Vibrationally excited states of DC5N: Millimeter-wave spectroscopy and coupled cluster calculations

Journal of Molecular Structure 780–781 (2006) 148–156 www.elsevier.com/locate/molstruc

Vibrationally excited states of DC5N: Millimeter-wave spectroscopy and coupled cluster calculations L. Bizzocchia,*, C. Degli Espostia, P. Botschwinab a Dipartimento di Chimica ‘G. Ciamician’, Universita` di Bologna, Via F. Selmi 2, 40126 Bologna, Italy Institut fu¨r Physikalische Chemie, Universita¨t Go¨ttingen, Tammannstraße 6, D-37077 Go¨ttingen, Germany

b

Received 26 April 2005; revised 8 June 2005; accepted 8 June 2005 Available online 10 October 2005 For the special issue dedicated to Jean Demaison

Abstract The rotational spectrum of DC5N has been investigated in the millimeter-wave region for 16 vibrationally excited states which approximately lie below 760 cmK1, namely (v6 v7 v8 v9 v10 v11)Z(000001), (000002), (000003), (000005), (000010), (000020), (000100) (001000), (010000), (100000), (000011), (000101), (001001), (010001), (001010), and (010010). Gas-phase copyrolysis of fully deuterated pyridine and phosphorus trichloride was used to produce the semi-stable DC5N molecule. In addition to the usual l-type resonances, several vibrational interactions have been taken into account to fit properly the measured transition frequencies. The most important perturbations are caused by the cubic anharmonic interactions which mix the v6 stretching state with the 2v10 overtone and the v8Cv11 and v7Cv11 bending combination states. The analysis of the spectra was facilitated by theoretical predictions from CCSD(T) calculations with the cc-pVQZ basis. q 2005 Elsevier B.V. All rights reserved. Keywords: Rotational spectroscopy; DC5N; Vibrationally excited states; Resonances; CCSD(T) calculations

1. Introduction Millimeter wave (mm-wave) lines of vibrationally excited HC5N have been observed in space toward the proto-planetary nebula CRL 618 [1–3], stimulating earlier laboratory work aiming at a detailed analysis of the mmwave spectra for low-lying excited states of HC5N [4,5]. Accurate spectroscopic constants were determined for a total number of 23 vibrational states in the wavenumber range 100–850 cmK1. Most of the excited states which lie above 500 cmK1 were found affected by various vibrational or rovibrational resonances, whose analysis was greatly facilitated by the results of CCSD(T) calculations with the cc-pVQZ basis, which provided accurate predictions of a large variety of spectroscopic constants like harmonic vibrational wavenumbers,

* Corresponding author. Tel.: C39 051 2099504; fax: C39 051 2099456. E-mail address: [email protected] (L. Bizzocchi).

0022-2860/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2005.06.050

vibration–rotation coupling constants, l-type doubling constants, and normal-coordinate cubic force constants. The present paper extends the study of the excitedstate rotational spectra of cyanodiacetylene to the deuterated variant DC5N, for which only ground-state data were determined previously [6]. The theoretical force field reported in [5] predicts a considerable lowering of the v7 bending energy passing from HC5N to DC5N, and then a significant modification of the resonances observed for the normal isotopomer is expected to occur in DC5N. Rotational spectra for 16 vibrationally excited states lying between 100 and 760 cmK1 have been recorded in the mm-wave region, and their analysis has provided accurate values for a large number of spectroscopic constants, which include the a6–a11 vibration–rotation coupling constants, the q7– q11 l-type doubling constants, the xL(11,11), xL(10,10), xL(10,11), xL(9,11), xL(8,11), xL(7,11), xL(8,10), and xL(7,10) anharmonicity constants, and several normal coordinate cubic force constants involved in anharmonic resonances. The experimental values were generally found in

L. Bizzocchi et al. / Journal of Molecular Structure 780–781 (2006) 148–156

excellent agreement with those derived from the CCSD(T)/cc-pVQZ cubic force field of Ref. [5].

2. Predictions from coupled cluster calculations Making use of the results of coupled cluster calculations published earlier [5], a variety of spectroscopic constants has been calculated for the deuterated species DC5N (see Table 1). These include harmonic vibrational wavenumbers (ur), vibration–rotation coupling constants (ar) as obtained by conventional 2nd order perturbation theory in normal coordinate space, and l-type doubling constants (qet and qtJ). According to vast experience, the present ur values should be accurate to a few cmK1. Those for the stretching vibrations (u1–u6) differ by at most 8 cmK1 from the results of earlier CCSD(T) calculations with a smaller basis set [7], while for the bending vibrations the differences range from 2 to 10 cmK1, with the maximum deviation occurring for u9. High accuracy in the harmonic wavenumbers of the bending vibrations is crucial in view of the various vibrational resonances occurring in DC5N. The experimental values for the vibration–rotation coupling and l-type doubling constants determined in the present work (see Section 5) are compared with the corresponding CCSD(T)/cc-pVQZ values in Table 1. As far as ar constants are concerned, the agreement between experimental and CCSD(T)/cc-pVQZ values is very good for a6 and a9–a11, but less satisfactory for a7 and a8. Since the two bending states v7Z1 and v8Z1 are nearly degenerate (u7Ku8Z7.6 cmK1), it is likely that they are significantly mixed by quartic anharmonic force constants of the type frr78, which produce perturbed a constants. This hypothesis is supported by the nearly perfect agreement between experimental and theoretical values for the sum a7Ca8. Table 1 CCSD(T)/cc-pVQZ spectroscopic constants for DC5Na u1 (cmK1) u2 (cmK1) u3 (cmK1) u4 (cmK1) u5 (cmK1) u6 (cmK1) u7 (cmK1) u8 (cmK1) u9 (cmK1) u10 (cmK1) u11 (cmK1) qe7 (MHz) qe8 (MHz) qe9 (MHz) qe10 (MHz) qe11 (MHz) De (Hz) a

2670.7 2318.6 2208.6 1993.6 1153.7 601.7 508.6 501.0 458.6 247.1 103.3 0.241 (0.251) 0.279 (0.279) 0.296 (0.305) 0.459 (0.470) 1.058 (1.094) 24.18 (26.89)

a1 (MHz) a2 (MHz) a3 (MHz) a4 (MHz) a5 (MHz) a6 (MHz) a7 (MHz) a8 (MHz) a9 (MHz) a10 (MHz) a11 (MHz) q7J (Hz) q8J (Hz) q9J (Hz) q10J (Hz) q11J (Hz)

1.602 4.024 3.105 2.109 2.862 1.055 (1.001) K0.658 (K0.804) K1.668 (K1.530) K1.466 (K1.440) K2.288 (K2.288) K2.530 (K2.605) K0.027 K0.006 (K0.105) K0.027 (K0.053) K0.157 (K0.163) K0.903 (K0.993)

Experimental values from the present work in parentheses.

149

As is usually observed for linear molecules, the qet values obtained by perturbation theory are slightly lower than the corresponding experimental values. Among the small qtJ constants, excellent agreement between theory and experiment is noted for q10J and q11J, for which the most accurate experimental data could be obtained.

3. Experimental details The rotational spectra of DC5N have been recorded in selected frequency regions between 60 and 460 GHz for the two lowest bending states, and from 60 to 190 GHz for the remaining states, using the same mm-wave spectrometer already employed to record the groundstate spectra of numerous isotopic variants of cyanodiacetylene [6]. We can only mention that the radiation sources were phase-locked Gunn oscillators with subsequent harmonic generation and the absorption cell was a glass tube sealed by PTFE windows. Source frequency modulation was applied and the signal was demodulated at 2f, thus obtaining the 2nd derivative of the actual spectrum profile. The experimental uncertainty of the measured line positions is about 15 kHz. DC5N was produced by gas-phase copyrolysis (Tz1200 8C) of fully deuterated pyridine (SigmaAldrich) and phosphorus thrichloride in a flow reactor connected to the absorption cell of the mm-wave spectrometer, as already described in [6].

4. Observed spectra and analysis The vibrationally excited states investigated in the present work are labelled using the contracted notation (v6 v7 v8 v9 v10 v11). We have investigated the mm-wave spectra of DC5N in the (000001), (000002), (000003), (000005), (000010), (000020), (000100), (001000), (010000), (100000), (000011), (000101), (001001), (010001), (001010), and (010010) excited states, for which CCSD(T)/cc-pVQZ calculations predict vibrational energies ranging from 100 to 760 cmK1. The present investigation was focused on the vibrational states of single and double excitation, since they provide information on the most significant spectroscopic constants (i.e. vibration– rotation coupling constants, l-type doubling constants, and anharmonicity constants). The complete vibrational energy level diagram, based on the theoretical ur values, is illustrated in Fig. 1. It shows clearly that the density of states becomes progressively higher as energy increases, so that many accidental near-degeneracies occur above 500 cmK1. With the exception of the v6Z1 state, all the states investigated involve excitation of at least one bending quantum, so that multiplets of rotational lines were usually observed for each JC1)J transition owing to l-type resonance effects between the different l sublevels. The

150

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750

(001010)

(000030) (000007)

700

(000022)

(000110)

(000014)

(000102)

(001002)

(010010) (010002)

(100001)

650 (000006) (001001)

(000021)

600

(000013)

(010001)

(100000)

(000101)

550

Vibrational energy / cm–1

(000005) (001000)

(000020)

500

(000012)

450

(010000)

(000100)

(000004)

400 (000011)

350 (000003)

300 (000010)

250 (000002)

200 150

u6K2u10Z107.5 cmK1, with the corresponding normalcoordinate cubic force constants jf6,7,11jZ3.8 cmK1, jf6, K1 , and jf6,10,10jZ96.5 cmK1. It is, there8,11jZ5.2 cm fore, likely that the v6Z1 stretching state is appreciably mixed with the (010001), (001001), and (000020) bending states by Fermi-type interactions, which may produce a considerable low-frequency displacement of the rotational lines for the 0C sublevel of these bending states paralleled by a high-frequency shift of the v6Z1 transitions. The plot of the reduced transition frequencies for the lines of the (010001) and (001001) combination states is presented in Fig. 2, it shows clearly the anomalous low-frequency shifts exhibited by the curves corresponding to the 0C sublevels, which are the only ones which can be coupled to the v 6Z1 state. Accordingly, the lines of the stretching state were found at frequencies corresponding to an effective B constant ca. 2.2 MHz greater than the predicted unperturbed value. These cubic resonances were taken into account through the off-diagonal matrix-elements given by:

(000001)

100 50 0

ground state

Fig. 1. Approximate vibrational energy level diagram of DC5N up to 760 cmK1. Solid lines indicate the states for which rotational lines were observed.

spectra were analysed using the formalism originally developed by Yamada and co-workers [8,9], and the related diagonal and off-diagonal matrix elements can be found in the articles published recently on the excited-state rotational spectra of the normal isotopic species HC5N [4,5]. Using Wang-type linear combinations of the jl7, l8, l9, l10, l11;ki unsymmetrized basis functions (where kZ l7 C l8 C l9 C l10 C l11 ), the resulting energy matrix is factorized into symmetric and antisymmetric blocks, so that any sublevel belonging to a given vibrational state can be labelled through its k (or lt) value followed by the ‘C’ or ‘K’ superscript which indicates the chosen linear combination of wavefunctions [8]. In addition to the usual l-type resonances, various vibrational interactions had to be taken into account in order to fit properly the measured transition frequencies. The corresponding off-diagonal matrix elements were expressed using the formalism developed by Okabayashi et al. [10]. Some details dealing with the resonances analyzed are given in the following subsections. 4.1. The cubic anharmonic resonances coupling (v6, v7, v11) with (v6K1, v7C1, v11C1), (v6, v8, v11) with (v6K1, v8C1, v11C1), and (v6, v10) with (v6K1, v10C2) The present CCSD(T) calculations predict u6 Kðu7C u11 ÞZK10:2 cmK1 , u6 Kðu8 C u11 ÞZK2:6 cmK1 , and

11 hv6 ; vl77 ; vl11 ; J; kjH^ 30 jðv6 C1Þ; ðv7 K1Þl7G1 ;ðv11 K1Þl11H1 ; J; ki pffiffiffi 2 ð6;7;11Þ Z ½ðv6 C1Þðv7 Hl1 Þðv11 Gl11 Þ1=2 (1a) C 2 30

11 hv6 ; vl88 ; vl11 ; J; kjH^ 30 jðv6 C1Þ; ðv8 K1Þl8G1 ;ðv11 K1Þl11H1 ; J; ki pffiffiffi 2 ð6;8;11Þ Z ½ðv6 C1Þðv8 Hl8 Þðv11 Gl11 Þ1=2 (1b) C 2 30

10 hv6 ; vl10 ; J;kjH^ 30 jðv6 C1Þ; ðv10 K2Þl10 ; J; ki pffiffiffi ð6;10;10Þ Z 2C30 ½ðv6 C1Þðv10 Kl10 Þðv10 Cl10 Þ1=2

(1c)

The C30 coefficients can be related to the corresponding normal-coordinate cubic force constants by the expressions: 0

ðstt Þ fstt0 Z4C30

(2a)

stt fstt Z 8C30 :

(2b)

4.2. The sextic anharmonic resonance between (v7, v11) and (v7K1, v11C5) We observed that the two l-type doubling components of the v7Z1 bending state show a pronounced perturbation in a narrow J range, indicative of a rovibrational avoided crossing. A similar perturbation, at the same J values, was also observed for the two jl11jZ1 components of the nearby v11Z5 bending overtone, so that a high order anharmonic interaction was assumed between these nearly degenerate states. The off-diagonal matrix element employed to

L. Bizzocchi et al. / Journal of Molecular Structure 780–781 (2006) 148–156 k=2

+

k=0

–

k=2

–

k=0

–

k=2

+

151 k=2

–

70 60 50 40

J

0+ (010001)

0+ (001001)

30 20 (010001)

10 0 1272.6

1273.0

1273.4

1273.8

1274.2

1274.6

(001001)

1275.0

1275.4

ν / 2 (J + 1) / MHz Fig. 2. Plot of the reduced transition frequencies for the (010001) and (001001) vibrational states of DC5N. Open and solid symbols identify the observed transitions for the (010001) and (001001) bending combinations, respectively. Triangles are used for the sublevels perturbed by cubic anharmonic resonances.

account for this interaction has the form: 11 hvl77 ; vl11 ; J; kjH^ 60 jðv7 K1Þl7H1 ; ðv11 C 5Þl11G1 ; J; ki

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Z C60 ðv7 Gl7 Þðv11 Gl11 C 6Þðv11 Gl11 C 4Þðv11 Gl11 C 2Þðv11 Hl11 C 2Þðv11 Hl11 C 4Þ 8

(3)

(3) Similar localised perturbations have also been detected in the rotational spectra of the (010001) and (010010) bending combination states which can be coupled with the (000006) and (000015) states, respectively, through the same off-diagonal matrix element.

10 ; J; kjH^ 30 jðv6 C1Þ; ðv7 K1Þl7G1 ; ðv10 K1Þl10H1 ; J; ki hv6 ; vl77 ; vl10 pffiffiffi 2 ð6;7;10Þ (4a) Z C ½ðv6 C1Þðv7 Hl7 Þðv10 Gl10 Þ1=2 2 30 10 hv6 ; vl88 ; vl10 ; J; kjH^ 30 jðv6 C1Þ;ðv8 K1Þl8G1 ; ðv10 K1Þl10H1 ; J; ki pffiffiffi 2 ð6;8;10Þ (4b) Z ½ðv6 C1Þðv8 Hl8 Þðv10 Gl10 Þ1=2 C 2 30

4.3. Further weak resonances The vibrational resonances discussed in the previous sections produce anomalies in the spectral patterns, which are recognizable even before any detailed analysis of the measured frequencies is performed. Furthermore, during the fitting procedures, we found that two further weak cubic anharmonic resonances had to be considered in order to fit the measured transition frequencies within experimental accuracy (ca. 15 kHz). We observed that the 0C components of both (010010) and (001010) bending combination states exhibit small low-frequency shifts which can be accountable admitting a certain degree of mixing with the v6Z1 stretching state, which is characterized by a lower value of the rotational constant. These cubic interactions have been included via the off-diagonal matrix elements given by Eqs. (4a) and (4b):

where the C30 coefficients are related to the corresponding cubic force constants through Eq. (2a). As a consequence of the various resonances taken into account, we found that only eight of the investigated states could be properly analysed as isolated. These are (v6 v7 v8 v9 v 10 v 11)Z(000001), (000002), (000003), (000010), (000100), (001000), (000011), and (000101). The two states (010000) and (000005) form a resonance dyad whose offdiagonal matrix elements are given by Eq. (3), while the six remaining states, namely (v6 v7 v8 v9 v10 v11)Z(000020), (100000), (001001), (010001), (001010), and (010010), were included in a large rovibrational energy matrix, whose off-diagonal elements are given by Eqs. (1a)–(c) and Eqs. (4a) and (b). In addition to the investigated states, the (000006) and the (000015) states were also included into

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L. Bizzocchi et al. / Journal of Molecular Structure 780–781 (2006) 148–156

(010010)

760

C60

(000015)

5.1. The isolated states

(001010)

The rotational spectra for the fundamental bending states (001000), (000100), (000010), and (000001) of DC5N have been identified for the first time. Each rotational transition of these states is split into two components because of l-type doubling, and their assignment was facilitated by the CCSD(T) values of the at and qt constants reported in Table 1. For the low-lying bending states (000010) and (000001) the measurements have been performed in the frequency interval from 60 to 460 GHz reaching a J value as high as 176. The lowfrequency components of the doublets of these states are accidentally superimposed up to 170 GHz, but at higher frequency they are well separated. Owing to this, the absorption frequencies measured for blended transitions were always assigned to the most populated (000001) state, but they were analysed using a six times smaller weighting factor ðwi Z 1=s2i Þ. The spectra of the (000010) and (000001) states were analysed fitting the rotational constant B, the quartic and sextic centrifugal distortion constants D and H, and the l-type doubling parameters qt, and qtJ. In addition, the high-order l-type parameter q11JJ had to be included in the fit of the (000001) state to reproduce the measured transition frequencies within the experimental uncertainties. Measurements up to 190 GHz have been performed for the couple of bending fundamentals (001000) and (000100), spanning J values from 24 to 73. The recording of the JZ44)43 transition is reported in Fig. 4, which shows that these two states are characterized by nearly equal values of the at vibration– rotation coupling constant and qt l-type doubling constant, as it was found for the corresponding pair of states of normal cyanodiacetylene [4,5] and of the isovalent carbon chain HC5P [11]. The observed transition frequencies have been analysed as for the v11Z1 and v10Z1 states. The results of the least-squares fits for the singly excited bending states are collected in Table 2 along with the

740 720

(6,8,10)

C30

700 (6,7,10)

Vibrational energy / cm−1

680

C 30

660 640 620

(6,7,11)

C30

(010001)

C 60

(000006) (001001)

(100000) 600

(6,8,11) C30

580 560 (6,10,10)

540

C30

520 500

(000020)

Fig. 3. Vibrational energy level diagram for the resonance system of DC5N. Arrows indicate the vibrational interactions taken into account. Dashed lines indicate unobserved states.

this resonance system, because they are connected to the (010001) and (010010) states, respectively, through matrix elements expressed by Eq. (3). No line was measured for these highly-excited states because their spectroscopic constants can be very well extrapolated from the results obtained for states of lower vibrational excitation. The scheme of the vibrational interactions taken into account for the analysis of the main resonance system of DC5N is summarized in Fig. 3. Finally, quartets of lines belonging to the (000110) combination were also identified, but it was not possible to achieve a satisfactory fit of the measured transition frequencies, probably because of some high-order rovibrational interaction with one or more than one nearly degenerate states lying in the 700 cmK1 energy region.

(000100)

1−

1+

(000100) 1−

1+

(001000)

(001000) (100000)

5. Experimental results Over 900 transition frequencies of vibrationally excited DC5N have been measured and analysed, and the complete list is available as Electronic Supplementary Material. In the following subsections, some details of the analysis performed for the various vibrational states are given.

111954

111964

111974

111984

111994

Frequency / MHz Fig. 4. Recording of the JZ44)43 rotational transition of DC5N in the vibrationally excited states (000100), (001000), and (100000). Single scan with time constant 0.1 s and baseline subtracted.

L. Bizzocchi et al. / Journal of Molecular Structure 780–781 (2006) 148–156

153

Table 2 Spectroscopic constants determined for the (000001), (000010), (000100), and (001000) singly excited states of DC5N

Bv (MHz) av (MHz) Dv (Hz) Hv (mHz) dJL(tt) (kHz) qt (MHz) qtJ (Hz) qtJJ (mHz) s (kHz) No. of lines J range

Ground statea

(000001)

(000010)

(000100)

(001000)

1271.057842(19)

1273.662796(23) K2.605 28.3010(14) 2.653(25) K3.065b 1.094211(46) K0.9929(28) 1.425(50) 12.6 61 24–176

1273.345332(23) K2.288 27.4844(13) 1.632(23)

1272.498022(44) K1.440 27.1679(60) 1.388b

1272.587542(33) K1.530 27.1781(44) 1.388b

0.470085(26) K0.16271(59)

0.305033(89) K0.053(12)

0.279126(66) K0.1049(89)

7.0 46 24–176

10.8 36 24–73

7.9 35 24–73

26.8896(12) 1.388(22)

6.4 42 10–179

Standard errors in units of the last digit are given in parentheses for the fitted parameters. a From Ref. [6]. b Fixed in the analysis.

experimental values of the vibration–rotation coupling constants a8Ka11. For the sake of completeness, the spectroscopic parameters previously determined for the ground vibrational state [6] are also reported in the first column of the same table. For the overtone bending states (000002) and (000003) we have performed measurements up to JZ73, thus making possible an accurate analysis of the l-type resonance effects among the various sublevels produced in these states by progressive excitation of the lowest-energy bending mode. The constants q11 and q11J were fitted for the (000003) state, but constrained to interpolated values for the (000002) state. Accurate determination of the xL(11,11) and dJL(11,11) constants have been obtained for both states. The results of the least-squares fit performed for these overtone bending states are reported in Table 3. An estimate of the g11,11 value can be derived by the change of the rotational constant B produced by progressive excitation of the v11 vibrational mode. The experimental results of the present work make it possible to calculate DB(v11) values from v11Z1 to v11Z3, and a linear regression analysis of these data yields g11,11Z 3.705(3) kHz, a value slightly smaller than that obtained previously [5] for the normal isotopomers (4.115 kHz). The quadruplets of lines belonging to the combination states (000011) and (000101) have been also identified in the frequency range 60–190 GHz. No anomaly was observed in the spectral patterns, and the measured transition frequencies were simply analysed taking into account the usual rotational and vibrational l-type resonance effects. The qt constants involved in the off-diagonal matrix elements were held fixed at the values determined for the singly excited bending states when the lines of the (000011) state were analysed, but we found it useful to release q11 in the analysis of the (000101) state transitions, in order to improve the agreement between measured and calculated frequencies. The change in the q11 value of the latter state is very small, as expected for a normal vibrational dependence of l-type doubling constants. The results of the least-squares fits are given in Table 4.

5.2. The interacting states (010000) and (000005) The doublets of rotational lines belonging to the (010000) bending fundamental have been readily identified with the help of the theoretical values of the a7 and q7 constants of Table 1. Both 1C and 1K components show evidence of a very localised perturbation which produces small but significant deviations of the rotational lines from the predicted unperturbed positions. The anomalies observed are indicative of a rovibrational avoided crossing with a state of lower vibrational energy, but greater rotational constant. The most perturbed line is the JZ 62)61 transition of the (010000)1C sublevel, which exhibits a low-frequency shift of 13.7 MHz. Nearly symmetric perturbations were observed also for the two jl11jZ1 components of the nearby (000005) overtone bending state, which can be coupled to the (010000) state through the high-order H^ 60 term of the Hamiltonian. Measurements for this resonance system have been performed spanning J values from 24 to 73. The measured transition frequencies have been simultaneously analysed coupling the interacting states through the off-diagonal Table 3 Spectroscopic constants determined for the (000002) and (000003) overtone states of DC5N

Bv (MHz) Dv (Hz) Hv (mHz) xL(11,11) (GHz) dJL(11,11) (kHz) q11 (MHz) q11J (Hz) q11JJ (mHz) s (kHz) No. of lines J range

(000002)

(000003)

1276.275172(43) 29.7397(40) 3.918a 5.89693(29) K3.087(11) 1.098671a K1.0023a 1.425a 8.5 50 24–73

1278.894946(34) 31.1934(31) 5.183a 5.87710(38) K3.1087(48) 1.103130(34) K1.0117(43) 1.425a 7.1 55 32–73

Standard errors in units of the last digit are given in parentheses for the fitted parameters. a Fixed in the analysis.

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L. Bizzocchi et al. / Journal of Molecular Structure 780–781 (2006) 148–156

Table 4 Spectroscopic constants determined for the (000011) and (000101) bending combination states of DC5N

Bv (MHz) Dv (Hz) Hv (mHz) xL(t,11) (GHz) dJL(t,11) (kHz) dJL(11,11) (kHz) rt,11 (GHz) rt,11J (kHz) qt (MHz) qtJ (Hz) q11 (MHz) q11J (Hz) q11JJ (mHz) s (kHz) No. of lines J range

(000011)

(000101)

1275.958610(33) 28.9080(44) 2.897a 6.89812(74) 3.050(40) K3.065a K4.71933(82) K0.899(25) 0.470085a K0.16271a 1.094211a K0.9929a 1.425a 10.9 68 24–73

1275.107361(39) 28.5800(55) 2.653a 7.4063(19) 7.604(62) K3.065a K8.4462(33) K9.810(32) 0.305033a K0.053a 1.097802(93) K0.9929a 1.425a 13.8 76 24–73

Standard errors in units of the last digit are given in parentheses for the fitted parameters. a Fixed in the analysis.

matrix element given by Eq. (3), and the fitted parameters are reported in Table 5 together with the value of the a7 vibration–rotation coupling constant. Together with the usual single-state parameters, accurate values of the unperturbed vibrational energy differences, DGv, and of the sextic coupling coefficient C60 have been obtained. 5.3. The main resonance system Taking into account the off-diagonal matrix elements given by Eqs. (1a)–(c) and (4a) and (b), a rather large rovibrational energy matrix is produced. The (100000) stretching state is connected through cubic anharmonic Table 5 Spectroscopic constants determined for the resonance system (010000)– (000005) of DC5N (010000) Bv (MHz) av (MHz) Dv (Hz) Hv (mHz) xL(11,11) (GHz) dJL(11,11) (kHz) qt (MHz) qtJ (Hz) qtJJ (mHz) DGvb (cmK1) C60 (MHz) s (kHz) No. of lines J range

Interaction

1271.861734(37) K0.804 26.5046(49) 1.388a

(000005) 1284.157030(30) 34.1777(40) 7.713a 5.84151(14) K3.1308(14) 1.112110(28) K1.0198(42) 1.425a

0.250844(28) 0.0a 0.0a 1.946663(23) 13.443(23) 8.9 40 24–73

69 31–72

Standard errors in units of the last digit are given in parentheses for the fitted parameters. a Fixed in the analysis. b Vibrational energy difference between the upper (010000) state and the lower (000005) state.

interactions to the kZ0C(SC symmetry) sublevels of the bending states (000020), (001001), (010001), (001010) and (010010). Because of the sextic anharmonic interaction described in Section 4.2, the two states (000015) and (000006), for which no line was recorded, have been also included in the resonance system in order to fit properly the perturbed spectral patterns of the (010010) and (010001) bending combination states. The cubic anharmonic interactions which mix the (100000) stretching state with various bending excited states push the (100000) lines at frequencies higher than those of the respective ground state lines, thus producing a negative effective value for the a6 vibration–rotation coupling constant. Fig. 4 shows that the JZ44)43 transition of the (100000) stretching state is located in the proximity of the same transitions of the (001000) and (000100) bending fundamentals, which corresponds to an effective a6 value of ca. K1.3 MHz. Since most of the vibrational states considered produce several substates because of different k and lt values, 21!21 (e symmetry) and 18!18 (f symmetry) rovibrational energy matrices were actually diagonalized for each J value to get the required eigenvalues. The vibrational energies Gv of the resonant states were generally held fixed at the values calculated using the theoretical ur constants, but when nearly degenerate states were considered, the corresponding Gv values were also optimized. More than 400 transition frequencies were simultaneously analysed, fitting independently a total number of 40 parameters. Many other spectroscopic constants were constrained to values derived from states of lower vibrational excitation. The standard deviation of the fit was 14.5 kHz. The spectroscopic constants determined or assumed for each vibrational state of the main resonance system of DC5N are collected in Tables 6 and 7. The values obtained for the coefficients included in the off-diagonal matrix elements are listed in Table 8, where a simplified notation is employed to identify the interacting states. The experimental value of the a6 vibration–rotation coupling constant agrees very well with that provided by the CCSD(T) calculations (cf. Table 1), and no serious anomaly appears in the Dv and qt constants fitted for the various overtone and combination states involved in the resonance system, indicating that the main resonance effects have been well treated. From the optimized set of unperturbed vibrational energies it is possible to derive experimental values for the energy differences v6 Kðv8 C v11 ÞZK0:72 and v6 Kðv7 C v11 ÞZK9:20 cmK1 , which are near to the corresponding values of K2.6 and K10.2 cmK1 calculated using the CCSD(T)/cc-pVQZ harmonic wavenumbers of Table 1. A few parameters of the unobserved states (000015) and (000006) were also adjusted to obtain a satisfactory fit of the perturbed patterns exhibited by the quartets of lines belonging to the (010010) and (010001) states. Using Eqs. (2a) and (b) it is possible to derive from the fitted C30 parameters the absolute values of the corresponding

L. Bizzocchi et al. / Journal of Molecular Structure 780–781 (2006) 148–156

155

Table 6 Spectroscopic constants determined for the (000020), (100000), (001001), and (010001) resonant states of DC5N (000020) Gv (cm ) Bv (MHz) av (MHz) Dv (Hz) Hv (mHz) xL(11,11) (GHz) xL(10,10) (GHz) xL(t,11) (GHz) dJL(11,11) (kHz) dJL(t,11) (kHz) hJL(10,10) (Hz) rt,11 (GHz) rt,11J (kHz) q11 (MHz) q11J (Hz) q11JJ (mHz) qt (MHz) qtJ (Hz) No. of lines J range K1

a

494.2 1275.609494(68) 28.182(14) 1.866a

(100000) a

601.7 1270.05737(24) 1.001 26.437(30) 1.388a

(001001)

(010001)

602.4287(46) 1275.203601(55)

610.911(25) 1274.462535(50)

28.5612(76) 2.653a 5.91676a

27.9374(71) 2.653a 5.91676a

5.432(15) K3.065a 2.119(78)

6.907(16) K3.065a K5.402(54)

K3.243(28) 0.0a 1.094211a K0.9929a 1.425a 0.27665(20) K0.1049a 78 24–73

0.915(29) 0.0a 1.094211a K0.9929a 1.425a 0.250884a 0.0a 77 24–73

19.00(37)

K0.0784(45)

0.470085a K0.16271a 48 24–73

18 24–73

Standard errors in units of the last digit are given in parentheses for the fitted parameters. a Fixed in the analysis.

normal-coordinate cubic force constants, which are jf6,10,10jZ65.5 cmK1, jf6,7,11jZ4.30 cmK1, jf6,8,11jZ 3.48 cmK1, jf6,7,10jZ26.3 cmK1, and jf6,8,10jZ27.7 cmK1. The corresponding CCSD(T)/cc-pVQZ values are 96.5, 3.8, 5.2, 8.8, and 17.6 cmK1, respectively. The agreement is acceptable for the constants involved in the strongest resonances, that are f6,10,10, f6,7,11, and f6,8,11, but less satisfactory for f6,7,10, and f6,8,10, which are responsible of the

weak anharmonic coupling between the (100000) stretching state and the (010010) and (001010) bending combinations. The latter two states are located near 750 cmK1, where the density of states is very high, and they might be affected by further rovibrational interactions not included in the present analysis. The related C30 coefficients should therefore be considered as effective parameters, since they might adsorb the effects of several perturbations, thus providing not

Table 7 Spectroscopic constants determined for the (000006), (001010), (010010), and (000015) resonant states of DC5N

Gv (cmK1) Bv (MHz) Dv (Hz) Hv (mHz) xL(11,11) (GHz) xL(10,10) (GHz) xL(t,10) (GHz) dJL(11,11) (kHz) dJL(t,10) (kHz) rt,10 (GHz) rt,10J (kHz) q11 (MHz) q11J (Hz) q11JJ (mHz) q10 (MHz) q10J (Hz) qt (MHz) qtJ (Hz) No. of lines J range

(000006)

(001010)

(010010)

(000015)

607.646(25) 1286.7620a 35.589a 8.978a 5.8604a

748.1a 1274.864305(39) 27.6591(55) 1.632a

755.7a 1274.166184(42) 27.0517(60) 1.632a

19.00a 10.599(17)

19.00a 23.450(23)

29.727(39) K7.129(40) 0.0a

K8.142(20) K8.138(46) 0.0a

0.470085a K0.16271a 0.279126a K0.1049a 104 24–73

0.470085a K0.16271a 0.250844a 0.0a 110 24–72

753.82501(78) 1286.4445a 34.773a 7.957a 5.84151a 19.00a 6.9509(27) K3.1308a 3.050a K4.5620(15) K0.899a 1.11211a K1.02a 1.425a 0.470085a K0.16271a

K3.1525a

1.11657a K1.029a 1.425a

Standard errors in units of the last digit are given in parentheses for the fitted parameters. a Fixed in the analysis.

156

L. Bizzocchi et al. / Journal of Molecular Structure 780–781 (2006) 148–156

Table 8 Off-diagonal coefficients determined for the main resonance system of DC5N Interacting states

Parameters

Fitted values

Units

(2v10)K(v6) (v6)K(v8Cv11) (v6)K(v7Cv11) (v6)K(v8Cv10) (v6)K(v7Cv10) (v7Cv11)K(6v11) (v7Cv10)K(v10C5v11)

ð6;10;10Þ C30 ð6;8;11Þ C30 ð6;7;11Þ C30 ð6;8;10Þ C30 ð6;7;10Þ C30

8.1836(21) 0.87090(16) 1.0741(37) 6.9331(40) 6.5316(75) 13.01(23) 13.969(22)

cmK1 cmK1 cmK1 cmK1 cmK1 MHz MHz

C60 C60

Standard errors in units of the last digit are given in parentheses for the fitted parameters.

completely reliable values of the corresponding cubic force constants.

6. Conclusion The present paper extends the study of the rotational spectra of cyanodiacetylene to the vibrationally excited states of the deuterated variant DC5N, for which only ground-state data were reported previously [6]. A total number of 16 vibrational states has been investigated, which lie in the wavenumber range from 100 to 760 cmK1 above ground. As already observed for the normal isotopomer [5], the high density of states existing above 500 cmK1 produces numerous accidental near-degeneracies which cause anomalies in the observed spectra. Their assignment and analysis have been facilitated by the availability of accurate theoretical predictions for vibrational energies, cubic normal coordinate force constants, and various vibration–rotation coupling parameters derived from the cubic force field reported in [5]. The comparison between the main resonance effects observed in HC5N and DC5N, respectively, shows two significant differences. First, it can be noted that passing from HC5N to DC5N the u7 harmonic wavenumber decreases from 650.5 to 508.6 cmK1, which makes the (010001) combination of DC5N nearly degenerate with the v6Z1 stretching state, thus producing a strong anharmonic resonance which is not present in HC5N. On the contrary, in DC5N there is no evidence of the highorder Coriolis resonance which was observed in HC5N between the v8Z1 and v10Z2 states. In both isotopic variants these levels are nearly degenerate, but with inverted positions. In DC5N it results 2u10Ku8ZK6.8 cmK1, but the v10Z2 state is actually pushed down by the Fermi resonance with the v6Z1 stretching state, thus making the Coriolis interaction with the v8Z1 state negligible. The opposite effect is instead observable in HC5N, for which 2u10 is greater than u8 [5].

Acknowledgements L. B. and C.D.E. gratefully acknowledge financial support from MIUR and from the University of Bologna (Funds for Selected Research Topics). Thanks are due to the Fonds der Chemischen Industrie for providing support to P.B.

Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.molstruc.2005. 06.050

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