities) from free monomers to complexes arising from the hydrogen bonding. The shifts in the vibrational characteristics (νscal ) of HONO (trans, cis) and CH4 upon formation of the hydrogen-bonded complexes have been calculated by ab initio calculations at the SCF and MP2 levels with 6-311++G(d,p) basis set and B3LYP calculations. The corresponding scale factor is used for each vibration. The predicted frequency shift is: complex

νiscal = ki (νi

− νimonomer ),

where ki is the corresponding ‘optimal’ scale factor. The predicted changes in the vibrational frequencies and infrared intensities are shown in Tables 5 and 6 together with the experimentally observed [25] shift for the stretching ν(O–H) vibration. In our previous studies [20,34], it was established that the hydrogen bonding leads to the substantial changes in the vibrational characteristics for the vibrations of the monomer bonds participating in the hydrogen bonding. For the complexes CH4 · · · HONO-trans (1A) and CH4 · · · HONO-cis (1B), these vibrations are the stretching O–H vibration (ν1 ) and the deformation τ(HONO) vibration. As can be seen from the results in Tables 5 and 6, the most sensitive to the complexation is the stretching O–H vibration (ν1 ). In agreement with the experiment [25] its vibrational frequency in the complexes is shifted to lower wavenumbers. The calculated frequency shift ν(O–H) for the complex CH4 · · · HONO-trans (1A) is larger than for the complex CH4 · · · HONO-cis (1B). In the same time, the intensity of this vibration increases upon hydrogen bonding. The calculated increase for the complex 1A is to two times and for the complex 1B is to three times. The ab initio and B3LYP calculations show that the torsional HONO vibration in the complexes is shifted to higher frequencies. The predicted infrared intensity for the torsional HONO vibration in the complexes decreases significantly. The ab initio and B3LYP calculations show that the changes in the vibrational characteristics (vibrational frequencies and infrared intensities) of CH4 upon the

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complexation are more insignificant than the changes in the vibrational characteristics of HONO-trans and HONO-cis. The stretching C–H vibrations are shifted to lower frequencies in the complexes, in the same time their infrared intensities decreases upon hydrogen bonding. As can be seen from the data in Tables 5 and 6, the remaining vibrations (stretching, bending and torsion) are less sensitive to the hydrogen bonding. The predicted changes in their vibrational characteristics are smaller. 3. Conclusions The structure, stability and vibrational spectra of the nitrous acid complexes with methane have been studied by ab initio and DFT calculations. The main results of the study are: 1. The bond lengths and angles for the binary complexes CH4 · · · HONO-trans (1A) and CH4 · · · HONO-cis (1B) are slightly perturbed from their values in the monomers. The more sensitive to the complexation are the structural parameters of HONO-trans than the structural parameters of HONO-cis. 2. The charge rearrangement upon hydrogen bonding for HONO-trans is more significant than for HONO-cis. 3. The ab initio calculations at MP2 level and B3LYP calculations predict that the trans- CH4 · · · HONO complex (1A) is more stable by 0.41 kcal mol−1 than the cis-CH4 · · · HONO complex. The MP2 correlation contribution to the dissociation energy δE(MP2) for the trans complex (1A) is 52% from the uncorrected dissociation energy while for the cis complex (1B) is 69%. 4. The calculated vibrational frequencies at the MP2 level are in better agreement with the experimental data, than the frequencies calculated at the SCF level. The predicted values with B3LYP calculations are very near to the results, obtained with MP2/6-311++G(d,p). 5. The comparison between the predicted values of the infrared intensities for the vibrations of the monomers with the available experimental data show that the calculations used in this study give a satisfactory description of the infrared intensities for the stretching and deformation vibrations. 6. In agreement with the experiment, the calculated frequency shift ν(O–H) for the complex CH4 · · · HONOtrans (1A) is larger than for the complex CH4 · · · HONOcis (1B). In the same time, the intensity of this vibration increases upon hydrogen bonding. The calculated increase for the complex 1A is to two times and for the complex 1B is to three times. 7. The ab initio and B3LYP calculations show that the changes in the vibrational characteristics (vibrational frequencies and infrared intensities) of CH4 upon hydrogen bonding are more insignificant than the changes in the vibrational characteristics of HONO-trans and HONO-cis. The stretching C–H vibrations are shifted to

lower frequencies in the complexes, in the same time their infrared intensities decrease upon hydrogen bonding. References [1] Z. Mielke, Z. Latajka, J. Kolodziej, K.G. Toknadze, J. Phys. Chem. 100 (1996) 11610. [2] B.J. Gertner, J.T. Hynes, Science 271 (1996) 1563. [3] J. Sadlej, V. Buch, J. Chem. Phys. 100 (1994) 4272. [4] J. Sadlej, B. Rowland, J.P. Devlin, V. Buch, J. Chem. Phys. 102 (1995) 4804. [5] J. Lundell, Z. Latajka, J. Phys. Chem. A 101 (1997) 5004. [6] J.P.D. Abbath, G.C.H. Washewsky, J. Phys. Chem. A 102 (1998) 3719. [7] A.J. Barnes, E. Lasson, C.J. Nielsen, J. Chem. Soc., Faraday Trans. 91 (1995) 3111. [8] M.-T. Nguyen, A.J. Jamka, R.A. Cazar, F.-M. Tao, J. Chem. Phys. 106 (1997) 8710. [9] F.-M. Tao, J. Chem. Phys. 108 (1998) 193. [10] R.N. Musin, M.C. Lin, J. Phys. Chem. A 102 (1998) 1808. [11] A.J. Barnes, J. Mol. Struct. 100 (1983) 259. [12] S.R. Davis, L. Andrews, J. Phys. Chem. 86 (1987) 3765. [13] A.C. Legon, B.P. Roberts, A.L. Wallwork, Chem. Phys. Lett. 173 (1990) 107. [14] Y. Ohshima, Y. Endo, J. Chem. Phys. 93 (1990) 6256. [15] J. Graw, R.G.A. Bone, G.B. Bacskay, J. Chem. Soc., Faraday Trans. 89 (1993) 2363. [16] Z. Mielke, K.G. Tokhadze, M. Hulkiewicz, L. Schriver-Mazzuoli, A. Schriver, F. Roux, J. Chem. Phys. 99 (1995) 10498. [17] Y. Dimitrova, S.D. Peyerimhoff, Chem. Phys. 254 (2000) 125. [18] Y. Dimitrova, J. Mol. Struct. (Theochem.) 532 (2000) 41. [19] Y. Dimitrova, Bulg. Chem. Commun. 33 (2001) 206. [20] Y. Dimitrova, Recent Res. Dev. Phys. Chem. 6 (2002) 127. [21] J.V. Bevan, in: A. Weber (Ed.), Structure and Dynamics of Weakly Bound Molecular Complexes, Reidel, Dordrecht, 1987, p. 149. [22] L. Andrews, in: L. Andrews, M. Moskovits (Eds.), Chemical and Physics of Matrix Isolated Species, North Holland, Amsterdam, 1989, p.15. [23] Z. Mielke, Z. Latajka, J. Kolodziej, K.G. Tokhadze, J. Phys. Chem. 100 (1996) 11610. [24] Z. Mielke, K.G. Tokhadze, Z. Latajka, E. Ratajczak, J. Phys. Chem. 100 (1996) 539. [25] M. Krajewska, Z. Mielke, K.G. Tokhadze, J. Mol. Struct. 404 (1997) 47. [26] B.J. Finlayson-Pitts, J.N. Pitts Jr., Atmospheric Chemistry Fundamentals and Experimental Technics, Wiley, New York, 1986. [27] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman et al., Gaussian 98, Revision A.7, Gaussian Inc., Pittsburgh, PA, 1998. [28] T. Bürgi, M. Schütz, S. Leutwyler, J. Chem. Phys. 103 (1995) 6350. [29] M. Gerhards, K. Kleinermanns, J. Chem. Phys. 103 (1995) 7392. [30] C. Jacoby, W. Roth, M. Schmitt, C. Janzen, D. Spangenberg, K. Kleinermanns, J. Phys. Chem. A 102 (1998) 4471. [31] D. Hadzi, Theoretical Treatment of Hydrogen Bonding, Wiley, New York, 1997. [32] J.E. Del Bene, M.J.T. Jordan, Intern. Rev. Phys. Chem. 18 (1999) 119. [33] J. Smets, W. McCarthy, G. Maes, L. Adamowicz, J. Mol. Struct. 476 (1999) 27. [34] Y. Dimitrova, Recent Res. Dev. Phys. Chem. 3 (1999) 133. [35] Y. Dimitrova, Spectrochim. Acta Part A 57 (2001) 2457. [36] T. Hirano, T. Taketsugu, Y. Kurita, J. Phys. Chem. 98 (1994) 6936. [37] A. Destexhe, J. Smets, L. Adamowicz, G. Maes, J. Phys. Chem. 98 (1994) 1506. [38] D.L. Gray, A.G. Robiette, Mol. Phys. 37 (1971) 1901. [39] R.E. Hiller, J.W. Straley, J. Mol. Spectrosc. 5 (1960) 24.