Bender, Charles F.

Schaefer, Henry F.

Schwenzer, Gretchen M.

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Lawrence Berkeley National LaboratoryRecent WorkTitleCONFIRMATION OF THE DISCREPANCY BETWEEN THEORY AND EXPERIMENT FOR THE B1-A"" STATE OF HCNPermalinkhttps://escholarship.org/uc/item/796547mmAuthorsSchwenzer, Gretchen M.Bender, Charles F.Schaefer, Henry F.Publication Date1975-04-01eScholarship.org Powered by the California Digital LibraryUniversity of California" .. •• ·~ Submitted to Journal of the American Chemical Society I 7 LBL-3486 Preprint C'. I CONFIRMATION OF THE DISCREPANCY BETWEEN THEORY AND EXPERIMENT FOR THE B 1 A 11 STATE OF HCN Gretchen M. Schwenzer, Charles F. Bender, and Henry F. Schaefer III April 1975 Prepared for the U. S. Energy Research and Development Administration under Contract W -7405-ENG -48 For Reference Not to be taken from this room .. I t"' tJj t"' I w ~ 00 00' . -DISCLAIMER This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or the Regents of the University of California. f 0 0 f. I y 0 7 8 LBL-3486 -i-CONFIRMATION OF THE DISCREPANCY BETWEEN THEORY AND EXPERIMENT 1 ' ' FOR THE B A STATE OF HCN * Gretchen M. Schwenzer, Charl,es F. Bender and Henry F. Schaefer III Department of Chemistry and Lawrence Berkeley Laboratory University of California, Berkeley, California 94720 ABSTRACT Ab initio calculations have been carried out on the first 1 '' and second A states of HCN using relatively large and flexible basis sets. The. predicted geometries have been com-pared with the experimental results of Herzberg and Innes and with earlier calculations on HCN. These calculations concur with earlier theoretical results and the Walsh diagram pre-diction that Herzberg and Innes' 1 t I, assignment of the fJ A state with bond angle 114.5° is incorrect. * M. H." Fellow. Permanent address: Lawrence Livermore Laboratory, University of California, Livermore, California 94550. 0 0 Q ') ~ 0 6 7 9 -1-1 In a recent publication we reported a new theoretical approach for the treatment of excited electronic states and used this method to study the geometries of the ground state and twelve excited states of HCN. The results were generally ~/ consistent with qualitative predictions based .on Walsh's . 2 orbital binding energy diagram for HAB molecules. Herzberg 3 4 and Innes ' have,experimentally studied three of the excited states of HCN, providing geometry determinations and assigning electron configurations. However, there appears to be a 1 2 3 4 serious discrepancy between the theoretical ' and experimental ' 1 '' molecular structures for the second A state of HCN. Herzberg 1 '' and Innes identified this state as the B A state, with a bond . '2 ' ''2 " :·angle of 114.5° and assigned the configuration Sa 6a la 2a 2 However Walsh's rules predict a linear or slightly bent state 1 for this configuration; and the ab initio study concurred, giving 1 ' ' a bond angle of 164.4° for .the second A state. The primary goal of the present research was to perform a 1 ' ' more exhaustive study of the second A state in order to help clarify this inconsistency. In particular, the most serious 1 weakness of our earlier study was the use of a double zeta basis set. Here the importance of both polarization functions and diffuse (or Rydberg) functions has been carefully explored. 1 II The first two A states are known from our previous study 1 2 1 2 II I to have the predominant configurations Sa 6a la 7a and '2 I "2 II Sa 6a la 2a respectively. Separate SCF calculations should be meaningful for both of these configurations (although -2-they are of the same symmetry) because their orbital symmetries are different. The virtual orbital to be occu~ied in the first I I I configuration is 7a while it is 2a in the second. A flexible double zeta plus polarization basis set was initially adopted, s Aside from the polarization functions, this is Dunning's . contraction of Huzinaga's6 primitive gaussian basis set. The final basis set is shown in Table A, contained in our complete report 7 of this research. The geometries of the two excited states were obtained by minimizing the total energy with respect to the two bond distances r(HC) and R(CN) and the bond angle 8(HCN). A guess was made at (r , R , 8 ) and calculations were carried out at g g g this point and six others 0 (r +O.OSA, R, 8) g g g 0 (r - 0. OSA, R , 8 ) g \ g g 0 (r , R + 0. OSA, 6 ) g g g 0 (r, R -O.OSA, 8) g g g (r , R , 8 + S0 ) g g g (r , R 6 - S0 ) g g' g If (r , R , 8 ) yielded an energy lower than the other six then g g g the equilibrium geometry was obtained by fitting these seven points to the simple analytic formE = a+ b(r-r ) 2 + c(R-R ) 2 + e e d(8-8 ) 2 . Otherwise, the lowest computed energy was used to e define a new geometry (r , R , 8 ) and the process repeated. g g g -Table I gives the optimized parameters for the ground . 8 1 ,, state and the first two A states of HCN with this basis 0 0 u '} - 0 6 0 -3-set, as well as the experimental geometries of Herzberg and Innes. The ground state and the first excited state are in good agreement with Herzberg's determinations, as was the case in our previous study, for which a summary is given in Table C. The SCF results show slightly shorter bond lengths than experi-9 1 11 ment; this is typical of SCF calculations. The second A state however is predicted to be linear, which is essentially in agreement with Walsh's rules, which predict it to be a 1 slightly bent state. Our previous calculations showed a slight mixing of the two configurations for this state. It 1 2 1 2 I 1 1 was the mixing of the Sa 6a la 7a configuration with '2 i "2 "; the Sa 6a la 2a configuration to which we attributed the slightly bent 164° character of this state. Thus it seems likely that configuration interaction (Cl) calculations with this large basis would yield a bond angle near 164° for the 1 I I 2 A atate. - 1 '' The observed B A state is sufficiently high ( 6. 8 eV) in energy, that one cannot completely rule out the possibility of a significant amount of Rydberg character. Were this the case, of course, both the Walsh and ab initio theoretical pre-dictions would be inappropriate, since they assume a valence-like 1 I I description of the second A state. For this reason a further extension of the basis set was carried out to include Rydberg functions on carbon and nitrogen. The Rydberg functions, shown 10 in Table B, were obtained by adding diffuse even tempered functions to Dunning's basis set. This final larger basis set -4-was employed (a) at the optimized geometry for the double zeta plus polarization basis set and (b) at the experimental 4 - 1 '' geometry for the B A state. The results are summarized in Table II. There is an energy lowering of approximately 1 ' ' 0.003 hartrees for both the first and second A states upon extension of the basis set. Approximately the same change in the energy is observed for the calculation at Herzberg's geometry. It seems clear that no further extension of the basis set will cause the dramatic shift in energy needed in 1 ,, order to obtain a 2 A state of lesser bond angle. An examination of the coefficients of the different gaussian 1 '' functions in the orbitals shows that the second A state is not a Rydberg state_. The energy separation between the ground state and the 1 ' ' first A state is 6.48 eV experimentally and 5.50 eV in the present study. 9 Errors of this magnitude are to be expected from the Hartree-Fock level of theory: The separation between 1 '' 1 '' the 1 A and the 2 A states is 0.94 eV, in comparison with 1.04 eV from our previous calculations and 0.29 eV from Herzberg and Innes. Hence the two theoretical treatments are in essential agreement concerning both the structure of the 2 1" -1" A state and its position relative to the A A state. In conclusion, it seems very difficult to reconcile the present theoretical predictions with Herzberg and Innes' 1 '' assignment of a 114.5° bond angle to the B A state of HCN. L 0000--~20 -5-This research was supported by the National Science Foundation (Grants GP-39317 and 41509X) and the Energy Research Development Administration. Computations were carried out on the Datacraft 6024/4 minicomputer. .i References 1. G. M. Schwenzer, S. V. O'Neil, H. F. Schaefer, C. P. Baskin, and C. F. Bender, J. Chem. Phys. 60, 2787 (1974). 2. A. D. Walsh, J. Chem. Soc. 1953, 2288. 3. G. Herzberg and K. K. Innes, Can. J. Phys. 35, 842 (1957); and further unpublished work referred to in Ref. 4 below. 4. G. Herzberg, Electronic Spectra of Polyatomic M:>lecules, (Van Nostrand Reinhold, New York, 1966). 5. T. H. Dunning, J. Chem. Phys. 53, 2823 (1970). 6. s. Huzinaga, J. Chem. Phys. 42, 1293 (1965). 7. G. M. Schwenzer and H. F. Schaefer, Lawrence Berkeley Laboratory Report LBL-3486, March, 1975. 8. P. K. Pearson, H. F. Schaefer, and U. Wahlgren, J. Chem. Phys. 62, 350 (1975). 9. H. F. Schaefer; The Electronic Structure of Atoms and M:>lecules: A Survey of Rigorous Quantum Mechanical Results (Addison Wesley, Reading, Mass. 1972). 10. R. C. Raffenetti, J. Chem. Phys. ~' 5936 (1973). TABLE I. Geometries predicted by SCF calculations with a double zeta plus polarization basis set. Experimental quantities in parentheses refer to the lowest vibrational level (v1 = v2 = v3 = 0) and are taken from Herzberg.4 0 0 I 0\ r (HC) A R (CN) A . 8 (HCN) deg. Configuration I e e e lE+ lAI 1.062 (1.064) 1.136 (1.1S6) 180 (180) 12 12 11 2 Sa 6a la 1 I I I 2 I 2 I I I A 1.104 (1.14) 1. 28S (1. 297) 124.S (12S.O) Sa 6a la 7a 1 II .. I 2 I 112 I I 2 A 1. 060 (1.14) L 290 (1. 334) 180 (114.S) Sa 6a la 2a ;-._ TABLE II. Results of single configuration SCF calculations for HCN. 1 '' For the 2 A state, the total ll:+ lA' 1 '' A 1 ' ' 2 A energy calculated at the theoretical equilibrium geometry is followed (in parentheses) by the energy calculated at the Herzberg-Innes experimental geometry~ Energies are given in hartrees. Configuration '2 '2 "2 Sa 6a la I 2 I 2 ' ' ' Sa 6a la 7a '2 ' Sa · 6a "2 " la 2a a Reference 8. Double zeta plus polarization -92.88972a -92.687S4 -92~6S310 (-92.S9231) Double zeta plus polarization plus Rydberg functions -92.69068 -93.6S662 (-92.S9S29) I -..,J I .a 0: (';: 0 A f'I;J, C: o~ ec t-v -8-TABLE A. Double zeta plus polarization basis set for HCN Center Type Exponent Coefficient H s 19.2406 0.032828 2.8992 0.231208 0.6534 0.817238 s 0.1776 1.0 p 1.0 1.0 c s 4232.61 0.002029 634.882 0.015535 146.097 0.075411 42.4974 o. 257121 14.1892 0.596555 1.9666 0.242517 s 5.1477 1.0 s 0.4962 1.0 s 0.1533 1.0 p 18.1557 0.018534 3.9864 0.115442 1.1429 0.386206 0.3594 0.640089 p 0.1146 1.0 d 0.75 1.0 N s 5909.44 0.002004 887.451 0.015310 204.749 0.074293 59.8376 0.253364 19.9981 0.600576 2.6860 0.245111 o o n o~· ..,,. .._, "'J. ' · ...,.. ..,.~ 0 8 3 TABLE A. Continued -9-s 7.1927 1.0 s 0.7000 1.0 .,) s 0.2133 1.0 p 26.786 0.018257 5.9564 0.116407 1. 7074 0.390111 0.5314 0.637221 p 0.1654 1.0 d 0.8 1.0 TABLE B. Rydberg functions c s 0.0470 1.0 p 0.0370 1.0 N s 0.0650 1.0 p 0.0510 1.0 TABLE C. 0 Symmetry T (eV) e r (HC) A e 1r+ 1A' 0.00 1.055 1 ' ' A 6.48 1.096 2 1A' 7.52 1.076 a Reference 1. a Summary of previous HCN data 0 Most important R (CN) A e 9 (HCN) e , configuration 1.180 180 '2 '2 "2 5a 6a 1a '2 '2 ' ' 1.318 127.2 5a 6a .. 1a 78. ' 1.316 164.4 '2 ' "2 " 5a 6a 1a 2a '2 '2 " ' 5a 6a 1a 7a Coefficient I ~ 0 I 0.9684 0.9714 0.8209 0.5372 ·- ' 0 u ;) ,: l . l v .... d P-----------------LEGALNOTICE------------------~ This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights. TECHNICAL INFORMAtiON DIVISION LAWRENCE BERKELEY LABORATORY UNIVERSITY OF CALIFORNIA BERKELEY, CALIFORNIA 94720 ,., .. 

CONFIRMATION OF THE DISCREPANCY BETWEEN THEORY AND EXPERIMENT FOR THE B1-A"" STATE OF HCN

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