Equilibrium structure of methylcyanide

Journal of Molecular Spectroscopy 240 (2006) 260–264 www.elsevier.com/locate/jms

Note

Equilibrium structure of methylcyanide Cristina Puzzarini *, Gabriele Cazzoli Dipartimento di Chimica ‘‘G. Ciamician’’, Universita` di Bologna, Via Selmi 2, I-40126 Bologna, Italy Received 7 September 2006; in revised form 10 October 2006 Available online 17 October 2006

Abstract The quadratic and cubic force fields of methylcyanide have been calculated at the MP2 and CCSD(T) levels of theory employing a core-valence basis set of triple-zeta quality. Semi-experimental equilibrium structures have then been derived from the experimental ground-state rotational constants available for various isotopologues and the corresponding vibrational corrections calculated from the ab initio force fields. These structures have been found in excellent agreement with the pure ab initio structure calculated at the CCSD(T) level of theory using a basis set of sextuple-zeta quality and including core correlation corrections. Ó 2006 Elsevier Inc. All rights reserved. Keywords: Anharmonic force field; Ab initio; Equilibrium structure; Methylcyanide

The molecular structure of methylcyanide, CH3CN, was already investigated in the past. The main contributions that should be mentioned are the experimental determination carried out by Le Guennec et al. in 1992 [1] as well as the theoretical evaluation by Margule´s et al. in 2000 [2]. In Ref. [1] the ground-state rotational spectra of CH2DCN and its 13C and 15N substituted species have been measured, and accurate rotational and centrifugal distortion constants determined. In addition, making use of their results and those available in the literature, the authors derived various experimental structures: r0, rs, r,I, rqm , and rð1Þ m . In particular, the latest can be considered a very good approximation of the equilibrium geometry. Unfortunately, as stressed in Ref. [2], this structure is affected by large uncertainties, and this reason essentially stimulated the accurate ab initio investigation on CH3CN carried out in Ref. [2]. In that study, the equilibrium C–C bond lengths for a large set of molecules were theoretically evaluated accounting for the extrapolation to the complete valence basis set limit, the effect of additional diffuse functions and the core correlation corrections. *

Corresponding author. Fax: +39 051 209 9456. E-mail address: [email protected] (C. Puzzarini).

0022-2852/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2006.10.005

Since the combination of experimental ground-state rotational constants with calculated vibrational corrections has turned out to be the best approach to accurately determine ‘‘experimental’’ structures for polyatomic molecules (see for example Refs. [3,4] and references therein), we decided to apply this procedure to the evaluation of the equilibrium structure of methylcyanide as ground-state rotational constants are available for 17 isotopic species. Therefore, in the present study the anharmonic force field of CH3CN has been accurately calculated and used to determine such vibrational corrections. Furthermore, improved pure ab initio results for equilibrium geometry are also presented. Geometry optimizations have been carried out with the MOLPRO suite of programs [5], employing the coupledcluster level of theory with single and double excitations, and a quasiperturbative account for triples substitutions [CCSD(T)] [6–8]. Correlation consistent basis sets have been used in the present investigation: the valence cc-pVnZ (n = Q, 5, 6) basis sets [9], and the weighted core-valence cc-pwCVQZ basis [10]. The frozen core (fc) approximation, i.e., correlation of valence only electrons, has mostly been adopted in these computations. To evaluate the corevalence correlation effects on molecular structure, the

C. Puzzarini, G. Cazzoli / Journal of Molecular Spectroscopy 240 (2006) 260–264

geometry optimization has also been carried out correlating all electrons in the case of the core-valence basis set. To obtain a best estimate of the equilibrium structure, making use of the additivity assumption, the core correlation corrections have been added to the CCSD(T)/ccpV6Z geometrical parameters as: re ’ rðV6Z; valenceÞ þ rðwCVQZ; allÞ  rðwCVQZ; valenceÞ;

ð1Þ

where r(wCVQZ, all) and r(wCVQZ, valence) are the geometries optimized at the CCSD(T)/cc-pwCVQZ level correlating all and only valence electrons, respectively. The optimized geometries of methylcyanide obtained at the CCSD(T) level employing different basis sets and the best estimate derived from Eq. (1) are summarized in Table 1. From these results, it is first observed that the valence correlation limit is nearly reached at the (fc)CCSD(T)/cc-pV6Z level; in fact, the changes between r(V6Z) and r(V5z) are very small: the bond lengths decrease ˚ and the \CCH angle by 0.01°. It should by about 0.0002 A also be noted that the core-valence corrections are relevant, ˚ for bond lengths i.e., they are of the order of 0.002–0.003 A and 0.04° for the angle. As far as previous theoretical investigations are concerned, in Ref. [2] geometry optimizations at the MP2 and CCSD(T) levels were carried out employing from double- to quadrupole-zeta basis sets. In addition, a best estimate of the equilibrium structure was obtained accounting for the extrapolation to the complete basis set limit, the effect of additional diffuse functions on nitrogen and the core correlation corrections. This structure is also reported in Table 1, where it is compared with our best estimate. From this comparison, a very good agreement is evident. The anharmonic force fields have been evaluated using the Mainz-Austin-Budapest version of the ACES2 program package [11]. The MP2, i.e., the second-order

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Møller-Plesset perturbation theory [12], and CCSD(T) levels of theory have been employed in such calculations in conjunction with the weighted core-valence cc-pwCVTZ basis [10] correlating all electrons. The harmonic part has been obtained using analytic second derivatives of the energy [13], and the corresponding cubic force field has been determined in a normal-coordinate representation via numerical differentiation of the analytically evaluated force constants as described in Refs. [14,15]. The cubic force fields have been initially obtained for the main isotopic species (i.e., CH3C14N) and then transformed to the normalcoordinate representations of all the other isotopic species for which experimental ground-state rotational constants are available. Subsequently, for each isotopologue the cubic force field has been used to compute vibration– rotation interaction constants air (where r denotes the vibrational mode and i is the inertial axis) using the usual second-order perturbation treatment of the rovibrational problem [16]. The empirical equilibrium structure has then been obtained by a least-squares fit of the molecular structural parameters to the mixed experimental/theoretical equilibrium rotational constants Bie , derived from the experimental ground-state constants Bi0 theoretically corrected for vibrational effects: 1X i Bie ¼ Bi0 þ a: ð2Þ 2 r r The empirical equilibrium structures have been obtained by using the experimental ground-state rotational constants available in the literature for 17 isotopic species [1,17–23] and the corresponding vibrational corrections from the anharmonic force fields computed at either the (all)MP2/ cc-pwCVTZ or (all)CCSD(T)/cc-pwCVTZ levels of theory. It should be noted that the B rotational constants have essentially been employed in the least-squares fits, but also the A and C (when defined) rotational constants have been used when available. It is worth noting that both force

Table 1 Equilibrium structure of methylcyanide

CCSD(T)/cc-pVQZ CCSD(T)/cc-pV5Z CCSD(T)/cc-pV6Z (fc)CCSD(T)/cc-pwCVQZ (all)CCSD(T)/cc-pwCVQZ Best estimatea Best estimateb Empiricalc Empiricald Experimente a

˚) C–N (A

˚) C–C (A

˚) C–H (A

\CCH (°)

Reference

1.1585 1.1579 1.1577 1.1581 1.1557 1.1553 1.1557 1.1552(4) 1.1554(3) 1.156(2)

1.4634 1.4628 1.4625 1.4631 1.4596 1.4590 1.4595 1.4585(4) 1.4586(3) 1.457(2)

1.0882 1.0880 1.0880 1.0882 1.0867 1.0865 1.0865 1.0869(1) 1.0865(1) 1.087(3)

109.83 109.81 109.80 109.83 109.87 109.84 109.851 109.84(1) 109.85(1) 110.1(3)

This This This This This This [2] This This [1]

work work work work work work work work

Evaluated from Eq. (1). Evaluated from Eq. ‘‘CCSD(T)/cc-pV1Z(f.c.) + aug(N) + CV corrections’’. See Ref. [2]. c Semi-experimental re (see text). Theoretical force filed at the (all)MP2/cc-pwCVTZ level. The uncertainties reported are three times the statistical errors. d Semi-experimental re (see text). Theoretical force filed at the (all)CCSD(T)/cc-pwCVTZ level. The uncertainties reported are three times the statistical errors. e ð1Þ rm structure. b

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fields provide reliable results, as the residuals are rather small (i.e., about a few kHz). The determined structural parameters are given in Table 1. The comparison of the empirical equilibrium geometries, the best purely theoretical structure obtained in this work and that reported in Ref. [2] shows a very good agreement: the bond lengths ˚ and the \CCH bond angle agree within 0.0004–0.001 A within 0.01°. This result confirms on one hand the good accuracy of the purely theoretical equilibrium geometries obtainable nowadays, and on the other hand the validity of the semi-experimental approach for deriving accurate equilibrium structures. Furthermore, another conclusion can be drawn from the results of Table 1: as already noticed in Ref. [4], the CCSD(T) force field only provides a negligible improvement over the MP2 force field in determining the equilibrium structure. Therefore, the MP2 method appears to be adequate for obtaining the required vibrational corrections. As already mentioned in Ref. [4], this conclusion is particularly important, as for larger and/or less symmetric molecules than methylcyanide the evaluation of a MP2 force field is often still feasible, while computation of a CCSD(T) force field is no longer possible. As concerns the comparison to experiment, as previously mentioned, the best experimental determination available

in the literature is the rð1Þ m structure, which is a quite good approximation of the equilibrium geometry. This result is also given in Table 1. By comparing it to the empirical re structures evaluated in the present investigation, one can notice a perfect agreement, though the accuracy of the present empirical equilibrium structure is about one order of magnitude higher due to the more consistent treatment of vibrational corrections. For the main isotopic species the evaluation of the harmonic (fij) and cubic (fijk) force constants also allow the derivation of the semidiagonal quartic (fijkk) normal-coordinates force constants. Therefore, in addition to the centrifugal distortion constants, the vibration–rotation interaction constants, and the harmonic frequencies, also the anharmonic constants and frequencies can be derived from the computed force fields using the second-order rovibrational perturbation theory [16]. The experimental and computed spectroscopic parameters for the main isotopic species are compared in Table 2: this comparison permits to further check the quality of the harmonic as well as anharmonic part of the theoretical force fields. In general, from Table 2 it is evident that the discrepancies between the experimental and ab initio values are only a few percent. In particular, the agreement between computed and experimental ground-state rotational con-

Table 2 Spectroscopic constants of CH3C14N Parameters a

A0 (MHz) B0 a (MHz) A0  Ae (MHz) B0  Be (MHz) DJ (kHz) DJK (kHz) DK (kHz) x1 (cm1) x2 (cm1) x3 (cm1) x4 (cm1) x5 (cm1) x6 (cm1) x7 (cm1) x8 (cm1) m1 (cm1) m2 (cm1) m3 (cm1) m4 (cm1) m5 (cm1) m6 (cm1) m7 (cm1) m8 (cm1) a

(all)MP2/cc-pwCVTZ

(all)CCSD(T)/cc-pwCVTZ

Exp.

158196.57 9191.16 1814.94 32.08 3.62 172.67 2715.73 365.28 940.59 1069.01 1422.59 1498.73 2231.80 3108.55 3202.95 368.14 933.58 1047.74 1387.67 1462.99 2189.00 2999.21 3061.64

158068.23 9192.23 1943.28 31.01 3.67 172.40 2690.32 364.90 926.72 1065.56 1419.32 1491.04 2309.99 3073.75 3158.18 367.78 919.80 1044.22 1384.46 1455.26 2267.02 2964.25 3017.16

158099.063(78)b 9198.899132(14)c

3.807523(15)c 177.40737(28)c 2831.8(45)b

365.05(5)d 920.2910(17)e 1041.8446(15)d 1385 1453 2266.6819(4)f 2954 3009

CCN bending (E) CC stretching (A1) CH3 rocking (E) CH3 deformation (A1) CH3 deformation (E) CN stretching (A1) CH stretching (A1) CH stretching (E)

Obtained by adding to the best estimated equilibrium rotational constants (Eq. (1)) the vibrational corrections (at either the MP2 or CCSD(T) level). See text. b Ref. [27]. c Ref. [23]. d Ref. [28]. e Ref. [29]. f Ref. [30].

C. Puzzarini, G. Cazzoli / Journal of Molecular Spectroscopy 240 (2006) 260–264 Table 3 Dipole moment and hyperfine parameters of CH3C14N Parameters

(all)CCSD(T)/cc-pwCVTZ Equilibrium

l (D)

Exp.

Vibrat. averaged

3.90a

3.89b

4.22a 1.94 1.59

– 1.94 1.75

3.92197(13)c

14

N eQq (MHz) CN (kHz) CK (kHz) H Cxx (kHz) Cyy (kHz) Czz (kHz) Cxz (kHz) Czx (kHz)

0.04 1.01 15.72 6.13 0.47

0.04 0.96 14.25 5.52 0.45

4.22473(8)d 1.798(93)d 0.72(37)d

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reported in Table 3 and compared to experiment. With respect to the dipole moment, it should be noted that the discrepancy between experiment and theory is lower than 1%. On the other hand, it has to be mentioned that the vibrational correction seems to be entirely negligible, being lower than 0.3%. As far as the hyperfine parameters are concerned, it is interesting to notice the extremely good agreement between theoretical and experimental value for the nitrogen quadrupole coupling constant. In regards to spin–rotation constants, an agreement within 3r is observed.

0.7(5)e

a

Value obtained at the (all)CCSD(T)/cc-pwCVQZ level of theory. Value obtained by adding to the equilibrium (all)CCSD(T)/ccpwCVQZ value the vibrational correction at the (all)CCSD(T)/ccpwCVTZ level. See text. c Ref. [31]: absolute value. d Ref. [23]. e Ref. [32]: (Cxx + Cyy)/2. b

Acknowledgments This work has been supported by ‘PRIN 2005’ funds (project ‘‘Trasferimenti di energia e di carica a livello molecolare’’), and by University of Bologna (funds for selected research topics and ex-60% funds). The authors gratefully thank Prof. J. Gauss for providing the ACESII program. References

stants is really impressive: the deviations are lower than 0.1%. As far as the quartic centrifugal distortion constants are concerned, one can notice a rather good agreement, being 5% the largest discrepancy. It has also to be noted the rather good agreement between the calculated and the experimental vibrational frequencies mi; in fact, the deviations are of the order of 0.1–0.7%. With respect the comparison between the MP2 and CCSD(T) levels of theory, it can be deduced that, as already noticed for the empirical re structure determination, the MP2 method can be considered sufficient for obtaining quite accurate spectroscopic parameters. Harmonic and anharmonic force constants, and spectroscopic parameters not reported here and/or those of other isotopic species are available from the authors upon request. The ACES2 package [11] also allows to evaluate firstorder and magnetic properties at the CCSD(T) level of theory. More precisely, the dipole moment, the nitrogen quadrupole coupling constant, and the nitrogen and hydrogen spin–rotation tensors of CH3C14N have been computed in the present study. Additionally, the anharmonic force field calculations allow the determination of the zero-point vibrational (ZPV) corrections to these molecular properties. Their addition to the equilibrium values provides the vibrationally averaged values that can thus be directly compared to the available experimental data. These ZPV corrections have been obtained using the perturbational approach described in Ref. [24] for NMR shielding tensors and which has already successfully been applied in Refs. [25,26] for nuclear spin– rotation constants. The equilibrium and vibrationally averaged results for electric dipole moment and spin–rotation constants are

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