Journal of Molecular Structure (Theochem), 231 (1991) 267-275 Elsevier Science Publishers B.V., Amsterdam

267

AB INITIO CALCULATIONS OF THE PROPERTIES OF THE CNH---NCH AND CJVH--.NCH LINEAR COMPLEXES

JOAO BOSCO, P. da SILVA and MOZART N. RAMOS’

Departamento de Q&mica Fundamental, Universidade Federal de Pernambuco, 50739 - Recife (PE) (Brazil)

(Received 5 September 1990)

ABSTRACT

Ab initio LCAO-SCF calculations with a 4-3lG** basis set are used to predict hydrogen-bond energy, spectroscopic constants and various electronic and vibrational properties of the CNH. * *NCH and C&NH. - *NCH linear complexes. Our calculations reveal that the addition of a Cz unit to the proton donor molecule increases the H-bond energy by 2.7 kcal mol-’ and the intermolecular charge transfer by 0.020 e. The intramolecular vibrational frequencies and their shifts, the new intermolecular frequencies, as well as the absolute intensities and their changes due to complex formation, are analyzed. The latter are interpreted in terms of equilibrium atomic charge and charge-flux contributions.

INTRODUCTION

HCN, HNC and C&NH are molecules of great interest in interstellar chem- istry [ 11. The formation of hydrogen-bonded complexes involving HCN and HNC is also of interest in prebiotic synthesis [ 21. These aspects in particular have stimulated several experimental [ 31 and theoretical [ 4,5] studies involv- ing such complexes. C&NH in turn has been the target of some theoretical studies concerning its structure-polarity relation [ 6-81. Recently, we have shown [9] by an ab initio MP2/4-31G** calculation, that &NH is in the sin- glet state and bent with a CNH angle of 146’) and sufficiently polar to be a good proton donor in forming an H bond.

In this paper we describe our molecular orbital ab initio calculations using a 4-31G** basis set [lo] with the GAUSSIAN 86 program [ 111 to analyze H- bond formation involving the CNH l l l NCH and &NH*- *NCH linear com- plexes. In this analysis we have considered particularly the hydrogen bond energy, vibrational ground state rotational spectroscopic constants and the

*Author to whom correspondence should be addressed.

0166-1280/91/$03.50 0 1991- Elsevier Science Publishers B.V.

268

effect of hydrogen-bond formation on the vibrational spectra of the isolated molecules.

RESULTS AND DISCUSSION

Hydrogen bond energy and electronic properties

Table 1 shows the hydrogen-bond distances (r,. . .N) and energies ( AE), di-

pole moments (p), enhancement of the dipole moments (A,u), and charge transfers (AQ) of the complexes CNH - - *NCH and &NH* l l NCH calculated by the 4-31G** basis set. In this procedure both the monomer and complex geometries were fully optimized. In Fig. 1 we show the 4-31G** optimized ge- ometries and atomic charges for CNH- - *NCH and C&NH* - -NCH.

Initially, we can observe that the H-bond energy in C&NH. - .NCH is stronger than that in CNH.. -NCH by 2.7 kcal mol-‘. In contrast to their HCN and HC3N isomers [ 121, the addition of a Cz unit to the proton donor carbene tends to increase the stabilization energy of the formed complex and to decrease the H-bond distance. However, the H-bond energy of complexes involving HCN and H&N as proton donor to NCH becomes weaker by 0.7 kcal mol-’ in going from NCH. - *NCH to NC&H- - *NCH, whereas the N. - -C distance is increased by 0.052 A using a 4-31G basis set [ 121.

Though the molecular geometry of the HCN proton acceptor is not altered by addition of a Cz unit to CNH, the charge transfer to the proton donor is increased by 0.02 e. The latter must be an important factor in the greater sta- bilization energy of &NH - - *NCH with respect to CNH* l l NCH. The second factor favoring &NH* l l NCH is associated with its greater dipole-dipole elec- trostatic interaction compared to that in CNH* l l NCH. In fact, we can see in Table 1 that the dipole moment and the enhancement of polarity in the latter case are respectively 6.95 D and 0.98 D, whereas for C&NH* l l NCH they are 11.30 D and 1.97 D, i.e. a difference of a factor of about 2.

It is interesting to point out that the 4-31G** H-bond energy for CNH- * *NCH

-.27 -.33 .66 -50 .37 -34 .I5 .26

--.04 .oo -.03 .06 -.06 .oo .07 .oo

-.I5 -.32 .42 -.34 .I3 .26

-.04 .03 -.04 .oo .05 .oo

Fig. 1.4-31G** optimized geometries, corrected Mulliken charges (see text) and change of atomic charges on complex formation.

TABLE 1

4-31G** values for the hydrogen-bond distances and energies, dipole moments, enhancements of polarity and charge transfers for the CNH * * * NCH and &NH* - * NCH complexes

Complex TN...N (A) AE P (kcal mol-‘) (D)

& (D)

AQ (e)

CNH. * .NCH 3.091 6.30 6.95 0.98 0.05 C,NH**.NCH 2.984 8.96 11.30 1.97 0.07

is decreased by 1.0 kcal mol-’ (about 14%) with respect to that previously reported by us [5] using a 4-31G basis set. This is perfectly reasonable since the double-zeta basis sets without polarization functions tend to overestimate H-bond energies [ 12,131.

It is important to draw attention to the fact that the atomic charges in Fig. 1 are indeed corrected Mulliken charges [ 14,151, which reproduce the calcu- lated dipole moment. These charges are obtained by adding to standard Mul- liken charges an overlap tensor element of the charge-charge flux overlap (CCFO ) model [ 161 for IR intensities

or

(2)

where x is the direction perpendicular to the molecular plane and dp/&r, is the element of the atomic polar tensor matrix [ 171 of an cy atom corresponding to its molecular out-plane cartesian displacement. These corrected charges have been shown to be of better quality than the standard ones, as far as electronic description, especially in studying hydrogen bonded complexes, is concerned [ 181. Recently, Dinur and Hagler [ 191 have shown in a refined way some conceptual aspects involving the atomic charge defined by the atomic polar tensor element apx/ax,.

For comparison purposes we give in Table 2 corrected and standard Mulliken charges for the CNH* l l NCH complex. These differ substantially in two aspects.

(i) Firstly, the corrected atomic charge of the terminal carbon in CNH is negative ( -0.11 e) whereas it is positive (0.17 e) by standard Mulliken par- tition. Therefore, corrected Mulliken charges indicate, for example, that CNH must be a good proton acceptor, in contrast to the result obtained using stan- dard Mulliken charges. Nevertheless, the calculations of Hasanein and Hinch- liffe [ 201 point to the electronic description revealed by corrected charges, i.e. CNH is a good proton acceptor in forming hydrogen bonded complexes with the HX acids (X = F, Cl, Br ). For instance, the H-bond energy for HF. - -C!NH

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TABLE 2

Corrected and standard Mulliken charges and their change upon CNH- * *NCH complex formation

Atom

C N Hb Nb C H

q (e)

Corrected

-0.15 -0.32

0.42 -0.34

0.13 0.26

Standard

0.12 -0.53

0.38 -0.41

0.16 0.28

Aq (e)

Corrected

-0.04 0.03

- 0.04 0.00 0.05 0.00

Standard

- 0.05 -0.01

0.03 -0.04

0.05 0.02

is 6.3 kcal mol-’ using a Dunning’s basis set including polarization functions on each centre.

It is also interesting to point out that Fig. 1 indicates that C&NH must be a still better proton acceptor than CNH; the terminal carbon corrected charge in &NH is even more negative (-0.27 e) than that in CNH (-0.15 e) by a factor of almost 2.

(ii) Secondly, according to the corrected Mulliken charge, the bridge hydro- gen becomes more negative ( - 0.04 e) when forming the H bond, in contrast to its standard Mulliken charge ( + 0.03 e). By contrast it is well known [ 211 that when an X-H bond is stretched it leads to X*+ - H’- polarity and (a~/ c~F)+~ is negative. When the CNH. - *NCH complex is formed, the N-H bond length increases from 0.982 to 0.992 A, i.e. it undergoes an internal displace- ment of 0.01 A, which is of the same order of magnitude as the vibrational displacement involved in calculating dipole moment derivatives [ 171. Hence, the electronic description for the bridge hydrogen revealed by corrected Mul- liken charges is at least in agreement with that occuring during a vibrational stretching.

Spectroscopic constants

In Table 3 we give 4-31G** values of spectroscopic constants for the CNH* l l NCH and C&NH. - *NCH complexes. Here the spectroscopic con- stants of interest are, the force constant K. and frequency us associated with N- l l H stretching, the rotational constant B. and the centrifugal distortion constant OJ. In order to calculate DJ we used the expression [ 221

D,dBi=j/v; (3)

For comparison we give in Table 3 the 4-31G results [ 51 for CNH- * *NCH, whose force constant K, was obtained by differentiating a polynomial fit to a potential energy surface following the procedure of van Duijneveldt-van de

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TABLE 3

Vibrational ground state rotational spectroscopic constants for the CNH. * *NCH and &NH* * * NCH complexes

Complex &I DJ (MHz) &Hz)

KS 0 (mdyn A-‘)

V, (cm-‘)

CNH...NCH” 1988.65 2.27 0.106 141 (2089.17) (1.64) (0.24) (179)

&NH. -. NCH 831.49 0.16 0.112 143

“4-31G values are given in parentheses [5].

Rijdt and van Duijneveldt [ 231. Besides the inclusion of polarization functions and the approximate estimate for K,, the ys frequency was calculated in ref. 5 by assuming that the high frequency motions of the HCN and HNC units were weakly coupled to the low frequency stretch. Thus, it is probable that such aspects can explain the 4-31G and 4-31G** difference found for KS, v, and DJ in CNH- * l NCH in Table 3. However it is possible that the 4-31G** value of KS (0.106 mdyn A-‘) is somewhat underestimated in CNH*- *NCH, because the corresponding experimental value in HCN. - -HCN, whose hydrogen bond is weaker than that in HCN. ..HNC, is 0.11 mdyn A-’ [24]. Hence, we may expect the experimental value of KS to be greater than 0.11 mdyn A-’ in HCN- l .HNC.

With respect to the hydrogen bond frequency, vS, it is reasonable to expect a difference of about 20% to be found between 4-31G and 4-31G** values in CNH. - *NCH, in spite of KS being underestimated by the 4-31G** basis set. Curtiss and Pople [25] also found a difference of 20% for yS by comparing 4-31G and experimental results in HCN. ..HF, i.e. 193 cm-l and 155 cm-‘, respectively. Therefore, it is possible that the 4-31G** value of 141 cm-’ for yS in CNH- - - NCH is nearer to the experimental value than that predicted using a 4-31G basis set [5], i.e. 179 cm-‘.

Vibrational frequencies and intensities

In Tables 4 and 5 we give 4-31G** values for both vibrational frequencies and IR intensities of the CNH- - -NCH and &NH* l l NCH complexes. We also give frequency shifts and intensity ratios for the complexes as compared to the monomer, whose values are given in parentheses.

Initially, we can observe that for the CNH- . *NCH complex the hydrogen- bond formation results in a downward shift of 159 cm-’ in the N-H stretching frequency compared with that of the free CNH molecule. This shift is still greater (249 cm- ’ ) for C&NH* - .NCH. It is interesting to note the upward shift of the bending mode frequency in CNH upon forming the hydrogen complex.

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TABLE 4

Harmonic frequencies, frequency shifts for the intramolecular modes, the new intermolecular modes and IR intensities for CNH . . . NCH

Mode ui

(cm-‘)

VP _ pa

(cm-l\ Ai

(km mol-‘) ADIArb

vi (donor) 3932 - 159 1024 2.9 un (donor) 2326 9 32 0.4 us (donor) 742 208 354 1.0 v,(acceptor) 3647 -5 94 1.4 v2 (acceptor) 2459 13 24 2.0 V3 (acceptor) 900 13 66 0.9 “bend” 59 17 “stretch” 141 3 “shear” 155 55

“Shift from monomer values. bRatio for the complex to the monomer.

TABLE 5

Harmonic frequencies, frequency shifts for the intramolecular modes, the new intermolecular modes and IR intensities for &NH* * * NCH

Mode vi

(cm-‘)

p-pa

i (cm-’ A i (km mol-‘)

v1 (donor) 3626 v,(donor) 2516 vs (donor) 2200 Y,(donor) 1028 z+,(donor) 691 v,(donor) 600 u,(donor) 176 vi (acceptor) 3643 vz (acceptor) 2462 vs (acceptor) 906 “bend” 32 “stretch” 143 “shear” 104

- 249 2787 2.9 21 1730 0.8 11 424 1.6

-9 61 4.1 16

410 1

-9 145 2.2 16 90 7.5 19 63 0.9

1 7

49

“Shift from monomer values. bRatio for the complex tc the monomer.

Thus, bending frequency and force constant are 534 cm-’ and 0.22 mdyn A-’ in CNH, whereas their values are, respectively 742 cm-’ and 0.37 mdyn A-’ in CNH- - l NCH.

The new intermolecular vibrational frequencies are of three different types: (i) H-bond stretching frequency, whose values are 141 cm-l and 143 cm-l in

273

CNH* l l NCH and C&NH* l .NCH, respectively. Hence, the upward frequency shift is only 2 cm-l, whereas the H-bond energy increases by 2.7 kcal mol-l in going from CNH - - l NCH to &NH* l l NCH; (ii) and (iii) the “bend” and “shear” modes, whose frequencies are associated with bending at the HCN (proton acceptor) end and with bending of the hydrogen bond at the CNH or &NH (proton donor) end, respectively. For instance, the frequencies of the “bend” and “shear” modes are 59 and 155 cm-’ in CNH. * l NCH, and their corresponding force constants are 0.008 and 0.084 mdyn A-’ respectively. This means that the hydrogen bond is more easily bent at the proton acceptor,end than at the proton donor end, analogously to &NH* l *NCH in Table 5 and HF. l *NCH in ref. 25.

With respect to IR intensities, we can initially observe in Tables 4 and 5 that the H,,-N stretching intensities are enhanced by a factor of 3 in both hydrogen complexes. Since the equilibrium atomic charge of the bridge hydrogen re- mains practically unaltered after the hydrogen-bond formation, this enhance- ment is due to the charge-flux term. In fact, we can see from Table 6 that the PzzHb element directly associated with the H,,N stretching intensity goes from 0.492 to 0.929 e in CNH,-,* *. N&N. This change is mainly due to the flux term, i.e. it contributes around 90% to the overall enhancement.

It is still more interesting to observe the enhancement of the C=N,, stretch- ing intensity. The theoretical ratio is 2 in CNH,* l *N&H, whereas it is 7.5 in CBNHb* - - N&H. Thus, the enhancement caused by the addition of a C, unit to CNH is surprising. In Table 6 we can see that this increase is due to the charge-flux term. Here both the magnitude and the sign of this term are mark- edly altered as a result of hydrogen-bond formation. It goes from 0.220 e in the free HCNb molecule to - 0.028 e in the HCN,,. - .H,NC complex, and finally to - 0.166 e in the HCNb* - l HbNC3 complex. It is important to note that the intermolecular charge transfer from the proton acceptor molecule to the pro- ton donor molecule is greater in &NH l l l NCH than in CNH. - .NCH, i.e. 0.070

TABLE 6

htensity parameters (in units of electrons, e) for bridge atoms in CNHbS * *NbCH and CaNHb *.*NbCH

(Y Molecule Atomic

charge

Charge flux

Nb HcNb -0.124 - 0.344 0.220 HCNb *.*HbNC - 0.370 - 0.338 - 0.028 HCNb. -. HbNCI - 0.505 - 0.339 -0.166

Hb CNH, 0.492 0.459 0.033 CNH,- *. NbCH 0.929 0.421 0.508

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rather than 0.050 e. This reflects that the charge-flux term is more negative for the C!=Nb stretching in C&NH* - .N&H than in CNH- l *N&H.

Another important change is the enhancement, by a factor of 4, of the CC terminal stretching intensity of CCCNH upon hydrogen-bond formation. It goes from 14.9 km mol-’ in the monomer to 61.0 km mol-’ in the hydrogen complex.

Finally, it is also interesting to point out that the bending intensity in HCN is not altered by complexation. This merely reflects the small change in the equilibrium atomic charges after complexation. Since the charge-flux term is zero for out-of-plane normal modes in planar molecules [ 191, its intensity is simply given by the equilibrium charge of the hydrogen. In fact, the bending intensity predicted by qu is 64 km mol-1 for both the complexes, whereas their values are 66 and 63 km mol-’ in C&NH* l l NCH and CNH* l l NCH, respectively.

CONCLUSION

Hydrogen-bonded complexes involving &NH. - .NCH with n= 1 and 3 are correspondingly stronger than those involving cyanopolyacetylenes as the pro- ton donor, i.e. NC,H* l l NCH. Our calculations also show that the addition of a Cz unit to CNH tends to increase the stabilization energy of the formed com- plex by 2.7 kcal mol-‘. Corrected Mulliken charges in turn indicate that the C,NH (n= 1 and 3) carbenes must also act as proton acceptors, in contrast to standard Mulliken charges. At the moment, we are performing studies in our laboratory in order to analyze the nature of the C,NH carbenes as proton ac- ceptors by considering the C,NH - l *f&NH complexes with n= 1 and 3.

The IR spectral changes of the &NH, CNH and NCH molecules have shown similar characteristics to those observed in other molecules when forming hy- drogen-bonded complexes. These changes have appropriately been interpreted in terms of atomic charges and charge-fluxes.

ACKNOWLEDGMENT

The authors acknowledge partial financial support from the Conselho Na- cional de Desenvolvimento Cientifico e Tecnologico (CNPq) of Brazil.

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