5 August 1994
CHEMICAL PHYSICS LETTERS
Chemical Physics Letters 225 ( 1994) 480-485
Large-scale ab initio calculations of spectroscopic constants for CNCN Peter Botschwina Institut fir Physikakwhe Chemie, Universitdt Giittingen, D-37077 Gdttingen, Germany Received 13 May 1994
Various spectroscopic constants of CNCN have been calculated by means of the single, double and perturbative triple excitation coupled cluster (CCSD (T) ) method. Throughout, good agreement with experiment is obtained and many predictions for isotopic species are made. The recommended equilibrium geometry, derived by combination of experimental and theoretical data,isR,,(C,,,N,,,)=l.l802A,R,, (N~,&)=1.3121 AandR,, (C~z,N~2,)=1.1584A.Theequilibriumdipolemoment is predicted to be A= - 0.701 D, with the positive end at the terminal carbon site. The corresponding SCF value is more than twice aa large.
1. Introduction Isocyanogen (CNCN), a less stable isomer of cyanogen (NCCN ) , has attracted much interest over the last few years, both experimentally [ l-l 3 ] as well as theoretically [ 14-221. The most extended previous ab initio calculations [ 19,221 were carried out by the coupled electron pair approximation [ 23 1, version 1 ( CEPA- 1) , making use of basis sets of 104
and 84 contracted Gaussian-type orbitals ( cGTOS) for linear and nonlinear nuclear configurations, respectively. On the basis of the CEPA-1 calculations, we predicted Fermi resonance interaction between v3 and 2 v4 which was overlooked in the earlier spectra ,butconfirmedlateron [9,11-131. With recent developments in hardware and software, much more extended ab initio calculations are feasible and will form the contents of this paper. Particular emphasis will be devoted to the calculation of an accurate quadratic force field from which accurate harmonic vibrational wavenumbers may be obtained. Reliable experimental values of the latter are
so far available only in two cases, o3 and 0, [ 12 1. These were derived by analysis of the Fermi resonance (FR) system mentioned above. Combination of the new force constants with the cubic coupling terms from our previous work [ 221 will enable us to calculate more accurate values for the vibration-rotation coupling constants than previously [ 221 and, by combination with experimental ground-state rotational constants, determine a very accurate equilibrium geometry ( z 0.000 18, accuracy in bond length). In addition, an accurate value for the equilibrium dipole moment will be reported.
2. Details and results of calculations The potential energy hypersurface in the near vicinity of the equilibrium structure has been calculated by the CCSD (T ) method. This acronym stands for coupled-cluster theory with single and double excitation operators plus a quasi-perturbative treatment of the effects of connected triples [ 241. The
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P. Botschwina /Chemical Physics Letters 225 (I 994) 480-485
present CCSD (T) calculations have been carried out with the MOLPR092 suite of programs ‘. The implementation of the CCSD method has been described by Hampel et al. [ 251; the contribution from connected triples was added by Deegan and Knowles
WI. For linear arrangement of the four nuclei the present CCSD (T) calculations make use of a basis set of 220 cGTOs, with real spherical harmonics for the angular parts of the functions. It corresponds to Dunning’s [ 27 ] correlation consistent polarized valence quadruple-zeta (cc-pVQZ) basis set and is described as ( 12s, 6p, 3d, 2f, lg) in contraction [ 5,4, 3,2, 11. All electrons are correlated in these calculations. Although the cc-pVQZ basis was not designed for the description of core and core-valence correlation effects it worked very well in all the cases we have studied so far (see, e.g., Refs. [28-301). E.g., CCSD(T) calculations with this basis set ( 165 cGTOs) for the electronic ground state of C3 [ 311 produced R,=1.29431 A and o,=1211.9 cm-‘, where o1 is the harmonic wavenumber of the symmetric stretching vibration. A much larger basis set of 255 cGTOs which provides extra flexibility to properly describe the effects of core and core-valence correlation effects yields R,= 1.29452 A and o1 = 1208.5 cm-‘, in close agreement with the above values. The CCSD (T) equilibrium geometry for CNCN is: R,&,,N,,,)=l.l8077A, Rzc(N&z,)=l.31138 AandRje (C~2,N~2,)=1.15913A.Thecorresponding total energy and equilibrium rotational constant MHz. The are V,= - 185.482277 E,and&=5173.4 latter agrees closely with our previous recommended value of 5 174.07 MHz [ 221 and the recent experimental value of 5172.60( 16) MHz 1131, with the standard deviation of a least-squares fit to the adjusted rotational constants of an effective Hamiltonian being given in parentheses. The ‘true’ uncertainty of the experimental value is unclear but it may well be of the order of several tenths of a MHz. Making use of our previous results for HCN, HNC and NCCN [ 28,291 we may correct for the slight errors in the CCSD(T) equilibrium structure and ar’ MOLPR092 is a package of ab initio programs written by H.-J. Werner and P.J. Knowles, with contributions of J. Ahnliif, R. Amos, M. Deegan, S. Elbert, C. Hampel, W. Meyer, K.A. Peterson, E.A. Reinsch, R. Pitxer, A. Stone and P.R. Taylor.
rive at Ri,=1.1802 A, R2,=1.3120 A and Rse = 1.158 5 A. The corresponding Be value is 5 174.3 MHz. Calculations at nonlinear geometries were carried out with a reduced basis set of 184 cGTGs in which the g functions were left off. To further reduce the computational expense core electrons were left uncorrelated. CCSD(T) quadratic and diagonal cubic force constants are listed in Table 1 and compared with our previous CEPA- 1 values as well as the recent experimental values [ 13 1. The experimental valence force field is based on anharmonic vibrational wavenumbers for several isotopic species, partly from matrix IR spectra [ 31 with appropriate corrections. Approximately deperturbed v3values were employed but no further corrections for anharmonicity effects were made; therefore, theoretical and experimental force constants are not strictly comparable. The present CCSD(T) values for the diagonal quadratic stretching force constants should be accurate to x 1%. Compared to the previous CEPA- 1 value
Table 1 Quadratic and diagonal cubic force constants for CNCN Force constant L
?I: k k; k k,s, k:
15.8164 15.7938 8.0463 8.5777 18.1303 17.8565 0.4437 0.4037 -0.3928 -0.4117 0.5013 0.4885 0.1401 = 0.1490 0.3851 0.3611 0.0125 0.0135 - 106.59 - 105.39 -47.98 - 52.55 - 123.65 - 120.90
15.11(10) 8.263(96) 17.11(14) 0.631(65) -0.214(84) 0.680(90) 0.1407(26) 0.3605(77) 0.0146(30)
* Force constants are defined as derivatives of the potential energy with respect to the stretching coordinates, taken at equilibrium. Units are aJ A+ where n denotes the number of stretching coordinates involved. b Ref. [ 191. Valence electron correlated. Basis sets: 104 cGTGs for stretching, 84 cGTOs for bending force constants. c This work (see the text). d Effective valence force field [ 13 ] ; standard deviation in units of the least significant figure given in parentheses. ’ Misprinted in Ref. [ 221. The correct value (in au) there should read0.016071 (seealsoRef. ).
P. Botschwina/Chemical PhysicsLetters225 (1994) 480-485
the quadratic force constant for the central bond,
experiences a significant increase by 6.6% which fRzR2, is mainly due to basis set enlargement. A similar situation was found for cyanogen (cf. Refs. [ 19,291). The force constants fRIR, and fRflRaare reduced by 0.1% and 1 .5%, respectively. Likewise, the previous CEPA- 1 values for the off-diagonal quadratic stretching force constants differ only slightly from the present CCSD (T) values. The latter are believed to be accurate to 0.02 aJ A -*. The previous CEPA- 1 value for faa appears to be an underestimate while the present CCSD (T) value is probably slightly too large (by 1%3%). The previous CEPA-1 value for fBp is too large by = 6%; the error in the present CCSD( T) value is estimated to be on the order of 1%. Theoretical and experimental values for various spectroscopic constants of CNCN are listed in Table 2. The present CCSD (T) values for o3 and o4 differ from the experimental values [ 121 by only 1.3 and 5.2 cm-‘, respectively. We now obtain the relationship w3> 2w4 and thus give theoretical support to the analysis of the FR system made by Winnewisser and co-workers [ 11,121. Very good agreement with experiment is also obtained for the I-type doubling constants q; and qj, with differences between CCSD( T) and experimental values not exceeding 31. The calculation of the vibration-rotation coupling Table 2 Spectroscopic constants for CNCN
WI(cm-‘) w2 (cm-‘) a3 (cm-‘) w, (cm-‘) us (cm-‘) B. (MHz) IV, (cm-‘) 01 (MHz) a, (MHz) a3 (MHz) a, (MHz) as (MHz) q: (MHz) 45 (MHz) 4: (Hz) 4: (Hz) l
CCSD(T)/ CEPA-1 b
2347.7 2100.6 921.9 477.5 194.0 5138.6 38.8 26.52 18.17 13.99 -9.77 - 19.63 4.54 9.40 - 3.20 -34.8
2357.0 2102.4 941.0 467.9 198.5 5173.2 42.7 27.80 18.13 13.72 - 10.55 - 19.44 4.62 9.32 - 3.65 -33.4
Refs. [ 19,221. bThiswork (seethetext).
939.7(11) 462.7(4) 5172.60(16) 44.97( 13) 27.598( 16) 18.434(29) 14.088(85) -11.83(21) -19.516(31) 4.6854( 1) 9.5740(2) -4.43(S) -36.0(2) ‘Refs. [12,13].
constants cr, and those small I-type doubling constants describing the dependence on rotational quantum number J, termed qf, by means of conventional perturbation theory in normal coordinate space requires the knowledge of the complete cubic force field. We have therefore completed the set of CCSD( T) force constants given in Table 1 with the set of offdiagonal cubic terms from our previous CEPA- 1 calculations [ 19,22 1. The resulting ar, and qf values are compared with the previous CEPA-1 values and experiment in Table 2. Compared with the former some significant improvement has been made for cy4.The remaining difference from experiment of x 1 MHz appears to be tolerable since the present theoretical value may well be in error by a few tenths of a MHz and since one has to keep in mind that the theoretical value, obtained by second-order perturbation theory, and the experimental value do not exactly correspond to the same quantities (even though some higher-order y terms have been taken into account in the analysis of the experimental data [ 13 ] ) . For all other cy, values agreement between theory and experiment is excellent. In view of the smallness of the qf values differences of 18% for q< and of 7% for q: have to be considered to be very satisfactory. Table 2 lists also theoretical and experimental values for the Fermi constant of the v3/2v4 FR system which is calculated as W,= 4 1qj3,+,)& where #344is the relevant cubic normal coordinate force constant. Agreement between the present CCSD (T) value and experiment [ 12 ] is very good. Calculated spectroscopic constants for six further isotopomers of isocyanogen along with the few experimental values available at present are given in Table 3. Our calculations clearly support the assump tion of using equal W, values for CrSNCi5N and CNCN which was made in Ref. [ 12 1. Using the present ar, values to calculate the differences B, - B,, by means of the formula
where dj is a degeneracy factor ( 1 for stretching, 2 for bending modes) and making use of experimental B. values [ 6,7 ] we arrive at the Be values given in Table 4. These were employed in the calculation of a very accurate equilibrium structure which was obtained by least-squares fit to the corresponding six equilibrium
P. Botschwina /Chemical Physics L.&ten 225 (1994) 48&485
Table 3 Spectroscopic constants for different isotopomers of isocyanogen a ‘“CNCN
co, (cm-‘) w, (cm-‘) w3 (cm-‘)
2353.4 2070.9 927.9
2307.4 2093.4 936.2
2345.6 2072.0 935.8
2339.2 2093.5 928.7
2301.8 2064.0 923.0
26.60 17.90 (17.94) b 12.91
27.01 17.65 (17.82) b 13.75
-3.32 - 30.7
Cl5NCL5N 2326.9 2065.0 923.5 (922.3) 462.3 (457.4) 194.6 42.2 (45.1) 26.75 16.85 13.01 (13.36) - 10.16 (-11.34) - 18.06 (- 18.25) 4.34 (4.41) 8.85 (9.08) -3.34 (-3.71) -30.1 (-31.9)
* Experimental values [ 7,9,12,13,32] in parentheses. b Calculated as differences of rotational constants, thus neglecting nonlinear terms in the vibrational quantum numbers.
Table 4 Ground-state and equilibrium rotational constants (in MHz) and centrifugal distortion constants (in Hz) for different isotopomers of isocyanogen
&dew) ’ Bee 0, &(exp)
5174.138 5173.984 670 738
4997.172 4996.785 622 686
5154.403 5154.225 668 734
5148.897 5149.033 667 732
5015.918 5015.721 628 691
(4976.599) b (4976.188) * 620
4989.883 4989.966 624 685
‘Refs. [9,13,32]. b Recommendedvalue (see the text). c From experimental B. and theoretical ASo values. * Calculated from the final equilibrium structure. moments of inertia. The resulting equilibrium geometry is Rlc= 1.180196 A, RZc= 1.312150 A and R >= 1.158413 A. This constitutes our recommended equilibrium structure. The systematic errors in the individual equilibrium bond lengths are estimated to be on the order of 10m4A. Compared with the corrected CCSD (T) equilibrium structure men-
tioned above there are differences of less than 0.0002 A in all three bond lengths. The major difference from our previous mixed experimental/theoretical equilibrium structure [ 221 concerns RI, where it amounts to 0.0011 A.Thedifferences in Rzc and Rk are 0.0005 A and 0.0003 A, respectively. From the recommended equilibrium geometry of this work and the
P. Botschwina /Chemical Physics Letters 225 (I 994) 480-485
present a, values we may calculate accurate values for B. and B,, of 13CNi3CNwhich are listed in parentheses in Table 4. The latter value should be accurate to ~0.01 MHz. The ratio Do/D, is a rather sensitive indicator of the degree of floppiness of a linear molecule. In normal semirigid linear molecules it has a value around 1.05 (see, e.g. Ref. [ 331). Making use of our CCSD (T) quadratic force field to calculate the equilibrium centrifugal distortion constant D, and employing experimental ground-state values Do (see Table 4) we arrive at a ratio of 1.10 for all three isotopomers for which accurate experimental Do values are available. The equilibrium electric dipole moment of CNCN has been calculated with a flexible basis set of 220 cGTOs. It consists of the (s, p, d) part of the augmented correlation consistent polarized valence quadruple-zeta basis set of Dunning and co-workers [ 341 plus the f functions from the cc-pVQZ basis [ 271. Valence electrons were correlated in these calculations. According to our experience with other molecules like HCN [ 35 1, CCSD (T ) calculations of this quality should yield pe values accurate to = 0.01 D. Comparison of the pe values obtained with different methods is made in Table 5. Electron correlation is important; the SCF value is too large by more than a factor of two. The CEPA-1 result is intermediate between CCSD and CCSD(T); a similar situation was found in the related molecules H&NC [ 36 ] and CNC3N [ 37 1. Second-order perturbation theory (MP2) over-estimates the electron correlation effect by 0.24 D. The CCSD(T) k value almost coincides with the Table 5 Equilibrium electric dipole moment of CNCN as obtained by different methods with a basis set of 184 cGTOS a Method
SCF MP2 CCSD
- 1.5744 -0.4598 -0.8258
CEPA- 1 CCSD(T)
-0.7775 b -0.7011
’ Calculated at the recommended equilibrium geometry from this work. The negative sign means that the positive end of the dipole is at the terminal carbon site. b Previous CEPA-1 value ( 104 cGT0 basis), calculated at a slightly different geometry: -0.704 D [ 191.
experimental ground-state value [ 6 1. According to our calculations the parallel component of the electric dipole moment experiences little change upon bending the molecule away from linearity by 5”. It is therefore not unlikely that the difference between A and & is only of the order of 0.0 1 D.
Acknowledgement Thanks are due to Professor H.-J. Werner (University of Stuttgart) for providing us with a copy of MOLPR092. Financial support by the Deutsche Forschungsgemeinschaft and the Fonds der chemischen Industrie is gratefully acknowledged. We thank Professor M. Winnewisser (Justus-Liebig-Universitat, Giessen) for providing us with experimental data prior to publication.
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