J. Phys. Chem. 1993,97, 8937-8943
8937
Accurate Quartic Force Fields and Vibrational Frequencies for HCN and HNC Timothy J. Lee’ NASA Ames Research Center, Moffett Field, California 94035-1000
Christopher E. Dateot ELORET Institute, Palo Alto, California 94303
Bela Gazdy and Joel M. Bowman’ Department of Chemistry, Emory University, Atlanta, Georgia 30322 Received: April 19, I993
The quartic force fields of H C N and H N C are determined using atomic natural orbital one-particle basis sets of spdf/spd and spdfg/spdf quality in conjunction with the CCSD(T) electron correlation method (singles and doubles coupled-cluster theory plus a perturbational estimate of the effects of connected triple excitations). The H C N force field is in good agreement with a recent experimentally derived force field and also with the force field recently computed by Wong and Bacskay. On the basis of the good agreement obtained for HCN, it is argued that the ab initio quartic force field for H N C is superior to a prior force field derived from experiment. The harmonic frequencies of H N C are predicted to be 3822 f 10,472 f 5 , and 2051 f 10 cm-’ for 01, 02, and 0 3 , respectively; the experimentally derived values are above these values and fall outside the estimated uncertainties. Using the quartic force field, spectroscopic constants are predicted for H N C based on a vibrational second-order perturbation theory analysis. It is also asserted that the gas-phase fundamental u3 for HNC is slightly lower than the matrix isolation value. The range of validity of the quartic force fields is investigated by comparison of variational vibrational energies computed with the quartic force fields to those obtained from our recently reported global H C N / H N C potential energy surface and also to experimental data.
Introduction The quantity and quality of experimental data available for the HNC linear molecule are rather limited compared to the data for the more stable isomer HCN. In fact, only one of the HNC fundamentals, VI,has been observed in the gas phase,’ while all three fundamentals have been observed in matrix isolation2 experiments. Creswell and Robiette3 determined a partial quartic force field and equilibrium structure for HNC in 1978, but the sparse experimental data that were available did not allow all of the quartic force constants to be determined. Hence, the accuracy of the remaining force constants is rather limited. The energy difference between the HCN and HNC isomers and the barrier separating them is firmly established.495 We have recently determined an accurate global HCN/HNC potential energy surface6.’ (PES),and in the course of thesestudies we have determined quartic force fields for HCN and HNC. It is the purpose of the present paper to report an accurate quartic force field for HNC from which accurate spectroscopic constants may be derived in order to aid in the interpretation of future high-resolution, rovibrationalspectroscopic studies of HNC. We also present analogous studies of the better characterized HCN molecule in order to estimate the reliability of the results for HNC. Spectroscopic constants from our HCN quartic force field are compared with quantities obtained from a recently determined experimental force field819 and also with the recent high-level calculations of Wong and Bacskay. 10 There have been several studies that have focused on the ab initio determination of quartic force fields (refs 10-1 3). Recently, the accuracy with which fundamental vibrational frequencies have been predicted is remarkable,l+12with typical errors between experiment and theory being less than 10 cm-1. In the present study, we have adopted a similar theoretical approach, and t Mailing address: NASA Ames Research Center,MS230-3, Moffctt Field,
CA 94035-1000.
therefore we believe that the HNC quartic force field reported herein is superior to the experimental 0ne.3 The range of applicability of the quartic force fields is investigated by variationally computingvibrational energy levels up to -10 000 cm-l for HCN and =7000 cm-I for HNC and comparing these to energy levels determined using our global’ HCN/HNC PES. For HCN, this PES has been shown to be very accurate up to 23 000 cm-1, which allows the rangeof validity of the HCN quartic force field to be closely examined. On the basis of this comparison,the range of validity of the HNC quartic force field may be established. The theoretical approach is described in the next section, with results and discussion given in the following section. Conclusions are presented in the final section. Theoretical Approach The ab initio calculationswere performed using the CCSD(T) electron correlation methcd,14 which is singles and doubles coupled-cluster theory augmentedwith a perturbational estimate of the effects of connected triple excitations. The molecular orbitals were taken from the closed-shell restricted H a r t r e e Fock self-consistent-field (SCF) procedure. Two one-particle basis sets have been used in the present study, both of which are atomic natural orbital (ANO) basis sets.ls The A N 0 basis sets are based on van Duijneveldt’sI6 (13s8p/8s) Gaussian primitive functionsfor the heavy atoms and hydrogen, respectively. These sets are augmented with an even-tempered sequenceof (6d4f2g/ 6p4d3f) polarization functions for (C, N) and H, respectively. The polarization orbital exponents are given by u = 2.5”uo for n = 0,...,k where (YO = 0.10, 0.30, and 0.91 for the N d, f, and g functions; (YO = 0.07,0.22, and0.66 for the Cd, f, andg functions; and (YO = 0.10,0.26, and 0.40 for the H p, d, and f functions. The AN01 basis set contains [4~3p2dlf/4~2pld] ANOs on (C, N) and H, respectively, while the AN02 basis set contains [%4p3d2flg/4~3p2dlflANOs. Only the puresphericalharmonic
0022-3654/93/2097-8937$04.00/00 1993 American Chemical Society
8938 The Journal of Physical Chemistry, Vol. 97, No. 35, 1993 TABLE I: Energies (hartree), Equilibrium Structures (A), Rotational Constants (MHz), Harmonic Frequencies (cm-l), and Quadratic Force Constants for HCN and HNC' HCN AN01
AN02 E 0.286119 0.303722 1.1566 rCN 1.1604 1.0663 ~ X H 1.0668 44031 44279 Be 3445.7 w1 (u) 3452.2 727.3 w2 ( 7 ) 725.6 2121.3 wp(u) 2109.7 F, 18.38043 18.57970 F r ~ -0.24319 -0.22163 FRR 6.28431 6.26161 FM 0.25965 0.26044
HNC
exptb
ANOl 0.262722 1.1752 1.1532 1.0650 0.9960 45040 44517 3441.2 3837.3 471.0 727.0 2044.5 2127.0 18.66766 16.79813 -0,20001 -0.34452 6.24845 7.98171 0.25940 0.10004
a
AN02 0.280104 1.1721 0.9961 45244 3821.6 472.0 2051.1 16.88203 -0.28327 7.92650 0.10043
expt' 1.1689 0.9940 45485 3842.3 489.7 2066.6 17.14 -0.29 8.01 0.1076
The total energy is reported as - E + 93). Force constants (in bond coordinates) in units of aJ/A2, aJ/( rad), and aJ/rad*; r = C-N, R = X-H, and the linear bending angle 0 = (T - a),where a is the actual bond angle. All theoretical data obtained at the CCSD(T) level of theory. b References 8 and 9. Reference 3. 0
components of the d-, f-, and g-type functions are included in the basis sets. The ab initio calculations were performed with the TITAN coupled-cluster programs'' interfaced to the SEWARD integral program18and the SWEDEN SCF and transformation programs.19 Quadratic, cubic, and quartic force constants were determined at the CCSD(T)/ANOl level of theory using standard bond coordinates and the linear bending angle B = (?r - a),where a is the actual bond angle (Le., B is zero at linearity). The force constants were obtained by a least-squares fit of a grid of energies centered about the CCSD(T)/ANOl minimum. The grid of points consistedof 60 uniquegeometrical structures (the minimum number for a central differences approach), with a single displacement step size of 0.005 A or radians. Based on the sum of the squared residuals (1.27 X l&14 cm-l for HCN and 1.29 X l&14 cm-l for HNC), the reliability of the fits is quite high. Quadratic force constants were also obtained at the CCSD(T)/ AN02 level of theory in order to establish accurate values. These were obtained by central differences of energies using simple bond coordinates. For the second-order perturbation theory vibrational analysis, the internal coordinate force constants were transformed to Cartesian coordinates using the INTDER programa20 The perturbation theory analysis was then performed using the SPECTRO program.21 For the variational calculations, the quartic force field was transformed into Simons, Parr, Finlan (SPF) bond coordinates22 using the INTDER program. Not surprisingly, it was found that the variational calculations converged more readily with the SPF bond coordinates and also that the range of validity of the quartic force fields was larger.
Results and Discussion A. Geometry,Harmonic Frequencies,and Perturbation Theory Analysis. The CCSD(T)/ANOl and CCSD(T)/ANO2 equilibrium geometries, rotational constants, harmonic frequencies, and quadratic force constants for HCN and HNC are presented in Table I. Note that the F quadratic force constants were obtained by central differences, whereas those reported in Table II,J were obtained by a least-squares fit as described in the previous section. Experimental data, where available, are also presented for comparison. As experimental studies and analyses of these studies are much more plentiful and detailed for HCN relative to HNC, it is expected that the experimental data are much more reliable for the former. It is also expected that the CCSD(T) level of theory should perform equally well for HCN and HNC. This assertion is supported by the earlier CCSD(T) investigations4.6J of HCN and HNC.
Lee et al. TABLE Ik Quartic Force Fields for HCN and HNC' HCN
f" J R
fm fse fm fmR
frm fRRR fM fRM
fm JrrR
f& JRRR
-f
fM JRM f m
HNC
theory
exptb
theory
exptc
18.37500 -0.24319 6.28280 0.25965 -121.6370 0.0839 0.1583 -36.0059 -0.67 19 -0,1648 651.969 -0.315 -1.045 0.212 181.505 0.365 0.358 0.009 0.103
18.66766 -0.20001 6.24845 0.25940 -125.9669 0.4097 0.0402 -35.3095 -0.6498 -0.1900 698.704 -14.079 -0.344 -1.945 177.488 0.468 0.475 0.162 0.020
16.79318 -0,34453 7.97932 0.10004 -110.7609 0.0899 0.1702 -51.0411 -0.7812 -0.1984 593.510 0.471 -1.291 0.345 287.032 1.302 0.409 0.282 0.368
17.14 -0.29 8.01 0.1076 -114.00 0.0 0.0 -52.86 -0.61 -0.35 620.0 0.0 0.0 0.0 254.0 0.0 0.0 0.0 0.68
fw a The theoretical results obtained at the CCSD(T)/ANOl level of theory. The force constants were obtained by a least-squares fit. Coordinates are defined in a footnote to Table I. Units are consistent with an aJ energy unit, an A bond unit, and a radian angleunit. * Reference 9. Reference 3.
Comparison of the CCSD(T)/ANOl and CCSD(T)/AN02 bond distances for HCN shows that augmentation of the oneparticle basis set causes a shortening of the C-N bond distance by 0.0038 A and a shortening of the C-H bond distance by 0.0005 A. These changes are consistent with previous studies that have involved X-Y multiple bonds (where X and Y are B, C, N, or 0) and X-H single bonds.11J2 The most recent and detailed analysis of the experimental equilibrium structure and quartic force field of HCN is due to Carter, Mills, and Handy.8.9 The remaining difference between the CCSD(T)/ANO2 HCN bond lengths and the experimental values (0.0034 and 0.0013 A for rCN and ~ C H ,respectively) is also entirely consistent with the previous studies,' 1,12 providing support for the Carter, Mills, and Handy interpretation. It is interesting that, although the HCN C-H bond distance shortens on going from the ANOl to the A N 0 2 basis set, the harmonic frequency 01 decreases by 6.5 cm-1 due to the coupling between the C-H and C-N modes. The C-N harmonic frequency, 03, increases by 11.6 cm-'. The differences between the ANOl and A N 0 2 harmonic frequencies show that w2 is converged with respect to improvements in the one-particle basis set and that 0 1 and 0 3 are nearly converged. Comparison of the A N 0 2 and experimentalharmonic frequenciesexhibitsa maximum deviation of only 5.7 cm-l (03). Thus, it is evident that the CCSD(T)/ A N 0 2 level of theory provides a very accurate description of the equilibrium geometry and quadratic force field of HCN, and there is every reason to expect similar accuracy for HNC. It should also be noted that the present CCSD(T) results for HCN are in good agreement with those of Wong and Bacskay,lo which is to be expected since the basis sets used in the two studies are comparable. The difference between the ANOl and A N 0 2 C-N bond distance for HNC is similar to the situation for HCN, while the change in the X-H bond distance is dissimilar. In fact, the N-H bond distance actually increases by 0.0001 A on going from the ANOl to the AN02 basis set. The agreement between experiment and the CCSD(T)/AN02 bond distances is also similar to that of HCN for the C-N bond distance (Le., too long by 0.0032 A), but the difference for the N-H bond length (0.0021 A) seems a bit large, suggesting that the experimentally derived equilibrium N-H bond length is slightly too short. The HNC harmonic frequencies exhibit qualitatively similar trends to those of HCN on going from the ANOl to the AN02
Quartic Force Fields of HCN and HNC basis, although the quantitative details are different. The N-H stretch decreases, as did the C-H stretch for HCN, but here the change is -15.7 cm-'-much larger than that for HCN. Alternatively, the increase in the C-N stretch is smaller for HNC (6.6 cm-1) than for HCN. The change in the HNC bending frequency w2 is very small, as for HCN. Comparison of the AN02 and experimentally determined harmonic frequencies shows much larger deviations than were found for HCN. Specifically, the CCSD(T)/ANO2 harmonic frequenciesare 20.7,17.7, and 15.5 cm-l below the respective experimental values. Errors such as these are considerably larger than expected from this level of theory, and thereforeit is probable that the experimental harmonic frequencies for HNC are in error by 10-20 cm-1. Based on the present results for HCN and on previous results,11J2it is expected that the CCSD(T)/AN02 w2 value is within 5 cm-1 of the true value while the CCSD(T)/ANO2 w1 and w3 quantities are within 10cm-I of the truevalues. Note that these estimateduncertainties are very conservative. The CCSD(T)/ANOl and experimental quartic force fields for HCN and HNC are reported in Table 11. Examining the force fields for HCN first, it is apparent that the agreement between theory and experiment is good, especially for thequadratic constants. The one force constant that exhibits quite a large difference between theory and experiment is fmrR. The CCSD(T)/ANOl value is in very good agreement with the value determined by Wong and Bacskay,Io suggesting that the experimental value may be somewhat large. The percentage and absolute deviations between the ab initio and experimental fields become larger as the order of force constant goes up, which is to be expected since these regions of the forcefield are more difficult to determine both theoretically and experimentally. Although there are some other minor differences, such as for frRRR and fmM, as stated above the agreement is generally very good. As a matter of note, the complete CCSD(T)/ANOl quartic force field for HCN is also in good agreementwith Wong and Bacskay's CCSD(T)/[4321;321] force field.1° The first point to note concerning the experimentallyderived force field for HNC is that several of the cubic and quartic force constants have been constrained to be zero. For these constants, the ab initio values are generally small, with the largest cubic constant cf,m)being 0.1702 a J/A3and the largest quarticconstant %d) being 1.302 aJ/(A* rad2). Comparison of the remaining ab initio and experimental quartic force constants shows that other than fee, fRee, f-, and fwt the differences are basically similar to those observed for HCN. FOrfil,fiR,andfm, although the differences between theory and experiment are only slightly larger for HNC than for HCN, these are large enough to cause the 10-20-cm-I discrepancy in the harmonicfrequencies discussed above. Table I11 contains the ab initio and experimentalspectroscopic constants for HCN and HNC obtained via second-order perturbation theory. Note that no resonances (Le., Fermi-type 1, Fermi-type 2, or Coriolis) were found for either molecule. An indication of the reliability of the vibrational second-order perturbation theory (PT) analysis is given by comparing the PT fundamentals obtained using Carter, Mills, and Handy's quartic force field9 (33 10.0,7 13.0, and 2097.3 cm-1) to the fundamentals obtained from their variational calculations and to the observed fundamentals23 listed in Table 111. The maximum deviation between the PT and variational fundamentals is only 1.9 cm-I (for u2) and that between the PT and experimental fundamentals isonly 1.5cm-1 (for ul), demonstratingthat thevibrational secondorder PT analysis is quite accurate for HCN. Thus, it is expected also to perform well for HNC. Not surprisingly,the agreement between the experimentaland the ab initio spectroscopic constants for HCN is very good. "Best predictions" of the fundamental vibrational frequencies may be obtained by applying the CCSD(T)/ANOl anharmonic cor-
The Journal of Physical Chemistry, Vol. 97, No. 35, 1993 8939
TABLE IIk Theoretical and Experimental Spectroscopic C ~ ~ t a nfor t s HCN and HNC' ~
~~~~
HNC
HCN
theory
exptb
theory
1.1649 1.0635 3473.1 3451.7 725.6 2109.4 3314.2 713.6 2079.4 -55.635 -19.445 -13.570 -1.902 -3.223 -9.983 5.036 1.46872 1.46199 2.80644 2.16755 0.01049 -0.00343 0.00984
1.1577 1.0617 3478.4 3441.2 727.0 2127.0 3311.5 713.5 2096.7 -52.764 -19.365 -12.654 -2.743 -2.578 -10.403 5.288 1.48492 1.47822 2.85314 2.14771 0.01049 -0,00355 0.01009
1.1809 0.9784 3377.5 3836.7 47 1 .O 2044.2 3666.0 474.4 2008.4 -70.743 -22.676 -13.020 5.467 -9.086 -10.069 2.938 1.50236 1.49678 3.15752 1.99673 0.01024 -0.00505 0.01103
exptC
3842.3 489.7 2066.6 3652.7 477 2029.2 -89.26 -35.73 -13.29 2.08 -9.79 -10.36 2.37 1.51722 1.51211 3.18 0.01064 -0.00564 0.01119
Theoreticalvaluesobtained fromtheCCSD(T)/ANOl quartic force fields given in Table 11. Units are cm-I except for the vibrationally averaged bond distances, which are in A. Fundamentals from ref 23; all other data are obtained from a second-order perturbation theory analysis of the quartic force field given in ref 9. V I and EO from ref 1; u2 and u3 from the matrix isolation data of ref 2; all other data from ref 3.
rections to the CCSD(T)/ANO2 harmonic frequencies. Performing this, weobtain 3308.2,715.3,and 2091.3 cm-' for u1, u ~ , and u3, respectively. These values are in excellent agreement with the observedz3fundamentals of HCN with the maximum deviation (5.4 cm-1) occurring for u3. The differences between the ab initio and experimental spectroscopicconstantsof HNC are much larger than those found for HCN. Based on the earlier discussion of the quartic force fields, this observation is not surprising. Some indication of the reliability of the ab initio quartic force field of HNC may be obtained by computingthe "best predictions" of the fundamentals and comparing them to the experimentally observed quantities. Using the procedure described above, the "best predictions" for the HNC fundamentals are 3650.9,475.4, and 2015.3 cm-1 for V I , YZ, and u3, respectively. The only gas-phase fundamental of HNC that has been reported' is ul(3652.7 cm-l). The agreement between theory and experiment in this case is also excellent. The other two fundamentals of HNC have been observed via matrix isolation techniques.2 The agreement between theory and experiment for the bend is again excellent, but the difference between theory and experiment for v3 (13.9 cm-l) is outside the expected uncertainty in the ab initio value, and therefore it is likely that the gas-phase u3 value will be somewhat lower than the matrix isolation value. We note that the matrix isolation2 value for V I is shifted lower by about 30 cm-l from the gas-phase value. A few other gas-phase vibrational transitions have been experimentally assigned for HNC.1.24 These are the (l,O,l)(0,0,1),(1,1,0)-(0,1,O),and(1,2,0)-(0,2,0)transitionsat 3649.5, 3630.2, and 3608.0 cm-1, respectively. Our "best predictions" using the term value expression derived from second-order perturbation theory give correspondingvalues of 3637.9,3628.3, and 3605.6 cm-1, which are below experiment by 11.6, 1.9, and 2.4 cm-1, respectively. Thedifferencefor the first transition seems anomalously high. From the second-order perturbation theory term value expansion, the differencebetween the (1,O,l)-(O,O,l) and the fundamental (O,O,l)-(O,O,O) transitions should be equal
8940 The Journal of Physical Chemistry, Vol. 97, No. 35, 1993
Lee et al.
TABLE IV: Comparison of Calculated Vibrational Energies from the Global PES and the SPF Fourth-Order Force Field with Experiment for Low-Lying States of HCN. exp- exp- PESexpexp- PESVI u2 u3 PES SPF4 expb PES SPF4 SPF4 u1 u2 u3 PES SPF4 ex9 PES SPF4 SPF4 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 2 1 1 0 0 0 0 2 1 1 1 0
1 2 0 3 1 4 0 5 2 1 0 6 3 2 7 1 4 3 0 8 2 5 4 1 0 9 6 3 0 5 2 10 1 7 4 1 6 0 3 11
0 0 1 0 1 0 0 0 1
0 2 0 1 0 0 2 1
0 1 0 2 1 0 1 3 0 1 2 0 0 1 0 3 1 2 0 0 2 1 0
718.4 1418.9 2090.3 2126.0 2806.4 2812.5 3334.1 3505.6 3507.4 4034.1 4161.5 4178.0 4213.9 4703.4 4863.2 4872.2 4899.9 5387.1 5399.4 5532.3 5570.5 5589.5 6054.0 6095.1 6211.4 6213.9 6256.5 6274.2 6553.2 6732.2 6765.5 6873.5 6915.4 6936.1 6958.5 7232.3 7390.3 7445.7 7449.3 7541.5
715.4 1413.8 2079.2 2122.3 2790.9 2813.5 3316.5 3515.5 3485.9 4012.5 4138.3 4199.8 4190.6 4691.9 4895.6 4846.1 4878.0 5381.1 5381.4 5573.1 5537.3 5576.1 6053.4 6073.8 6177.5 6263.3 6256.3 6238.1 6528.8 6736.4 6749.6 6934.7 6881.2 6948.0 6921.6 7205.6 7402.1 7426.8 7435.1 7620.6
713.5 1411.4 2096.7 2114.9 2807.1 2803.0 3311.5 3496.7 3502.1 4005.6 4173.1
-4.9 -7.5 6.4 -11.1 0.7 -9.5 -22.6 -8.9 -5.3 -28.5 11.6
-1.9 -2.4 17.5 -7.4 16.2 -10.5 -5.0 -18.8 16.2 -6.9 34.8
4202.7 4684.3
-11.2 -19.1
12.1 -7.6
4879.7 4888.0 5368.4 5393.7
7.5 -11.9 -18.7 -5.7
33.6 10.0 -12.7 12.3
5571.9
1.4
34.6
6037.0 6084.8 6228.6
-17.0 -10.3 17.2
-16.4 11.0 51.1
6519.6 6711.1 6761.3
-33.6 -21.1 -4.2
-9.2 -25.3 11.7
7194.2
-38.1
7455.4
9.7
-11.4 28.6
3.0 5.1 11.1 3.7 15.5 -1.0 17.6 -9.9 21.5 21.6 23.2 -21.8 23.3 11.5 -32.4 26.1 21.9 6.0 18.0 -40.8 33.2 13.4 0.6 21.3 33.9 -49.4 0.2 36.1 24.4 -4.2 15.9 -61.2 34.2 -11.9 36.9 26.7 -11.8 18.9 14.2 -79.1
0 0 0 2 1 1 1 0 0 0 0 0 2 2 1 1 1 0 0 0 0 0 2 2 1 1 0 1 1 0 0 0 3 0 2 2 1 1 0 1
8 2 5 2 7 4 1 12 0 9 6 3 3 0 8 5 2 13 10 1 7 4 4 1 9 6 14 0 3 11 2 8 0 5 5 2 10 7 15 4
0 Energies are given in cm-I and are relative to the zero-point energy of HCN. Experimental data from refs 23, and 25-28.
to the ~ 1 anharmonic 3 constant. The experimental difference is -3.2 cm-1 compared to our computed value of -13.0 cm-1, the latter of which is in much better agreement with the constant deduced by Creswell and Robiettes (-13.3 cm-l). Similarly, the difference between the (1,2,0)-(0,2,0) and (l,l,O)-(O,l,O) transitions, and also the (l,l,O)-(O,l,O) and the (l,O,O)-(O,O,O) transitions, should give the x12 anharmonic term. The experimentally observed differences of -22.2 and -22.5 cm-1 agree well with our computed x12 value of -22.7 cm- The x12 value deduced by Creswell and Robiette (-35.7 cm-l) is inconsistent with the observed data as well as with our computed value. The fact that there are three independent pieces of observational data that are all internally consistent regarding the determination of x12 allows the value of this constant to be firmly established. In the case of x13, there is only one additional piece of experimental data, the (l,O, 1)-(O,O,l) transition energy,24 and therefore the experimentally deduced value of -3.2 cm-1 cannot be verified. In the light of the excellent agreement between theory and experiment for the x12 constant, and also that there is no apparent reason that the ab initio methods employed in this study should perform better for the x12 constant than for the ~ 1 constant, 3 we conclude that the (l,O,l)-(O,O,l) transition has been misassigned or the band analysis was subject to error. In summary, it is evident that the ab initio quartic force field and spectroscopic constants reported here for HNC are more reliable than the analogous quantities reported by Creswell and
1 3 2 0 0 1 2 0 4 1 2 3 0 1 0 1 2 0 1 4 2 3 0 1 0 1 0 3 2 1 4 2 0 3 0 1 0 1 0 2
V I ,02,
7600.6 7609.4 7645.4 7878.8 8059.8 8115.2 8136.1 8185.3 8239.7 8279.1 8308.3 8308.9 8541.3 8595.9 8710.3 8789.0 8806.2 8840.0 8935.0 8936.2 8983.6 8990.5 9188.5 9270.6 9371.7 9441.3 9470.3 9474.5 9488.7 9598.9 9624.3 9644.9 9668.3 9674.5 9848.6 9918.1 10010.0 10105.8 10111.8 10152.3
7621.2 7568.4 7615.6 7866.1 8079.2 8103.7 8115.2 8289.5 8197.3 8307.0 8291.5 8265.0 8536.4 8578.6 8738.6 8782.7 8787.1 8978.6 8973.8 8896.3 8979.1 8944.3 9190.3 9252.1 9410.4 9444.3 9659.3 9453.6 9468.4 9655.1 9579.4 9647.7 9641.8 9634.2 9854.6 9909.4 10064.8 10117.2 10372.3 10132.8
8585.6
-10.3
7.0
8926.8
-8.2
-47.0
8995.2
4.7
50.9
9257.5
-13.1
5.4
9496.4
21.9
42.8
9648.7
24.4
69.2
9627.1
-41.2
-14.7
9914.4
-3.7
5.0
-20.6 41.0 29.8 12.7 -19.4 11.5 20.9 -104.2 42.4 -27.9 16.8 43.9 4.9 17.3 -28.3 6.3 19.1 -138.6 -38.8 39.9 4.5 46.2 -1.8 18.5 -38.7 -3.0 -189.0 20.9 20.3 -56.2 44.9 -2.8 26.5 40.3 -6.0
8.7 -54.8 -11.4 -260.5 19.5
and u3 refer to the CH stretch, the bend, and the CN stretch.
Robiette. It is hoped that these will aid in the gas-phase, highresolution rovibrational spectroscopic characterization of HNC. B. Variational Calculations. The SPF quartic forces fields, denoted SPF4, for HCN and HNC were used in variational calculations of vibrational energies. The methods used are the same as those described in our previous paper.' In addition to testing the predictions of second-order perturbation theory for the fundamentals (reported in the previous section), the variational calculations permit a detailed comparison of vibrational energies for the SPF4 force fields and the global PES that we fit previously to 2160 CCSD(T)/ANOl energies.' We also give a comparison of vibrational energies obtained by Wong and Bacskay'o using their sixth-order Morse force field, denoted M6, which was fit to high-quality CCSD(T) calculations. A more detailed analysis is presented for HCN since experimental data are available for many more HCN vibrational energy levels than for HNC. It is expected that the range of validity of the quartic force fields will be similar for HCN and HNC. Tables IV and V present vibrational energies for the SPF4 force field and the PES for HCN and HNC, respectively. Focusing on the fundamentals for the SPF4 force field, and comparing them with the results in Table 111, one sees a high level of accuracy for second-order perturbation theory. In general, force field expansions about a single point are valid only over a limited range. In addition, the HCN/HNC system is complicated by the existence of two distinct minima in which a saddle point separates the two isomers. Thus, the ranges of the
The Journal of Physical Chemistry, Vol. 97,No. 35, 1993 8941
Quartic Force Fields of HCN and HNC
TABLE V Comparison of Calculated Vibrational Energies from the Global PES and the SPF Fourth-Order Force Field with Experiment for Low-Lying States of HNC. exp- exp- PESuI u, vq PES SPF4 ex9 PES SPF4 SPF4 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 1 0 1 1
1 2 3 4 0 5 1 6 2 7 3 0 8 4 0 1 9 5 1 2 10 6 2 3 11 7 3 4 0 12 8 4 5 0 1 13 9 5 6 1 14 2 10 6 7
0 0 0 0 1 0 1 0 1 0 1 0 0 1 2 0 0 1 2 0 0 1 2 0 0 1 2 0 1 0 1 2 0 3 1 0 1 2 0 3 0 1 1 2 0
460.6 919.9 1410.2 1895.5 2024.6 2388.5 2475.0 2858.8 2929.2 3337.5 3414.9 3599.1 3794.7 3892.2 4024.4 4053.6 4270.1 4374.3 4464.6 4507.1 4727.3 4832.8 4912.6 4983.6 5198.7 5301.9 5392.8 5440.7 5628.7 5638.0 5752.6 5862.4 5900.8 5999.1 6072.3 6080.4 6223.6 6334.2 6337.0 6429.5 6482.6 6518.2 6676.6 6781.6 6789.6
475.7 951.4 1445.9 1937.7 2009.1 2448.0 2476.0 2954.1 2942.1 3478.0 3428.3 3670.2 3995.3 3911.4 3997.3 4124.7 4531.6 4413.3 4455.0 4580.6 5059.1 4907.4 4915.3 5055.4 5606.3 5427.0 5388.5 5528.7 5667.3 6142.7 5935.6 5862.7 6020.6 5965.1 6113.5 6699.5 6463.9 6355.9 6508.2 6413.0 7243.9 6561.3 6862.2 6842.8 7014.1
477 932 2029.2
3652.7
16 12 4.6
53.6
1 -19 20.1
-17.5
-15.1 -31.5 -35.7 -42.2 15.5 -59.5 -1.0 -95.3 -12.9 -140.5 -13.4 -71.1 -200.6 -19.2 27.1 -71.1 -261.5 -39.0 9.6 -73.5 -331.8 -74.6 -2.7 -71.8 407.6 -125.1 4.3 -88.0 -38.6 -504.7 -183.0 -0.3 -1 19.8 34.0 -41.2 -619.1 -240.3 -21.7 -171.2 16.5 -761.3 43.1 -185.6 -61.2 -224.5
0 Energies are given in cm-*and are relative to the zero-point energy of HNC. V I , u2, and u3 refer to the N H stretch, the bend, and the NC stretch. b Experimental data from refs 1, 2, and 24.
HCN and HNC bending coordinates are limited to values in the vicinity of the respective minima. The previously reported PES describesboth HCN and HNC, as well as the saddle point region. Thus, to establish the range of validity of the SPF4 force field with respect to the HCN bend coordinate, we calculated the difference in the SPF4 and PES vibrational energies for states with increasing levels of bend excitation. The set of states we have chosen has one quantum of C-N excitation and no C-H excitation; this set was chosen since there are experimental data for most of these states. We compare the SPF4 and PES energies to experiment for these states, and in addition we compare the energies from the M6 potential. These comparisons are shown in Figure 1. As seen in the upper panel, the SPF4 energies increase more rapidly with the bend quantum number than the PES vibrational energies do. This is due to the breakdown of the fourth-order SPF expansion at large bending angles. The positive deviation is due to the large positive value of fm(cf. Table 11) and the neglect of higher-order terms. This positive deviation shows up as an increasing inaccuracy of the SPF4 energies which are compared to experiment in the lower panel. The energies from the M6 force field of Wong and Bacskay are quite accurate
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8942 The Journal of Physical Chemistry, Vol. 97, No. 35, 1993
Lee et al.
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AN01 calculations. The nearly linear growth in the errors in the SPF4 and M6 force fields suggests that the errors are mainly caused by small inaccuracies in the electronic structure calculations, which are due primarily to limitations in the one-particle basis set. A comparison of the C-H stretch overtones is given in Figure 3. In this case, the M6 force field gives the most accurate results, followed by the SPF4 and PES results. The accuracy of the M6 and SPF4 force fields for these states is much better than that for the bend and the C-N stretch overtones. This indicates that the CCSD(T) method, with appropriate choiceof the one-particle basis set, describes the C-H stretch very well. Indeed, the accuracy of the M6 force field for the C-H stretch overtones is remarkable. Finally, we give a comparison of the differences in SPF4 and PES vibrational energies for the bend overtones of HNC in Figure 4. As discussed earlier, there are very limited experimental data available for the vibrational energy levels of HNC. It is evident from Figure 4 that the SPF4 energies deviate significantly from the PES ones, especially for u2 2 6. Hence, the HNC SPF4 force field breaks down for lower u2 values than is found for the HCN SPF4 force field. This is probably due to neglect of the HCN potential well in the dynamical vibrational energy calculations, as discussed above. It is interesting to note that the large discrepancies between the SPF4 force field and the PES occur well below the barrier to isomerization,4J which is 16 866 and 11 664 cm-I above the HCN and HNC potential minima, respectively. Support for this interpretation is given by examination of the last column in Tables IV and V, where similar behavior (i.e., similar PESSPF4 differences)for HCN and HNC is observed as long as the number of quanta in the bend remains
2
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HCN.
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Quartic Force Fields of HCN and HNC indicating that the analogous theoretical treatment for HNC should also be accurate. Analysis of the best CCSD(T) predictions for HNC then leads to the suggestions that the experimental re value for the N-H bond distance is somewhat too long and that the experimental estimates of the harmonic frequencies are in error by 10-20 cm-1. On the basis of the CCSD(T)/ANO2 calculations, the harmonic frequenciesfor HNC are predicted to be 3822 f 10,472 f 5 , and 2051 f 10 cm-1 for wl, w2, and w3, respectively. A second-order perturbation theory vibrational analysis is performed using the quartic force fields. Again, there is very good agreement between theory and experiment for the spectroscopicconstantsof HCN. The agreement between experiment and theory of HNC is very good for u1 and u2 but less so for u3. It is concluded that thegas-phasevaluefor u3 is probably somewhat lower than the value obtained from matrix isolation experiments. A comparison between second-order perturbation theory and experimentfor transitions other than the fundamentals that have been observed in the gas phase shows good agreement for the (l,l,O)-(O,l,O) and (1,2,0)-(0,2,0) bands but poor agreement for the (l,O,l)-(O,O,l) band. The first two bands allow a new experimental value for the X ~ constant Z to be determined which is in excellent agreement with our computed value. Similarly, the xi3 constant may be determined from the third band, but this value is in poor agreement with our computed value. It is therefore concluded that either the experimental (l,O,l)-(O,O,l) transition is misassigned or the band analysis was subject to error. Comparison between theory and experiment' for the other spectroscopic constants of HNC shows qualitative agreement. However, based on the comparisons for HCN, it is likely that for many of the constants(particularly thex constants)the theoretical predictions are more accurate. It is hoped that these will aid in the analysis of future high-resolution experiments on HNC. Finally, the range of validity of the quartic force fields for HCN and HNC is studied by accurate variational calculations of several vibrational energy levels and comparison of these to our recent global PES for HCN/HNC and also to the available experimental data. For both HCN and HNC, it is found that the fundamentals determined from variational calculations are in very good agreement with those obtained from second-order perturbation theory. For HCN, it is found that the quartic force field is reasonably accurate for low-lying vibrational levels but that the quartic force field breaks down for higher lying vibrational states. For HNC, there are fewer experimental data available, but comparison to our global PES shows that the quartic force field breiks down for smaller 02 values (Le., lower beiding levels) than found for HCN. This is attributed to treating HNC as a single-well potential (i.e., neglect of effects resultkg from the HCN and it is therefore that an accurate treatment Of excited bending states Of HNC requires that the HCN potential will be taken into account.
The Journal of Physical Chemistry, Vol. 97, No. 35, 1993 8943 Acknowledgment. Dr. G. Bacskay and Professor N. C. Handy are thanked for sending preprintsof their work prior to publication. C.E.D. was supported by a grant from NASA to ELORET Institute (NCC2-737). J.M.B. acknowledges support from the National Science Foundation (CHE-9200434) and the Cherry L. Emerson Center for Scientific Computation at Emory University. References and Notes (1) Maki, A. G.; Sams, R. L. J . Chem. Phys. 1981, 75, 4178. Milligan, D. E.; Jacox, M. E. J. Chem. Phys. 1967, 47, 278. Creswell, R. A.; Robiette, A. G. Mol. Phys. 1978, 36, 869. Lee, T. J.; Rendell, A. P. Chem. Phys. Lett. 1991, 177, 491. Pau, C.-F.; Hehre, W. J. J. Phys. Chem. 1982, 86, 321. Bentley, J. A.; Bowman, J. M.; Gazdy, B.; Lee, T. J.; Dateo, C. E. Chem. Phys. Lett. 1992,198, 563. (7) Bowman, J. M.; Gazdy, B.; Bentley, J. A,; Lee, T. J.; Dateo, C. E. J. Chem. Phys. 1993,99, 308. (8) Carter,&; Mills, I. M.;Handy,N. C.J. Chem. Phys. 1992,97,1606. (9) Carter, S.;Mills, I. M.; Handy, N. C. J. Chem. Phys., in press. (10) Wong, A. T.; Bacskay, G. B. Mol. Phys., in press. (1 1) Lee, T. J. Chem. Phys. Lett. 1992, 188, 154. Experimental values aregiven: Bryant, G.; Jiang, Y.;Grant, E. Chem. Phys. Lett. 1992,200,495. (12) Martin, J. M. L.; Lee, T. J.; Taylor, P. R. J . Chem. Phys. 1992.97, 8361. Martin, J. M. L.; Lee, T. J.; Taylor, P. R. J . Mol. Spectrosc. 1993, 160,105. Martin, J. M. L.;Taylor, P. R.; Lee,T. J. Chem. Phys. Lett. 1993, 205, 535 and references therein. (13) Csakar,A. G.J. Phys. Chem. 1992,96,7878. Allen, W. D.; Csalzar, A. G. J. Chem. Phys. 1993,98,2983. Botschwina, P.; Nachbaur, E.; Rode, B . M. Chem. Phvs. Lett. 1976.41.486. Botschwina, P.; Horn, M.; FlUgae, J.; Seeger, S . J . Chem. Soc.,Faraday Trans. 2, in press. Gaw, J. F.; HaGdy, N. C. Chem. Phys. Lett. 1985,121,321. Amos, R. D.; Handy, N. C.; Green, W. H.; Jayatilaka, D.; Willetts, A.; Palmieri, P. J. Chem. Phys. 1991, 95, 8323. Clabo, D. A.;Allen,W. D.;Remington,R. B.;Yamaguchi,Y.;Schaefer, H. F. Chem. Phys. 1988,123, 187. (14) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. Chem. Phys. Lett. 1989, 157, 479. (15) AlmlBf, J.; Taylor, P. R. J . Chem. Phys. 1987, 86, 4070. (16) van Duijneveldt, F. B. ZBM Res. Dept. 1971, RJ945. (17) TITAN is a set of electronicstructure programs, written by T. J. Lee, A. P. Rendell, and J. E. Rice. (18) Lindh, R.; Ryu, U.; Liu, B. J. Chem. Phys. 1991, 95, 5889. (19) SWEDEN is an electronic structure program system written by J. AlmlBf, C. W. Bauschlicher, M. R. A. Blomberg, D. P.Chong, A. Heiberg, S.R. Langhoff,P.-A.Malmqvist,A. P. Rendell, B. 0.Roos,P. E. M. Siegbahn, and P. R. Taylor. (20) INTDER a program which performs curvilinear transformations between internal and Cartesian coordinates, written by W. D. Allen. (21) SPECTRO, version 1.0 (1989). written by J. F. Gaw, A. Willetts, W. H. Green, and N. C. Handy. (22) Simons, G.; Parr, R. G.; Finlan, J. M. J . Chem. Phys. 1973,59,3229. (23) Smith, A. M.; Coy, S. L.; Klemperer, W.; Lehmann, K. K. J . Mol. Spectrosc. 1989, 134, 134. (24) Winter, M. J.; Jones, W. J. J . Chem. SOC.,Faraday Trans. 2 1982, (2) (3) (4) (5) (6)
278. 585. (25) Jonas, D. M.; Yang, X.;Wodtke, A. M. J. Chem. Phys. 1992,97, 2284. (26) Yang, X.;Rogaski, C. A.; Wodtke, A. M. J. Opt. Soc. Am. B. 1990, 7. . , 1835. - -- - .
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