Nitrogen quadrupole coupling constants for HCN and H2CN+: Explanation of the absence of fine structure in the microwave spectrum of interstellar H2CN+

Nitrogen 14 quadrupole coupling constants for H 2 CN+ and HCN are predicted via ab initio self consistent-field and configuration interaction theory. Effects of electron correlation, basis set completeness, and geometrical structure on the predicted electric field gradients are analyzed. The quadrupole coupling constant obtained for H 2 CN+ is one order of magnitude less than in HCN, providing an explanation for the experimental fact that the fine structure of the microwave spectrum of H 2 CN+ has not been resolved. This research also allows a reliable prediction of the nuclear quadrupole moment of 14N, namely Qe 4 N) = 2.00X 10- 26 cm 2•


INTRODUCTION
Despite the fact that HCNH+ has a small permanent dipole moment,l-4 the microwave spectrum of this molecular ion has very recently been observed in interstellar space. Ziurys and Turner observed the J = 1~, 2-1, and 3-2 rotational transitions of HCNH+ toward Sgr. B2 between October 28, 1984 andApril 16, 1985. The laboratory millimeter and submillimeter wave spectrum of HCNH+ was also recently detected by Bogey, Demuynck, and Destombes. 6 In this work we report ab initio values of the 14N nuclear quadrupole coupling constants (QCC) for HCN and HCNH+. Theoretical predictions of vibrational frequencies and infrared intensities for protonated HCN were the subject of a previous paper. 1 Normally, the microwave spectrum of a molecule which contains an atom with a nuclear quadrupole moment will exhibit fine structure due to the electric interaction between the nuclear quadrupole moment and the electric field gradient at the nucleus. However, it was emphasized by Ziurys and Turner that fine structure could not be resolved for HCNH+; the implication being that the electric field gradient at the 14N nucleus of HCNH+ , and hence the QCC, was very small. Thus we decided to predict the ab initio electric field gradient and corresponding 14N QCC for HCNH+. To our knowledge the present research represents perhaps the first thorough examination of the effects of electron correlation on predicted nitrogen quadrupole coupling constants.

THEORETICAL APPROACH
Nuclear quadrupole coupling constants may be obtained from the ab initio molecular electric field gradient (q) if the nuclear quadrupole moments (Q) are known. Numerous ab initio predictions of electric field gradients have been reported for deuterium 7 and for 14N containing molecules. S-27 The Hamiltonian representing the interaction between the nuclear quadrupole moment and the electronic where fA is the nuclear spin of nucleus A (fA> 1 is required for QA to be different from zero), and rjA = Irj -RA I is the distance between electronj and nucleusA. The total electric field gradient is a second-rank tensor whose components at the site of nucleus A are where a, f:l = x,y, and z; PI''' is the reduced one-pa!!icle d~n sitymatrix; tPl',tP .. are atomic orbitals andRAB = IRA -RB I are internuclear distances. Also in Eq.
(2), r A is the distance of the electron from nucleus A; r Aa is the difference in Cartesian coordinate a (i.e., x,y, or z) between the electron and nucleusA; and R ABa is the difference in Cartesian coordinate a between nucleus A and nucleus B. The two terms in Eq.
(2) correspond to the electronic and nuclear contributions, respectively. For linear molecules the QCC is straightforwardly obtained as e 2 ~ QN/h, with z being the axis of the molecule. One-particle density matrices were obtained for both the self-consistent-field (SCF) and configuration interaction (CI) wave functions and subsequently used in the evaluation of the electronic contribution to the electric field gradient [see Eq.
(2)]. The electric field gradient integrals over the atomic orbital basis were evaluated using standard techniques. 30 Initially the electric field gradient was evaluated with SCF wave functions in conjunction with the standard Huzinaga-Dunning 31 . 32 double zeta plus polarization (DZ + P) basis used previously. 1 This basis is designated  tor of 1.2, and the polarization function exponents were ad (C) = 0.75, ad (N) = 0.8, and a p (H) = 1.0. Correlation effects were analyzed by way of CI wave functions including all single and double excitations with respect to the SCF reference function with the exceptions that the Cis -and N Is -like orbitals were kept doubly occupied and the corresponding orbitals deleted from the virtual space. The SCF DZ + P and CISD DZ + P optimized geometries were taken from the literature 1 and are given in Table I for completeness.
The influence of the basis was investigated by using the less contracted triple zeta (TZ) Huzinaga-Dunning basis,33 the (1Is6p) and (13s8p) primitive set of van Duijnevelde 4 for C and N, and the 68, Ss, and lOs primitive sets of the same author 34 for hydrogen. All contractions of these basis sets were performed over the innermost primitives.
The polarization function orbital exponents given above were used when one set of polarization functions was added to these sp basis sets. However, the quadrupole coupling constants were also evaluated using basis sets including two sets of polarization functions on each atom. When two sets were added the polarization exponents were a p = 1.2 and 0.4 for H, ad = 1.5 and 0.5 for N, and ad = 1.2 and 0.4 for C.

RESULTS AND DISCUSSION
In Table I, the predicted equilibrium geometries and the corresponding energies for both HCN and protonated HCN, evaluated with SCF and CI wave functions, are presented. As usual, CI bond lengths are longer than the SCF ones.
The 14N QCC for HCN has been measured by DeLucia and Gordy,3S the experimental value being -4.7091 ± 0.00 13 MHz. The nuclear quadrupole moment of 14N has recently been deduced by Ha 2S to be 1.95 X 10-26 cm 2 . Therefore, theoretical values of the electric field gradient may be used to test the accuracy of theoretical predictions for the QCC, by way of combination with known or estimated nuclear quadrupole moments. On the other hand, theoretical values of the electric field gradient may be used to predict the quadrupole moment at a determined level of theory, provided the experimental QCC are known. In this paper, we have initially used Ha's suggested value of the 14N quadrupole moment to predict the QCC for H 2 CN+.
In Table II we report the basis set dependence of the electric field gradients ofHCN and H 2 CN+ at the SCF level of theory. These calculations were carried out at the corresponding CISD DZ + P optimized geometries (see Table   TABLE II. Energies, electric field gradients, and nuclear quadrupole coupling constants of 14N in HCN and H 2 CN+ for different basis sets at the SCF level of theory." The nuclear quadrupole moment of 14N was assumed to be 1.95 X 10-26 cm 2 , as proposed in Ref.  • Optimized CISD geometries with DZ + P basis sets were used (see Table I).
b Two innermost doubly occupied molecular orbitals and corresponding virtuals are frozen. C All single and double replacements are included. I). Without using polarization functions it is not possible to find convergence for the valence sp basis set. This is true even with the uncontracted C, N( 13s8p) H( lOs) set. It is apparent that polarization functions are of crucial importance for this property. We have also investigated the influence of diffuse polarization functions (see entry 10 of Table II), and such functions reduce the value of q slightly. From results presented in Table II we Table   III for both HCN and H 2 CN+ with DZ + P and TZ + 2P basis sets. In evaluating the electric field gradient we chose an expectation value approach. 36 This means that Eq. (2) was used for the electric field gradients, with p/ w being now the one-particle reduced density matrix obtained from the CISD wave function. Also examined was the influence of keeping the innermost doubly occupied molecular orbitals and corresponding virtuals frozen with the DZ + P basis set and, as expected, we found it ofless importance. The results presented in Table III show that in HCN correlation effects increase the predicted electric field gradient by -0.14 a.u., or 12%-14%. The same increase holds for H 2 CN+ but to a much smaller degree, 0.004-0.008 a.u. The influence of the assumed geometrical structure on the predicted electric field gradients and quadrupole coupling constants is another parameter to be analyzed. Such a study is reported in Table IV. Results obtained show that these properties are only somewhat sensitive to the small perturbations introduced ( ± 0.01 a.u. in all bond lengths with respect to the optimized CISD DZ + P structures).
However, it may be concluded that neither this structural dependence nor correlation effects will affect the order of magnitude of the predicted electric field gradients and consequently the calculated 14N QCC in these molecules.
Obviously, a precise quantitative prediction for the 14N QCC in H 2 CN+ will require a refinement in basis set, correlation effects, and geometrical structure and is not the purpose of this paper. Nevertheless, from the results obtained in this work we may conclude that the nuclear quadrupole coupling constant for 14N in H 2 CN+ is in the range of -0.55 ± 0.3 MHz or one order of magnitude less than in HCN. This prediction satisfactorily explains the experimental observation that the fine structure of the microwave spectrum of interstellar H 2 CN+ was not resolved. s

CONCLUDING REMARKS
There is no meaningful purely experimental value for the nuclear quadrupole moment of 14N. The most reliable values for this quadrupole moment may be obtained by com- • Optimized CISD structures with DZ + P basis sets (see Table I).
b All bond lengths are increased by 0.01 a.u. with respect to a the CI equilibrium geometry. C All bond lengths are decreased by 0.01 a.u. with respect to a.