Ab initio and DFT anharmonic spectroscopic investigation of 1,3-cyclopentadiene

Chemical Physics 327 (2006) 127–136 www.elsevier.com/locate/chemphys

Ab initio and DFT anharmonic spectroscopic investigation of 1,3-cyclopentadiene A. Alparone Dipartimento di Scienze Chimiche, Universita` di Catania, viale A. Doria 8, Catania 95125, Italy Received 4 January 2006; accepted 3 April 2006 Available online 21 April 2006

Abstract Anharmonic infrared spectra of 1,3-cyclopentadiene and its hexadeuterated isotopomer, 1,3-cyclopentadiene-d6, have been calculated by means of second-order perturbation theory using Møller–Plesset second-order perturbation and density functional theory (B3LYP and B97-1) methods with correlation consistent Dunning’s basis sets (cc-pVDZ and cc-pVTZ). Computed anharmonic frequencies of fundamental, overtone and combination transitions are in satisfactory agreement with available experimental data. With exception of low-frequency ring torsion vibrations, introduction of the anharmonic corrections reduces the harmonic wavenumbers. The largest anharmonic effects are found for CAH and CH2 stretches, which decrease the harmonic frequencies by 100–130 cm1 (3–4%) and 140–160 cm1 (5–6%), respectively, reproducing the observed values within ca. 1%. For the antisymmetric CH2 stretching mode, the most significant anharmonic corrections are given by the diagonal and coupling with the symmetric CH2 vibration terms, together contributing to about 80% of the total anharmonic adjustment. Anharmonic calculations are important for a reliable prediction of the H/D isotopic frequency shift involving the CAH and CH2 stretching vibrations. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Anharmonic vibrational frequencies; Density functional theory; Isotopomers

1. Introduction 1,3-Cyclopentadiene, is a prototypical cyclic diene commonly employed in the Diels-Alder cycloaddition reactions [1]. Molecular geometry of 1,3-cyclopentadiene has been determined experimentally by microwave spectroscopy [2,3], as well as by electron [4] and X-ray [5] diffraction measurements. Optimized geometries have been calculated by correlated ab initio and density functional theory (DFT) [6–11] methods. Experimental IR and Raman spectra of 1,3-cyclopentadiene have been obtained in the vapour, liquid and solid phases [12–14], as well as in argon matrices [15–17]. Vibrational spectra of deuterated isotopomers, 1,3-cyclopentadiene-d1, 1,3-cyclopentadiene-d5,1,3-cyclopentadiene-d6 are known [13–15]. On the theoretical side, previous vibrational studies are restricted to the harmonic

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approximation by using ab initio [6,9,16,18,19] and DFT methods [7,8,17]. Harmonic approximation usually employed in calculations of infrared spectra generally overestimates observed frequencies, in particular those regarding anharmonic high-frequency stretching vibrations by several hundreds of wavenumber. An useful approach widely used to correct the deficiencies of the harmonic approximation is given by scaling procedures [20]. Nevertheless, in recent years many efforts have been pursued to develop codes for anharmonic vibrational computations. Anharmonic corrections are usually obtained through second-order perturbative [21,22] or variational [23] methodologies. Second-order perturbative approach is generally recognized to be less accurate than a converged variational treatment [24]. However, recent theoretical works have demonstrated that, vibrational second-order perturbative theory is adequate for determination of anharmonic IR spectra of semirigid cyclic molecules [22,24–30]. Burcl et al. [24], studied

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anharmonic effects on fundamental, overtone and combination transitions of furan, pyrrole and thiophene, by using DFT-B97-1 functional with a triple-f plus double polarization basis set (TZ2P), showing that second-order perturbation theory gives results of comparable quality to those obtained through a variational approach. Boese and Martin [30] computed anharmonic frequencies by means of second-order perturbation method for benzene and azabenzene series of compounds (pyridine, pyridazine, pyrimidine, pyrazine, s-triazine, 1,2,3-triazine, 1,2,4-triazine, and s-tetrazine) at the B97-1/TZ2P level, obtaining root-mean-square (rms) deviations from observed values of about 15 cm1. Barone and co-workers reported anharmonic infrared spectra of pyrrole [28], furan [28], uracil [29], 2-thiouracil [29], phenoxy radical [22] and azabenzene series of compounds [27] using DFT-B3LYP method within second-order perturbation treatment, reproducing satisfactorily experimental wavenumbers with absolute average errors of 5–10 cm1. However, it is also important to mention that recently, very efficient variational procedures within the vibrational SCF theory have been developed and applied with success on molecular systems up to 12 atoms [31]. This work reports ab initio and DFT calculations on structure and vibrational properties of 1,3-cyclopentadiene and its hexadeuterated isotopomer. Vibrational frequencies are evaluated within the harmonic and anharmonic approaches. Anharmonic corrections to the frequencies of the investigated compounds are here calculated for the first time through vibrational second-order perturbation theory. Overtone and combination transitions are also computed. The results are compared with experimental and previous theoretical data. 2. Computational methods All calculations were performed with GAUSSIAN 03 program [32]. Geometry of 1,3-cyclopentadiene was fully optimized under C2v point group symmetry by ab initio Møller–Plesset second-order perturbation level (MP2) as well as DFT methods employing B3LYP [33] and B97-1 [34] functionals with cc-pVDZ and cc-pVTZ correlation consistent Dunning’s basis sets [35]. Equilibrium geometry was optimized using a convergence threshold for the residual gradients of 107 Hartree/Bohr (radian), in order to obtain sufficiently reliable anharmonic wavenumbers [22]. For DFT computations fine grids with 99 radial and 500 angular points were used. Harmonic frequencies of 1,3cyclopentadiene and 1,3-cyclopentadiene-d6, were calculated analytically at the MP2 and DFT levels. Anharmonic corrections to frequencies were obtained by means of second-order perturbation theory. Third and semidiagonal fourth energy derivatives with respect to normal coordinates were evaluated through a numerical differentiation procedure as described in detail in Ref. [22] and implemented in GAUSSIAN 03 [32]. A commonly used step size ˚ along the normal coordinate was displacement of 0.025 A

adopted [27–29]. Fundamental frequencies (mi) were determined from harmonic values (xi), diagonal (vii) and offdiagonal (vij) anharmonic constants [22] 1X mi ¼ xi þ 2vii þ v 2 j6¼i ij Fermi resonances have been taken into account through a procedure described in detail by Martin et al. [36] and implemented by Barone [22] in GAUSSIAN 03 [30]. 3. Result and discussion 3.1. Geometry, rotational constants and dipole moment Optimized geometrical parameters of 1,3-cyclopentadiene (Fig. 1) are given in Table 1, together with available microwave data for comparison [3]. The present equilibrium geometries are in reasonable agreement with those previously reported in the literature using correlated ab initio and DFT methods [6–11]. As shown in Table 1, when using the cc-pVDZ basis set, DFT methods give slightly better results than those obtained at the MP2 level, which in particular overestimates the experimental C@C bond ˚ . Comparison among the employed length by ca. 0.02 A functionals shows that differences between them are relatively small, the B3LYP method giving the best performance, with an rms deviation for the bond lengths of ˚ . With regards to bond angles, all the theoretical 0.008 A methods reproduce nicely the experiment, with rms deviations within 0.2–0.4°. As can be seen in Table 1, the calculated geometries are much more sensitive to the quality of the basis set. B97-1/cc-pVDZ and B97-1/cc-pVTZ computations give rms deviations from the experimental bond ˚ , respectively. The most imporlengths of 0.010 and 0.002 A tant differences between the cc-pVDZ and cc-pVTZ basis sets concern the CAH and C@C bond distances, which are systematically overestimated by the smaller basis set ˚ . Note that, the B97-1/cc-pVTZ geometry is by ca. 0.01 A in very good agreement with that recently determined by Bomble et al. [10] at the CCSD(T)/cc-pVQZ level (Table 1). In particular, the difference between the length of single ˚ by CAC and double C@C bond is predicted to be 0.121 A the B97-1/cc-pVTZ computations, in excellent agreement

Fig. 1. Atom numbering for 1,3-cyclopentadiene.

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Table 1 Geometrical parameters of 1,3-cyclopentadiene Parametera C1AH C2AH C3AH C1AC2 C2@C3 C3AC4 rmsd HAC1AH HAC2@C3 HAC3@C2 C1AC2@C3 C2@C3AC4 C2AC1AC5 rmsd

MP2/cc-pVDZ 1.107 1.093 1.093 1.507 1.365 1.473 0.012 106.5 126.6 126.0 109.1 109.1 103.6 0.4

(1.110) (1.095) (1.097) (1.513) (1.371) (1.478)

(106.3) (126.6) (126.0) (109.0) (109.2) (103.7)

B3LYP/cc-pVDZ 1.107 1.090 1.091 1.506 1.353 1.471 0.008 105.7 126.8 126.1 109.1 109.2 103.4 0.3

(1.111) (1.093) (1.095) (1.512) (1.358) (1.476)

(105.7) (126.8) (126.1) (109.1) (109.2) (103.5)

B97-1/cc-pVDZ 1.108 1.091 1.092 1.508 1.356 1.474 0.010

(1.112) (1.094) (1.095) (1.514) (1.362) (1.479)

B97-1/cc-pVTZ 1.098 1.081 1.082 1.504 1.347 1.468 0.002

105.8 (105.6) 126.8 (126.7) 126.1 (126.1) 109.1(109.0) 109.2 (109.3) 103.4 (103.5) 0.3

105.9 126.8 126.1 109.1 109.3 103.2 0.2

(1.102) (1.083) (1.085) (1.510) (1.352) (1.474)

(105.8) (126.8) (126.1) (109.0) (109.3) (103.3)

CCSD(T)/cc-pVQZb 1.093 1.077 1.078 1.499 1.346 1.466 0.004 106.6 126.6 126.1 109.3 109.1 103.1 0.2

Experimentalc 1.099 1.078 1.080 1.506 1.345 1.468 106.3 127.1 126.0 109.2 109.3 102.9

Values in parentheses refer to vibrationally averaged quantities (rz structure). a ˚ , bond angles in degrees. Bond lengths in A b Ref. [10]. c Microwave geometry [3].

with both the experimental and CCSD(T)/cc-pVQZ esti˚ , respectively. These results conmates of 0.123 and 0.120 A firm the satisfactory performance of the B97-1 functional in combination with a triple-f plus polarization basis set in structural parameter determinations [24]. Table 1 also reports vibrationally averaged geometries (rz structure) obtained through calculations of vibration–rotation interaction constants [22]. The results show that, inclusion of vibrational averaging elongates the bond distances by ˚ , while bond angles are almost unaffected. 0.002–0.006 A Rotational constants for 1,3-cyclopentadiene and its hexadeuterated isotopomer are collected in Table 2. The present results are somewhat independent on the level of calculation used and are in satisfactory agreement with the experimental data within 0.5% [3]. Differences between values computed at the equilibrium and vibrationally averaged geometries are very little (within 0.8%). On the other hand, the rotational constants are much more affected by the H/ D isotopic substitution, the values of 1,3-cyclopentadiened6 being reduced by ca. 20% with respect to the corresponding data of the parent compound, in good agreement with the experiment. Table 2 also reports calculated dipole moments. The experimental dipole moment of 1,3-cyclo-

pentadiene is known to be 0.420 D from gas-phase microwave measurements [3]. The MP2/cc-pVDZ l value computed at 0.419 D is in excellent agreement with the experimental datum and with a previous theoretical estimate obtained at the MP2/6-311G** level (0.418 D) [37]. By contrast, all the DFT functionals overestimate the observed value, the B3LYP method showing the best result, with an error of 13%. The expansion of the basis set from cc-pVDZ to cc-pVTZ has a little but not negligible effect on l, which is reduced by ca. 0.02 D (5%). 3.2. Vibrational frequencies of 1,3-cyclopentadiene Calculated harmonic and anharmonic vibrational frequencies and infrared intensities (IIR) of 1,3-cyclopentadiene are reported in Table 3 and compared with the observed fundamental frequencies [13]. Fig. 2 shows the simulated B97-1/cc-pVDZ infrared spectrum of 1,3-cyclopentadiene and its hexadeuterated isotopomer obtained by convoluting the anharmonic frequencies with Lorentz lineshapes with a half-width of 5 cm1. Experimentally, infrared spectra of 1,3-cyclopentadiene were measured in the gaseous, liquid and solid phases by Gallinella et al.

Table 2 Rotational constants (cm1) and dipole moments (D) of 1,3-cyclopentadiene Parameter

MP2/cc-pVDZ

B3LYP/cc-pVDZ

B97-1/cc-pVDZ

B97-1/cc-pVTZ

Experimentala

Ae Be Ce A0 B0 C0

0.2778 0.2721 0.1411 0.2759 0.2700 0.1400

0.2806 0.2732 0.1421 0.2787 0.2711 0.1410

0.2796 0.2722 0.1416 0.2777 0.2702 0.1405

0.2826 0.2748 0.1430 0.2807 0.2728 0.1419

0.2811 (0.2204) 0.2744 (0.2204) 0.1425 (0.1149)

l

0.419

0.473

0.485

0.461

0.420 ± 0.003

Values in parentheses refer to the 1,3-cyclopentadiene-d6 isotopomer. a Gas-phase values [3].

(0.2188) (0.2184) (0.1140) (0.2174) (0.2169) (0.1132)

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Table 3 Calculated vibrational harmonic, x, and anharmonic, m, frequencies (cm1) and infrared intensities, IIR (km/mol), of 1,3-cyclopentadiene Symmetry

No.

Descriptiona

MP2/ccpVDZ

B3LYP/cc-pVDZ

B97-1/cc-pVDZ

Experimentalb

B97-1/cc-pVTZ

x

m

x

xc

m

x

m

IIR

x

m

IIR

m

A1

1 2 3 4 5 6 7 8 9 10

mCAH mCAH mCH2 mC@C + dCAH dCAH + rCH2 rCH2 dCAH mCAC mCACH2 dring

3277 3252 3073 1551 1415 1394 1120 1034 945 802

3160 3122 2938 1506 1379 1355 1105 1021 930 792

3231 3206 3014 1562 1398 1376 1116 1016 927 810

3137 3113 2926 1517 1357 1336 1084 986 909 794

3087 3072 2863 1520 1368 1339 1104 998 913 801

3230 3205 3013 1553 1394 1372 1112 1014 925 802

3083 3072 2849 1512 1368 1333 1107 1002 919 798

3.1 9.8 8.8 2.2 0.2 23.1 0.2 0.1 12.3 0.0

3219 3194 3006 1543 1408 1394 1128 1010 922 810

3090 3083 2863 1501 1370 1362 1115 993 909 803

2.0 11.5 9.2 1.1 4.2 21.1 0.2 0.2 11.2 0.0

3091 3075 2886 1500 1378 1365 1106 994 915 802

A2

11 12 13 14

sCH2 cCAH cCAH sring

1113 922 701 505

1083 904 689 502

1110 956 711 522

1078 938 697 512

1076 928 697 515

1105 948 706 518

1071 916 690 510

0.0 0.0 0.0 0.0

1119 953 711 521

1087 944 700 519

0.0 0.0 0.0 0.0

1110d 941d 700 516d

B2

15 16 17 18 19 20 21 22

mCAH mCAH mC@C + dCAH dCAH xCH2 dCAH mCACH2 dring

3270 3243 1623 1319 1258 1100 988 806

3145 3115 1583 1285 1225 1083 972 795

3224 3196 1645 1308 1254 1096 969 811

3130 3103 1597 1270 1218 1064 950 795

3134 3057 1608 1277 1218 1084 952 800

3223 3195 1635 1303 1246 1093 968 803

3111 3057 1599 1279 1216 1088 954 796

18.4 3.1 0.1 1.1 1.4 2.8 13.0 6.5

3213 3183 1629 1314 1260 1110 968 812

3111 3082 1589 1289 1224 1096 953 802

17.7 3.7 0.1 0.9 2.4 1.9 14.2 6.1

3105 3043 1580 1292 1239 1090 959 805

B1

23 24 25 26 27

mCH2 cCAH qCH2 + cCAH cCAH sring + qCH2 rmsde rmsdf rmsdg

3124 934 907 678 325 93 191 25

2973 912 883 666 327 32 60 15

3041 951 907 681 343 67 136 24

2953 933 889 668 336 26 45 16

2873 925 884 667 341 16 20 14

3044 945 901 678 339 66 135 19

2866 916 878 662 338 17 22 16

7.2 0.1 23.5 56.9 9.6

3029 954 913 680 346 62 124 22

2868 939 893 673 348 14 24 8

6.4 0.0 31.2 70.4 7.8

2900 925 891 664 350

a Based on the B97-1/cc-pVTZ calculations. m = stretching; d = in-plane bending, r = scissoring, s = torsion, c = out-of-plane bending, x = wagging, q = rocking. b Liquid-phase values [13]. c Harmonic values corrected by scaling factors of 0.9709 and 0.9807 for x > 1000 and x < 1000 cm1, respectively, taken from Ref. [43]. d Solid-phase values [13]. e All vibrational modes. f mCAH and mCH2 modes. g All vibrational modes excluding mCAH and mCH2 modes.

[12] and by Castellucci et al. [13], which also provided the assignment of the fundamentals and of a large number of overtones and combination transitions. Ball et al. [15], Hilfiker et al. [16] and more recently Miyazaki and Yamada [17] reported infrared spectrum in Ar matrix at 14, 16 and 18 K, respectively. From computational work, vibrational frequencies were previously obtained within the harmonic approximation at the MCSCF/MIDI3+2p [6], HF/6-31G* [18], HF/6-31+G* [9], MP2/6-31+G* [9], MP2/6-311+G(d,p) [16], B3LYP/6-31G* [8] and B3LYP/ 6-311+G* [17] levels. Cuff and Kertsez [18] at the HF/321G level and later Truttmann et al. [7] at the B3LYP/631G* level derived scaling factors for different types of molecular vibrations through a fitting procedure of the observed [13] and calculated harmonic frequencies of 1,3cyclopentadiene, in order to elucidate the experimental vibrational spectra of fluorene [18], methylene bridged

planarized poly(p-phenylene) [18] and the radical cation of cyclopentadiene [7]. As far as known, anharmonic vibrational frequencies of 1,3-cyclopentadiene have never been computed before. The present compound belongs to the C2v symmetry point group, with 27 normal vibrations classified as 10A1 + 4A2 + 5B1 + 8B2. All except for A2 modes are infrared active. Current assignment of the vibrational transitions based on the B97-1/cc-pVTZ calculations are in reasonable agreement with the experimental [13] and previous theoretical investigations [6,9]. The results of Table 3 show that, harmonic wavenumbers are systematically higher than the experimental figures, with rms deviations of 93, 67, 66 cm1, respectively, for MP2, B3LYP and B97-1 methods with the cc-pVDZ basis set. Overall B3LYP and B97-1 hybrid functionals predict rather similar frequencies, with differences encompassed within 10 cm1. At the B97-1

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Fig. 3. Percentage error relative to the experiment [13] of the B97-1/ccpVTZ vibrational frequencies of 1,3-cyclopentadiene.

Fig. 2. B97-1/cc-pVDZ anharmonic vibrational spectra of 1,3-cyclopentadiene and 1,3-cyclopentadiene-d6. Lorentz lineshapes with half-width of 5 cm1 have been used.

level, the extension of basis set from cc-pVDZ to cc-pVTZ has a little but not negligible influence, reducing the rms deviation from the experimental values to 62 cm1, in consistency with improvements in the structural parameters (Table 1). As should be expected, when anharmonic corrections are taken into account, whatever the level of calculation employed, computed frequencies are generally in better agreement with the experiment in comparison to the harmonic approximation. Except for low-energy ring torsion modes (nos. 14 and 27), where harmonic and anharmonic frequencies are close to each other, the introduction of the anharmonic corrections reduces the harmonic wavenumbers by 10–160 cm1 (1–6%). As a result, on passing from the harmonic to the anharmonic treatment, the rms difference from the experimental data is reduced by three-four times. The best results are obtained at the B97-1/cc-pVTZ level with an rms deviation of 14 cm1, which is further decreased to 8 cm1 when excluding CAH and CH2 stretching modes. Fig. 3 shows the perm m centage deviation ð calcmexp exp  100Þ of the B97-1/cc-pVTZ harmonic and anharmonic vibrational frequencies from the observed value [13]. Present results confirm the very good performance of the B97-1 functional in combination with triple-f plus polarization basis sets in anharmonic vibrational frequency determinations, in line with recent investigations on furan [24], pyrrole [24], thiophene [24], azabenzenes [30] and a series of 17 little molecules with more than two atoms [38]. However, the use of the smaller cc-pVDZ basis set, which in the present case is about an order of magnitude computationally less demanding than the cc-pVTZ one, gives satisfactory results with an rms deviation from the experimental frequencies of 17 cm1. This result indicates that anharmonic contributions are almost independent on the quality of the basis set, as

pointed out previously [22,36,39]. Thus, the smaller ccpVDZ basis set in combination with hybrid DFT methods may be an adequate choice for anharmonic spectroscopic investigations of larger semi-rigid molecules. For high-frequency CAH and CH2 stretching vibrations (mode nos. 1, 2, 3, 15, 16 and 23), the B97-1/cc-pVTZ harmonic frequencies overestimate the experimental figures by 100–140 cm1 (4–5%), with an rms error of 124 cm1, the largest deviation being found for mode no. 16. The corresponding rms value obtained by the current MP2/cc-pVDZ computations is somewhat larger being 191 cm1. This result is in line with previous harmonic calculations performed at the MP2/6-31+G* level [9], which overestimate the experimental mCAH and mCH2 wavenumbers by ca. 200 cm1. It is evident from Table 3 and Fig. 3 that the anharmonic corrections to the CAH and CH2 stretching frequencies are substantial. In fact, at the B97-1/cc-pVTZ level, they decrease the harmonic values of the mCAH and mCH2 vibrations by 100–130 cm1 (3–4%) and 140– 160 cm1 (5–6%), respectively. Similar anharmonic corrections to CAH stretching frequencies have been recently reported on furan [24,28], pyrrole [24,28] thiophene [24], uracil [29], 2-thiouracil [29], phenol [40], phenoxy radical [22], benzene [24,25,29] and also on the azabenzene series of compounds [27,30], using various hybrid DFT methods. As a consequence, the present anharmonic mCAH and mCH2 frequencies are within 1–39 cm1 from experimental values (0.1–1.4%), with an rms deviation of 24 cm1. The largest discrepancy is found for the CAH stretching mode no. 16. For this vibration present computations give rise to a Fermi resonance with m4 + m17 modes, although, the difference between deperturbed and perturbed frequency values is calculated to be quite small (3 cm1). As shown in Table 3, the largest difference between the harmonic and anharmonic frequencies is found for mode no. 23, which is associated to the antisymmetric CH2 stretching vibration. Its harmonic and anharmonic B97-1/ cc-pVTZ frequency values are calculated to be 3029 and 2868 cm1, respectively, to be compared with the observed

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figure of 2900 cm1 [13]. For this vibration anharmonic constant values, v23,j (j = 1–27), which determine the anharmonic frequency correction, x23  m23, are illustrated in Fig. 4. The most significant contributes originate from the diagonal term (v23,23) and the coupling with the symmetric CH2 stretch (v23,3) which is placed at 2863 cm1 by the B97-1/cc-pVTZ anharmonic calculations, very close to mode no. 23. v23,23 and v23,3 values are calculate to be 35 and 135 cm1, respectively, together contributing to ca. 80% of the total anharmonic correction for mode no. 23. Other non-negligible contributes come from vibrations associated to the CH2 group: in particular mode nos. 5 and 6, characterized by the CH2 scissoring vibration and mode no. 11 ascribed to the torsional vibration of the CH2 group. Very recently, Gerber and co-workers, have computed anharmonic infrared spectra of H2SO4 [41] and 5,6-dihydrouracil [42] by means of the CC-VSCF technique, noting significant anharmonic couplings between vibrations involving movements inside the same group of atoms and also between modes having very close frequency value. As can be seen from Table 3, the anharmonic corrections for the remaining modes are generally much smaller than those obtained for the CAH and CH2 stretches. However, anharmonic calculations yet give better results with respect to those obtained under the harmonic approximation, with errors within 1.5%. A noticeable exception regards mode no. 11 (sCH2), as clearly illustrated in Fig. 3. Present B97-1/cc-pVTZ harmonic calculations locate this mode at 1119 cm1 in reasonable agreement with the observed value of 1110 cm1 (0.8%). The above result is probably due to an inappropriate representation of the torsional mode potential within the harmonic approximation, which, at the employed theoretical levels, furnishes a too low frequency value, fortuitously close to the observed figure. Inclusion of the anharmonic correc-

tions reduces the harmonic frequency by ca. 30 cm1 (3%), underestimating the experimental datum by ca. 20 cm1, with an error about double of that obtained by the harmonic approximation. In the case of mode nos. 4 and 17, which mainly involve C@C stretches, the calculated harmonic frequencies overestimate the experimental values by 40–50 cm1, with an error of ca. 3%, which is reduced to 0.1–0.6% (1–9 cm1) when accounting for the anharmonic contributions. An other vibration exhibiting a moderate degree of anharmonicity (ca. 3%) is mode no. 19 (xCH2). Table 3 also includes the B3LYP/cc-pVDZ harmonic frequencies corrected by scaling factors recently reported by Sinha et al. [43]. The scaling factors were evaluated through a least-squares optimization of calculated wavenumbers with experimental ones for a series of 41 common organic compounds [43]. Specifically at the B3LYP/ccpVDZ level they are 0.9709 and 0.9807, for modes with x > 1000 cm1 and x < 1000 cm1, respectively. The obtained scaled frequencies give an rms deviation from the experimental values of 26 cm1, to be compared with the corresponding value of 16 cm1 obtained from the anharmonic computations. This result is seriously conditioned by the CAH and CH2 stretching frequency values (in particular for mode nos. 1, 2, 3, 16 and 23), which are overestimated by the scaling procedure, with an rms error from the experimental data of 45 cm1, which is significantly greater than that obtained by direct anharmonic calculations (20 cm1). In comparison, the B3LYP/6-311+G* harmonic wavenumbers scaled by a single factor (0.98) recently reported by Miyazaki and Yamada [17], give somewhat larger rms deviations (32 and 65 cm1, for all the vibrational modes and for mCAH and mCH2 stretches, respectively). As shown in Fig. 2 and Table 3, current calculations place the most intense IR absorption of 1,3-cyclopentadiene at ca. 650 cm1, attributed to an out-of-plane CAH bending deformation (mode no. 18), in agreement with the experimental results [12,13]. Other intense peaks in the observed spectrum are located near 900 and 1350 cm1 [12,13] and are satisfactorily reproduced by the present calculations. They are ascribed to qCH2 + cCH (mode no. 25) and rCH2 (mode no. 6), respectively. It is worth noting that, the ratio between the sum of the IIR values of the aliphatic CH2 stretches (mode nos. 3 and 23) and the sum of the IIR values of the cis-butadienic CAH P mCH2 P mCH stretches (mode nos. 1, 2, 15 and 16), I IR = I IR , is calculated to be 0.45 in very good agreement with the observed value of 0.43 [44]. Note that, infrared intensities are slightly affected by the cc-pVDZ ! cc-pVTZ basis set enlargement (rms deviation of 3 km/mol). 3.3. Overtone and combination transitions of 1,3cyclopentadiene

Fig. 4. Anharmonic vibrational constants for the antisymmetric CH2 stretching vibration, v23,j (cm1), with the remaining modes of 1,3cyclopentadiene. B97-1/cc-pVTZ results.

Besides determination of fundamental wavenumbers, second-order perturbation approach may be usefully

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employed to predict frequencies of overtone and combination transitions [24,30]. B97-1/cc-pVTZ first overtone wavenumbers of 1,3-cyclopentadiene evaluated within the harmonic and anharmonic approaches are listed in Table 4. Theoretical predictions of overtone and combination bands of 1,3-cyclopentadiene had never been so far reported and have been calculated along with the fundamental transitions at no additional computational cost. Experimentally, overtone frequencies were identified only for mode nos. 4, 5, 6, 8, 9, 13, 17 and 25 [12]. Their values are included in Table 4. Note that, the fundamental frequencies of mode nos. 6–10 reported in Ref. [12] were correctly reassigned later to mode nos. 5–9 [13]. In line with the results obtained for xi values, the harmonic approximation overestimates the observed overtone frequencies by 0.8–3.3%, with an rms deviation of 64 cm1, the largest difference (ca. 100 cm1) being found for mode nos. 4 and 17. Except for mode no. 27, introduction of the anharmonic corrections decreases 2xi values by 2–391 cm1 (0.2–6.5%), improving noticeably the agreement with the experimental data within 0.1–1.0%, with an rms deviation of 15 cm1, which is similar to that obtained for the fundamentals. Note that the agreement is especially good (within 5 cm1) for mode nos. 4, 6, 13 and 25, validating the results of the corresponding computed fundamental frequencies, Table 4 B97-1/cc-pVTZ first overtones (cm1) of 1,3-cyclopentadiene Mode

m1 m2 m3 m4 m5 m6 m7 m8 m9 m10 m11 m12 m13 m14 m15 m16 m17 m18 m19 m20 m21 m22 m23 m24 m25 m26 m27 rmsd a b

Experimentala

Calculated Harmonic

Anharmonic

6438 6388 6012 3086 2816 2789 2255 2021 1844 1620 2239 1906 1422 1042 6426 6366 3258 2628 2519 2220 1936 1623 6058 1908 1826 1359 693

6149 6138 5663 2989 2730 2719 2230 1980 1817 1606 2170 1889 1398 1040 6180 6134 3186 2575 2437 2192 1903 1604 5667 1878 1782 1343 700

64

15

Liquid-phase values [12,13]. Solid-phase values [12,13].

2986 2753 2724 1988 1829

1395b

3154

1779

133

which are within 3 cm1 from the experimental values (Table 3). In Table 5 are collected the B97-1/cc-pVTZ frequencies of some selected combination transitions, together with available observed values for comparison [12]. The complete list of the computed mi + mj frequencies is available on request from the author. Wavenumbers of combination bands involving mode nos. 11 and 12 are reported in the Table but are excluded from this comparison, since in Ref. [12] their frequency values were incorrectly identified at 1135 and 920 cm1, respectively, 35 and 20 cm1 above the revised values reported in a subsequent paper [13]. By analogy to the overtones, the computed harmonic wavenumbers of the combination transitions systematically overestimate the experimental values by 6–153 cm1 (0.3– 4.9%), with an rms error of 70 cm1, the largest difference being found for the m16 + m22 band. Inclusion of the anharmonic contributions reduces the harmonic frequencies by 6–169 cm1 (0.6–4.7%), giving an rms deviation from the observed values of 16 cm1, very close to that obtained for the first overtones. It is of interest to mention that the agreement is particularly excellent (within 1 cm1) for m4 + m22, m8 + m25, m9 + m20 and m13 + m22 bands, which confirms the satisfactory results obtained in the related fundamental transitions (Table 3). 3.4. Vibrational frequencies of 1,3-cyclopentadiene-d6 In Table 6 are listed the B97-1/cc-pVDZ vibrational frequencies of the 1,3-cyclopentadiene-d6 isotopomer, together with available experimental data for comparison [13]. As far as known, previous theoretical results are restricted to MCSCF/MIDI3+2p computations obtained under the harmonic approximation [6]. As can be seen from Fig. 2, infrared intensities are sensitive to the isotopic substitution. For the hexadeuterated isotopomer present calculations give IIR values which are about half of the corresponding values obtained for the parent compound. Differently from 1,3-cyclopentadiene, for 1,3-cyclopentadiene-d6 about one-third of the harmonic frequencies underestimate the observed values, with rms deviation for all the modes of 38 cm1. Note that this value is significantly inferior to that obtained for the parent compound. Inclusion of the anharmonic contributions reduces the harmonic frequencies by 0.4–4.6%, giving an rms error from the experiment of 17 cm1. As previously noticed for 1,3-cyclopentadiene, when excluding the CAD and CD2 stretching modes, the agreement between calculated and experimental values significantly improves, the harmonic approximation giving an rms deviation of 19 cm1, very close to that obtained by the anharmonic computations (17 cm1). Present harmonic calculations overestimate the experimental mCAD and mCD2 wavenumbers by 60– 80 cm1 (rms deviation of 72 cm1), with an error of 3.2– 4.6%, while previous MCSCF/MIDI3+2p calculations [6] gave a much greater discrepancy (ca. 150 cm1). Introduction of the anharmonic corrections reduces the harmonic

134

A. Alparone / Chemical Physics 327 (2006) 127–136

Table 5 B97-1/cc-pVTZ selected combination bands (cm1) of 1,3-cyclopentadiene Modes

m26 + m27 m14 + m26 m24 + m27 m14 + m22 m13 + m26 m14 + m25 m14 + m24 m11 + m27 m13 + m22 m24 + m26 m13 + m24 m8 + m26 m6 + m27 m5 + m27 m12 + m22 m21 + m22 m24 + m25 m12 + m24 m8 + m25 m8 + m24 m8 + m21 m9 + m20 m11 + m25 m6 + m26 m5 + m26 m8 + m20 m14 + m17 m9 + m19 m4 + m26 m5 + m22 a b

Calculated Harmonic

Anharmonic

1026 1201 1300 1333 1391 1434 1475 1466 1523 1633 1665 1690 1741 1754 1765 1780 1867 1907 1923 1964 1979 2032 2032 2074 2088 2120 2150 2182 2223 2220

1020 1192 1286 1320 1368 1412 1459 1434 1501 1610 1634 1664 1710 1717 1746 1754 1830 1883 1885 1931 1945 2005 1978 2034 2042 2088 2109 2129 2174 2171

Experimentala

Modes

1013 1177 1275 1318 1394b 1404 1436 1480 1500 1591 1625 1660 1717 1728 1751b 1768 1833b 1844 1886 1913 1955 2005 2026 2040b 2044 2084 2093 2150 2169 2182

m7 + m20 m12 + m18 m6 + m25 m5 + m25 m13 + m17 m8 + m18 m4 + m22 m18 + m20 m4 + m21 m6 + m20 m12 + m17 m17 + m21 m8 + m17 m6 + m19 m5 + m19 m6 + m18 m5 + m18 m5 + m6 m17 + m19 m4 + m6 m4 + m17 m3 + m27 m23 + m27 m3 + m22 m3 + m25 m16 + m22 m2 + m22 m1 + m22 m15 + m22 m2 + m9

Experimentala

Calculated Harmonic

Anharmonic

2237 2267 2307 2321 2340 2325 2355 2424 2511 2504 2581 2597 2639 2654 2668 2708 2722 2803 2889 2938 3172 3352 3375 3818 3919 3995 4005 4031 4025 4116

2212 2235 2252 2257 2288 2279 2301 2382 2454 2455 2533 2543 2583 2585 2591 2646 2656 2722 2814 2857 3047 3211 3218 3664 3750 3887 3884 3891 3912 3992

2197 2204 2254 2270 2281 2290 2303 2378 2458 2466 2496 2536 2572 2605 2615 2657 2667 2735 2816 2857 3023 3227b 3251 3690 3770 3842 3877 3889b 3905 3985

Liquid-phase values [12,13]. Solid-phase values [12,13].

frequencies of the CAD and CD2 stretches (80–100 cm1), although to a lesser extent than in the parent compound, improving the agreement with the experiment within 1% (rms deviation of 18 cm1). Fig. 5 displays the comparison between calculated and observed H/D isotopic frequency shift involving the CAH and CH2 stretches. Experimentally, upon deuteration, mCAH and mCH2 frequencies are batochromically shifted by 720–790 cm1 [13]. The harmonic approximation overestimates the observed shifts by 40–70 cm1 (6– 10%), the largest discrepancy being found for mode no. 23. Introduction of the anharmonic corrections decreases the harmonic values by 70–80 cm1 (4–10%), improving the agreement with the experiment within ca. 2%. This is especially evident for mode nos. 1, 2, 3 and 15, where the differences between the experimental and calculated anharmonic values are less than 10 cm1 (Fig. 5). On the other hand, for the remaining modes, anharmonic corrections to the H/D isotopic red-shift are of minor importance. Specifically, for the most intense cCAH vibration (mode no. 18), upon deuteration a shift of 172 and 166 cm1 is calculated by the harmonic and anharmonic approaches, respectively, to be compared with the observed value of 170 cm1. For the rCH2 vibration an experimental isotopic

shift of 318 cm1 is reported, which is nicely reproduced by the harmonic calculations at 319 cm1, while it is somewhat underestimated by the anharmonic corrections (302 cm1). The harmonic approximation predicts an isotopic shift of 256 cm1 for the sCH2 vibration (mode no. 11), much closer to the experiment (256 cm1) than that obtained by the anharmonic calculations (241 cm1). By contrast, for the xCH2 mode, the observed isotopic shift of 525 cm1 is better reproduced by the anharmonic (514 cm1) than the harmonic (540 cm1) treatment. 4. Synopsis In this paper, the infrared spectra of 1,3-cyclopentadiene and its hexadeuterated isotopomer have been calculated within the harmonic and anharmonic approaches, using MP2 and DFT methods with the cc-pVDZ abd cc-pVTZ Dunning’s basis sets. The results have shown that anharmonic contributions greatly improve the agreement between calculated and experimental fundamental frequencies, with rms deviations 3–4 times inferior to those obtained by the harmonic approximation. Similar results are also obtained for overtone and combination transitions, confirming the good performance of the pres-

A. Alparone / Chemical Physics 327 (2006) 127–136

135

Table 6 B97-1/cc-pVDZ vibrational harmonic, x, and anharmonic, m, frequencies (cm1) and infrared intensities, IIR (km/mol), of 1,3-cyclopentadiene-d6 Symmetry

Mode no.

Descriptiona

A1

1 2 3 4 5 6 7 8 9 10

mCAD mCAD mCD2 mC@C + dCAD mCAC + mCACD2 + dCAD rCD2 mCAC + mCACD2 + rCD2 dring mCACD2 + mCAC dring + dCD

A2

11 12 13 14

sCD2 cCAD cCAD sring

B2

15 16 17 18 19 20 21 22

B1

23 24 25 26 27

Experimentalb

Calculated x

m

IIR

2412 2364 2196 1515 1255 1053 942 822 733 713

2333 2287 2094 1479 1232 1031 926 817 730 712

1.5 4.7 2.5 5.4 0.1 10.5 2.0 0.2 7.5 0

849 758 543 432

830 739 533 425

0 0 0 0

mCAD mCAD mC@C + dCAD mCACD2 + xCD2 + dCAD xCD2 + dCAD dring dring xCD2

2399 2353 1578 1201 995 833 765 706

2322 2277 1546 1175 981 826 759 702

9.6 1.7 0.2 0 0.1 5.8 2.6 7.4

2324 2294 1522 1231c 1000 835 765 714

mCD2 sring + qCD2 c–D cCAD qCD2 + sring rmsdd rmsde rmsdf

2251 810 721 506 265 38 72 19

2156 794 703 496 264 17 18 17

4.9 7.7 4.2 33.2 5.9

2177 807 707 494 276

2333 2289 2130 1466 1235 1047 934 823 734 710 847 751c 545 434

a Based on the B97-1/cc-pVDZ calculations. m = stretching; d = in-plane bending, r = scissoring, s = torsion, c = out-of-plane bending, x = wagging,q = rocking. b Liquid-phase values [13]. c Solid-phase values [13]. d All vibrational modes. e mCAD and mCD2 modes. f All vibrational modes excluding mCAD and mCD2 modes.

ent anharmonic treatment in the vibrational frequency determinations. The most significant anharmonic effects are found for the high-frequency CAH and CH2 stretching modes, the latter vibrations being more anharmonic than the former. The largest anharmonic correction is found for the antisymmetric CH2 stretching mode, mainly owing to the diagonal and coupling with the symmetrical CH2 vibration contributions, which together give ca. 80% of the total anharmonic correction. Inclusion of anharmonic effects is important for an accurate prediction of the H/D isotopic wavenumber shift of the CAH and CH2 stretching vibrations. Among the methods employed, the B97-1/cc-pVTZ level of calculation provides the best results in both structural and vibrational parameter determinations. Fig. 5. H/D isotopic wavenumber shift for the CAH and CH2 stretching modes between 1,3-cyclopentadiene and 1,3-cyclopentadiene-d6 isotopomers. Comparison between the experimental [13] and B97-1/cc-pVDZ values.

Acknowledgement Work partially supported by MIUR, Rome.

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