Charge-Transfer Complexes: Stringent Tests for Widely Used Density

J. Phys. Chem. 1996, 100, 12265-12276

12265

Charge-Transfer Complexes: Stringent Tests for Widely Used Density Functionals Eliseo Ruiz,† Dennis R. Salahub,* and Alberto Vela‡ De´ partement de Chimie, UniVersite´ de Montre´ al, C.P. 6128 Succursale centre Ville, Montre´ al, Que´ bec, H3C 3J7 Canada

Downloaded by UNIV OF SUSSEX on September 8, 2015 | http://pubs.acs.org Publication Date (Web): July 25, 1996 | doi: 10.1021/jp9533077

ReceiVed: NoVember 8, 1995; In Final Form: May 3, 1996X

Density functional calculations are reported for charge-transfer complexes (CT), also called electron donoracceptor systems, formed from ethylene or ammonia interacting with a halogen molecule (C2H4‚‚‚X2, NH3‚‚‚X2, X ) F, Cl, Br, and I). In all cases, the local density approximation provides a strong overestimation of the intermolecular interaction. The generalized gradient approximation moves the results in the right direction but, in general, not nearly far enough; large errors remain. We attribute the problem to the too rapid asymptotic decay of the exchange-correlation potential associated with the imperfect cancellation of the self-interaction. This breakdown of the potential is reflected in a set of incorrect eigenvalues (orbital electronegativities) that play a crucial role in governing the charge transfer and, hence, the interaction energy. The inclusion of some Hartree-Fock exchange using hybrid methods provides a large improvement, and the parameters related to the intermolecular interaction for the so-called half-and-half potential are in very good agreement with those obtained through second-order Møller-Plesset calculations and with available experimental data. However, the more widely used three-parameter, B3LYP, functional does not perform well; the hybrid methods are not a panacea.

I. Introduction Density functional theory (DFT) has known wide success for the description of strongly bonded systems,1-3 and because of this, DFT is currently being used by a rapidly growing community that cuts across many subdisciplines of chemistry. The challenge of describing hydrogen bonds has also been taken up.4,5 For these weak interactions the accuracy of current functionals, though not perfect, is sufficient for many purposes, which has raised serious interest in DFT for biochemical applications as well. The origin of the forces responsible for intermolecular binding has been the subject of many experimental6,7 and theoretical8-10 studies. Although the majority of these have focused on van der Waals11-13 and hydrogen-bonded systems,14-16 other kinds of interaction showing special importance are those present in the so-called charge-transfer or electron donor-acceptor complexes.17-20 This kind of complex has been known for a long time, at least since the classic study of the change of color and UV-visible spectrum of iodine solutions by Benesi and Hildebrand.21,22 A simple quantum mechanical theory (the charge-transfer resonance model) was formulated by Mulliken.23 According to this theory the ground state is a resonance between a nonbonded structure (D, A) and the transfer of an electron from the donor D to the acceptor A (D+-A-). The ground state wave function for such a complex can be written as GS ΨDA ≈ aψ(D,A) + bψ(D+,A-)

where a . b. The amount of charge transferred is reflected in the relative values of the coefficients a and b. This theory was widely used and developed because of its success at explaining spectroscopic and structural results and because of † Permanent address: Departament de Quı´mica Inorga ` nica, Diagonal 647, Universitat de Barcelona, 08028 Spain. ‡ Permanent address: Departamento de Quı´mica, Universidad Auto ´ noma Metropolitana-Iztapalapa, A.P. 55-534, Me´xico D.F. 09340, Me´xico. X Abstract published in AdVance ACS Abstracts, June 15, 1996.

S0022-3654(95)03307-7 CCC: $12.00

its simplicity.24-26 However, it failed to interpret the stability of some complexes showing that interactions other than simple charge transfer may be important.27,28 Current pictures include dispersion and electrostatic and polarization contributions along with the charge-transfer term.29 The accurate calculation of the different contributions to the energy has been a main topic in quantum mechanical studies of weak interactions (van der Waals forces, hydrogen bonds, and charge-transfer interactions). Several authors have shown that the inclusion of electron correlation is crucial to reproduce these properly.8-10 Density functional theory (DFT) offers an alternative treatment of electron correlation that has been successfully applied to the description of diverse molecular properties.2 Attempts to apply DFT to intermolecular interactions are rather recent and still relatively few. Hydrogen bond complexes have been described with the generalized gradient approximation (GGA) with an accuracy that, though still not perfect, is sufficient for many purposes.4,5,30,31 The few available results for weaker van der Waals systems, where dispersion forces come to the fore, can best be described as erratic.32-34 These clearly represent an important frontier for DFT. An important number of quantum mechanical studies35-49 have been made in order to understand the nature of the chargetransfer interactions. These studies used semiempirical or Hartree-Fock (HF) methods. Recently, more accurate calculations including electronic correlation have been carried out.50,51 The goal of the present paper (a preliminary account has appeared51a) is to test the applicability of the quantum methods based on density functional theory to describe the charge-transfer complexes. Since electron correlation is included in the DFT methods, one can analyze its role in the description of these systems. To analyze the role of the long-range behavior of the exchange potential in DFT, we also present results using a mixture of Hartree-Fock and density functional exchange, the recently proposed variation to Becke’s hybrid method known as HHLYP.52,53 The three-parameter B3LYP potential is also tested in some cases. For comparison, second-order MøllerPlesset (MP2)54 calculations were also performed. © 1996 American Chemical Society

12266 J. Phys. Chem., Vol. 100, No. 30, 1996


The charge-transfer complexes have been classified according to the nature of the donor-acceptor orbitals.55 This paper uses DFT to study π-σ type systems formed from ethylene interacting with a halogen molecule (C2H4‚‚‚X2, X ) F, Cl, Br, and I) and n-σ type ammonia-halogen complexes (NH3‚‚‚X2, X ) F, Cl, Br, and I). The charge-transfer complexes between ethylene and halogen molecules have been widely studied because of their importance in the mechanism of electrophilic addition of halogen molecules to ethylene.35,56 It is most generally admitted that the first step of this reaction begins with the formation of such complexes. The complex between ethylene and chlorine has received the most attention in previous works. The analysis of experimental infrared absorption spectra shows that the ethylene-chlorine complex has C2V symmetry.57 The semiempirical study of Nelander36,57 shows that the axial-perpendicular structure (1) is most stable. Recently, Hartree-Fock calculations42,58 for this

complex have yielded results in agreement with those of semiempirical calculations, but the stabilization energies are similar for different geometries. However, the optimized distance between the two molecules obtained with semiempirical methods is underestimated in comparison with ab initio calculations. It is worth noting that different semiempirical methods give significant variations in the binding energies (-1.1 to -6.2 kcal/mol).35,36,59 The analysis of ab initio results shows the importance of the dispersion contribution to the calculated stabilization energies,42 indicating that the inclusion of electronic correlation in the calculations is indispensable for an accurate description of the charge-transfer complexes. More recently, Matsuzawa et al.60,61 carried out a Hartree-Fock study of infrared absorption bands of the complexes between ethylene and ammonia as donors, with chlorine and chlorine fluoride as acceptors. One might expect that the interactions in the complexes with ammonia would be stronger than in the case of ethylene because of the stronger donor character of the lone pair in comparison with the π system. The Hartree-Fock calculations, in the complexes between ammonia and F2 and between Cl2 and ClF, performed by Lucchese et al.62 and by Umeyama et al.39 show some striking differences with later studies including electronic correlation energy. The electronic correlation energy in the calculations of these complexes has been included using the second-order Møller-Plesset method by Reed et al.51 and with the extended geminal models by Roeggen.50 The discrepancies between these calculations are due to an underestimation of the interaction energy at the Hartree-Fock level, reflected in a longer intermolecular distance and smaller binding energies. II. Computational Method Density functional calculations using Gaussian type orbitals were performed with the program deMon-KS (densite´ Montre´al-Kohn-Sham). A description of the theory and particular characteristics of the program have been reported previously.1,2,63 We used a triple-zeta plus polarization basis set for the carbon, nitrogen, and fluorine atoms, constructed as in ref 64, with a

Ruiz et al. (7111/411/1) contraction pattern. A set of the same quality was used for chlorine with a (73111/6111/1) contraction pattern. For hydrogen, bromine, and iodine, double-zeta plus polarization basis sets with (41/1), (63321/5321/41), and (633321/53321/ 531) contraction patterns, respectively, were used. The auxiliary basis sets used to fit the charge density and the exchangecorrelation potential were H (5,1;5,1), C (4,4;4,4), N (4,4;4,4), F (4,4;4,4), Cl (5,4;5,4), Br (5,5;5,5), and I (5,5;5,5). The charge density was fitted using an analytical, variational least squares fit, whereas numerical values on a grid were used in the least squares fit of the exchange-correlation potential.65 The grid corresponds to that defined with the key word FINE in deMon. During the SCF procedure the grid consists of 32 radial shells with 26 angular points, and in the last cycle the exchangecorrelation contributions were integrated numerically on an augmented grid with the same 32 radial shells but with 50, 110, or 194 angular points.66 The form of the local spin density approximation (LSDA) used is that derived by Vosko, Wilk, and Nusair (VWN).67 We have carried out three different nonlocal spin density calculations within the generalized gradient approximation (GGA). The first scheme used is Becke’s gradient correction for the exchange68 along with the correlation term of Perdew69 (BP). In the second, we have employed the exchange correction of Perdew and Wang70 with the correlation term of Perdew69 (PP). The final scheme is formed from the exchange and correlation terms proposed by Perdew and Wang71,72 (PW91). The optimization of the geometries has been done without symmetry constraints using the Broyden-Fletcher-Goldfarb-Shanno algorithm73-76 with a threshold of 5 × 10-4 au for the norm of the gradient. To obtain the harmonic frequencies, the force method of Pulay77 was applied (first derivatives of the energy with respect to the nuclear coordinates were calculated analytically and second derivatives by finite differences). The second-order Møller-Plesset (MP2), HHLYP, and B3LYP calculations have been performed with the Gaussian92/ DFT program.78 The HHLYP and B3LYP functionals are based on the work of Becke52,53 who built on earlier work79, 81 on the so-called adiabatic connection method to propose including a component of exact (Hartree-Fock-like) exchange in the exchange functional. It should be noted82,83 that HHLYP and B3LYP are not the functionals originally proposed by Becke. They are, however, in wide use so that the recent literature will provide validation in various contexts. It will suffice for our purposes to note that HHLYP contains a larger proportion of Hartree-Fock exchange (a coefficient of 0.5) than does B3LYP (a coefficient of 0.2). The 6-311G** basis set has been employed in the Gaussian 92/DFT calculations for H, C, N, and Cl. For Br and I we used the same orbital basis set as in the deMon-KS calculations. The density functional part of the exchange-correlation terms in the HHLYP calculations has been calculated numerically without auxiliary basis sets. In the same way, the Coulomb term has been calculated directly without fitting the charge density. The pruned grid,84 used by default, designated as SG-1 is applied in the numerical calculation of the exchangecorrelation energy, except for the systems with bromine and iodine atoms where a grid with 50 radial shells, each one including 194 angular points, was used. The calculations of the first and second derivatives of the energy with respect to the nuclear coordinates were carried out analytically.85 We have performed a comparative calculation using both programs with the same exchange-correlation functional in order to see the influence of the different grids, basis sets, and algorithms. In Table IS (in Supporting Information) we present

Charge-Transfer Complexes

J. Phys. Chem., Vol. 100, No. 30, 1996 12267

TABLE 1: Optimized Geometrical Parameters, Rotational Constants, Harmonic Cl-Cl Stretching Frequencies, Total and Interaction Energies, and Mulliken Population Analysis for the C2H4‚‚‚Cl2 Complex Calculated with Different Methodologies and the Available Experimental Datag VWN d(C-H) d(C-C) d(Cl-Cl) d(Cl‚‚‚plane) C-C-H plane (C-C)-H Ao Bo Co


Cl-Cl

BSSE corrected BSSE noncorrected BSSE Cl1 Cl2 C H

1.095 (1.097) 1.344 (1.326) 2.130 (2.023) 2.435 121.6 (121.8) 1.0 (0.0)

BP 1.092 (1.094) 1.348 (1.347) 2.137 (2.053) 2.649 121.6 (121.7) 0.5 (0.0)

PP

PW

Distances (Å) 1.092 (1.094) 1.079 (1.081) 1.347 (1.336) 1.345 (1.329) 2.123 (2.043) 2.157 (2.048) 2.730 2.448 Angles (deg) 121.6 (121.8) 121.6 (121.7) 0.8 (0.0) 1.1 (0.0)

HHLYP 1.077 (1.077) 1.322 (1.317) 2.038 (2.021) 3.055 121.7 (121.7) 0.1 (0.0)

MP2 1.085 (1.085) 1.341 (1.337) 2.044 (2.028) 3.003 121.4 (121.4) 0.1 (0.0)

expt .(1.085)a .(1.339)a .(1.988)b 3.128c,d .(121.1)a .(0.0)a

24.5335 1.5409 1.4796

24.4732 1.4042 1.3528

Rotational Constants (GHz) 24.4988 24.7310 1.4043 1.5148 1.3530 1.4554

25.3455 1.2383 1.1996

24.7689 1.2613 1.2202

25.520c,d 1.2244c,d 1.1841c,d

386 (544)

385 (519)

Frequency (cm-1) 392 (520) 373 (528)

515 (550)

506 (539)

527e (559)b

-995.263 931

-999.071 759

Total Energy (au) -999.435 567 -998.902 834

-998.927 808

-997.584 575

-12.6 -12.6

-5.2 -5.2

0.0

0.0

-0.017 -0.147 -0.297 (-0.286) +0.189 (+0.143)

-0.033 -0.177 -0.224 (-0.233) +0.150 (+0.116)

Interaction Energy (kcal/mol) -6.3 -6.8 -6.5 -6.9 0.2

0.1

Mulliken Analysis -0.026 -0.019 -0.100 -0.149 -0.229 (-0.226) -0.284 (-0.296) +0.141 (+0.113) +0.184 (+0.148)

-2.1 -2.5

-1.6 -2.9

0.4

1.3

+0.008 -0.057 -0.231 (-0.224) +0.128 (+0.112)

-1.7 to 2.7f

+0.028 -0.064 -0.231 (-0.222) +0.125 (+0.111)

a

Reference 90. b Reference 91. c Reference 87. d Reference 86. eReference 57. fReference 48. g The values for the free molecules are indicated in parentheses. The Mulliken populations in the MP2 column were calculated at the HF level.

the results for the isolated halogen molecules, ethylene, and ammonia. We report the geometries, frontier orbital energies, HOMO-LUMO gaps, harmonic frequencies, and total energies. Even though there are some small discrepancies, the overall agreement in the optimized geometries, harmonic frequencies, and orbital and total energies is acceptable. These discrepancies will not affect the strong qualitative trends discussed below. III. Results A. Ethylene-Halogen Molecule Complexes. In this section we present results for the complexes C2H4‚‚‚X2 (with X ) F, Cl, Br, and I). We will focus on the complex with chlorine because it is the most studied complex of this family. There are several geometrical possibilities for the C2H4‚‚‚X2 complexes.45 Using the VWN, PP, and MP2 methods, we have found, in agreement with all previous work, that the most stable structure corresponds to the so-called axial-perpendicular or T-shaped (1) structure. Thus, all results reported below have been obtained using this geometry. 1. Ethylene-Chlorine Complex. As mentioned previously, this system has been the most widely studied, and thus, it is the unique case where there are available experimental values for the ethylene-halogen distance,86,87 the rotational constants,86 the vibrational spectra,57,88 and estimated binding energies.59,89 In Table 1 we report the results corresponding to the ethylenechlorine complex together with the experimental values. The geometries for the free molecules calculated with all methods are in good agreement with experimental results. The most striking features in the calculations with the different methods are the chlorine-ethylene distances. The LSDA and GGA methods provide very short intermolecular distances compared with the experimental value. Even though the GGA methods improve the intermolecular distance, they are not accurate enough to describe this parameter properly . Since one of the important parts missing from the GGA is the correct

asymptotic behavior of the exchange-correlation potential,92 one might expect that the inclusion of HF exchange could play a crucial role in the description of these interactions. It is wellknown that the wrong asymptotic behavior and the derivative discontinuity of the exchange and correlation energy in DFT lead to a reduction of the HOMO-LUMO gap in comparison with the exact one.93 These interactions are controlled by the energy difference between the orbitals that participate in the charge-transfer process (normally the HOMO and LUMO).18 The small value of the HOMO-LUMO energy obtained with LSDA and the GGA would imply an overestimation of the strength of the interaction. Matsuzawa et al.61 obtained an intermolecular distance of 3.337 Å at the Hartree-Fock level with a double-zeta basis set. This large distance can be attributed to the lack of correlation in the HF calculations. The presence of HF exchange in the HHLYP and MP2 calculations provides larger intermolecular distances, which are closer to the experimental values compared with results from LSDA and GGA. The B3LYP results lie between those of the GGA and MP2. There is a clear relation between the intermolecular interaction and the amount of Hartree-Fock exchange involved. The amount of Hartree-Fock exchange present in the B3LYP method is smaller than in the HHLYP method, and thus, the results are intermediate between the pure density functional methods and the HHLYP method. As a further test, we have performed calculations with a pure Hartree-Fock exchange along with the Lee-Yang-Parr correlation functional. These yield an intermolecular distance of 3.142 Å, in excellent agreement with the experimental value, but completely wrong results are found for the frequencies and the bond distances. The drawbacks of this method have been reported previously.94,95 The complete neglect of correlation using the Hartree-Fock method underestimates considerably the intermolecular interaction. For this complex, the inclusion of the Hartree-Fock exchange with a coefficient of 0.5 in the HHLYP


12268 J. Phys. Chem., Vol. 100, No. 30, 1996 approach provides the best results among the density functional methods, with results being similar to those obtained with second-order Møller-Plesset (MP2) theory and to the available experimental data. The analysis of the calculated rotational constants shows that, of the methods we have considered, the HHLYP method provides the best description for these molecular parameters. The Bo and Co constants are related to the intermolecular distance, and the overestimation of the interaction is reflected in the larger values at the VWN and GGA levels. The charge transfer in this complex takes place from the π bonding orbital of ethylene (HOMO) to the σ antibonding orbital of the chlorine molecule (LUMO). Thus, as can be seen in Table 1, both the C-C bond and the Cl-Cl bond increase as a result of the interaction. It is worth noting that the short intermolecular distance obtained with the LSDA and the GGA reflects an overestimation of the interaction that is also manifested in the large variation of the Cl-Cl bond distance compared with the HHLYP and MP2 cases. This fact is related to the amount of charge transferred to the chlorine molecule as can be seen from the Mulliken population analysis reported in Table 1. On the other hand, the proximity of the chlorine molecule shifts the hydrogen atoms out of the molecular plane in the opposite direction (in Table 1, we report the quantity called “plane (C-C)-H” defined as the out-of-plane angle for the C-H bond). Also in this case, the magnitude of the shifts is related to the different strengths of the interaction obtained in each method. The harmonic vibrational frequencies for the ethylenechlorine complex and those corresponding to the isolated molecules are reported in Table IIS in Supporting Information along with the HF frequencies obtained by Matsuzawa et al.61 and the available experimental data.88,89 We only note here that, as expected, the Cl-Cl and C-C stretching frequencies are the normal modes that suffer the greatest changes with the interaction and correlate with the degree of charge transfer. The pure density functionals underestimate the Cl-Cl frequency seriously, giving values between 373 and 392 cm-1 compared with the experimental value of 527 cm-1; HF yields 520, MP2 505, and HHLYP 515 cm-1. The better agreement of these latter methods with the experimental changes in the stretching frequencies due to the intermolecular interaction may indicate that the inclusion of HF exchange (and its correct asymptotic behavior) is an important consideration for the accurate description of these complexes. We have employed the “supermolecule” approach to estimate the interaction energy (Eint).16 The full counterpoise correction proposed by Boys and Bernardi96 has been used to correct for the basis set superposition error (BSSE). The trend observed in the calculated interaction energies is closely related to the intermolecular distance. As expected, the interaction increases when the intermolecular distance decreases. Thus, the VWN functional produces an overestimated interaction energy in comparison with the GGA methods, as in the previously studied hydrogen-bonded systems.4 The inclusion of the HF exchange term (HHLYP, MP2) reduces the interaction energy dramatically, providing results that are in better agreement with the available experimental data than those corresponding to the GGA methods. Unfortunately, the experimental interaction energies are reported only in solution, but the values with five different solvents are within the range of -1.7 to -2.7 kcal/ mol,59,89 and they are in excellent agreement with the HHLYP and MP2 results. The lack of electronic correlation in the HF method is the reason for the small interaction energy -0.50 kcal/mol obtained by Matsuzawa et al.61 As has been reported

Ruiz et al.

Figure 1. Total electron density for C2H4‚‚‚Cl2, in the plane containing the carbon and chlorine atoms at the optimized geometry using (a) VWN functional, (b) PP functional, and (c) HHLYP methods. The isodensity lines are separated by 0.01 e/bohr3.

previously in hydrogen-bonded systems, the BSSE corrections in DFT are considerably smaller than for MP2.30 The BSSE correction in the HHLYP method is less than for the MP2 case, as expected for a mixture of the HF and DFT methods. The use of diffuse functions would reduce the BSSE in the MP2 and HHLYP methods,97 but to allow comparisons of the results, we have used the same basis set quality in all methods. The total electron density for the C2H4‚‚‚Cl2 complex is depicted in Figure 1 for three of the methods employed in the present work at the corresponding optimized geometries. One can see that the main differences among the three cases appear in the intermolecular region. In the VWN density plot, the electron density in the intermolecular region is enhanced because of the overestimation of the interaction with this method. The nonlocal correction in the PP functional reduces the electron density in the intermolecular region, but it is with the HHLYP method using the HF exchange that the accumulated density is smallest. Even though Figure 1 helps us to analyze the intermolecular interaction, more detailed features become visible when one takes the electron density differences into account (Figure 2). We choose the optimized geometry using the HHLYP method as the reference, since it provides the best



Figure 2. Total electron density differences for C2H4‚‚‚Cl2, in the plane containing the carbon and chlorine atoms at the HHLYP optimized geometry: (a) F(VWN)-F(HHLYP); (b) F(PP)-F(HHLYP); (c) F(VWN)-F(PP). The isodensity lines are separated by 0.002 e/bohr3.

overall DFT description. It is worth mentioning that the small asymmetries observed in the plots are due to the fact that the geometry is slightly distorted from C2V symmetry. The first noticeable characteristic is the topological similarity between parts a and b of Figure 2. It can be seen that the VWN and PP methods have a tendency to accumulate electron density in the region corresponding to the σ* Cl-Cl orbital. Also, the depletion of the density with the VWN and PP methods is important in the bonding regions. This behavior has also been reported previously in the comparison of total electron densities calculated using pure DFT methods with the HF and MP2 densities.98 Figure 2c shows that the main differences due to the inclusion of the gradient corrections in the exchangecorrelation term, relative to the LSDA, are centered around the C-C bond. The VWN functional tends to polarize the charge density along the C-C bond axis. The intermolecular interaction causes a polarization in the chlorine atom nearest the ethylene molecule. This means that the large differences between the pure DFT and HHLYP methods around the chlorine molecule are not only caused by the intermolecular interaction but also because of the particular description of the Cl-Cl bond provided by each method.

J. Phys. Chem., Vol. 100, No. 30, 1996 12269 2. C2H4‚‚‚X2 (X ) F, Br, and I) Complexes. Experimentally, it is well-known that the strength of the charge-transfer interaction for the halogen molecules increases normally as one goes down the periodic table.55 As will be further discussed in section III.C, this behavior is related to the different energies of the LUMO of the acceptor halogen molecule. To analyze this trend, in this section we present results for the intermolecular complexes between ethylene and fluorine and between bromine and iodine. Even though a transition state for the fluorine molecule with ethylene was found to have a parallel structure (2),99 all the theoretical methods considered in this work predict that the T-shaped (or perpendicular) structure is the most stable. The results for the fluorine complex are shown in Table 2. One expects that the interaction of ethylene with fluorine should be the smallest, and it is indeed the case for the description of this system with HHLYP and MP2. However, the VWN and GGA results are dramatically overestimated, as can be seen from the different parameters that are relevant to the description of these systems: the F-F bond distance and the intermolecular distance, the harmonic F-F stretching frequency and the interaction energies. In contrast with the results obtained in bonded systems, the inclusion of nonlocal corrections in the GGA methods for the complex with fluorine is not enough to improve the energy differences (interaction energies). The critical factor is the presence of HF exchange in the HHLYP and MP2 methods. Probably, the remarkable failure of the VWN and GGA descriptions of the fluorine complex is due to the fact that the fluorine atom, being the smallest among the halogens, has the worst long-range effective potential at distances corresponding to the intermolecular region. For the bromine ethylene complex (Table 3), the differences in the results between the theoretical models employed is less pronounced than in the previous cases. In particular, the intermolecular distance calculated with BP and PP levels is quite close to the HHLYP and MP2 values. However, there is a substantial weakening of the Br-Br bond reflected in the large decrease of the stretching frequency with respect to the isolated molecule. The analysis of the interaction energies shows a small increase of the intermolecular bond strength with respect to that of the chlorine complex (Table 1). This fact is in agreement with the experimental trend that the interaction increases as one goes down the periodic table. It is also important to note that in the Mulliken population analysis, the halogen atom closest to the ethylene has a positive charge in the VWN and GGA approaches, as is also the case in HHLYP and MP2 calculations. Prissette et al.42 presented results at the HF level for this complex. They obtain an intermolecular distance of 3.57 Å that reduces to 3.05 Å with the perturbative incorporation of the dispersion energy, and the interaction energy changes from -0.87 kcal/mol to -4.39 kcal/mol. Their results including the dispersion contribution are in good agreement with our MP2 values. Following the tendency of the previous halogens, the iodine complex (Table 4) has the smallest discrepancies between the calculated values of the intermolecular distances for the various theoretical levels considered. The VWN interaction energy shows the normal overestimation observed in LSDA energy differences. The GGA interaction energies are somewhat larger than the HHLYP and MP2 values. The differences are in the range of the electron correlation contributions not included at the MP2 level. Also for the iodine complex, Prissette et al.42 reported results at the HF level including the dispersion contribution, and they found a value for the intermolecular distance of 3.30 Å in very good agreement with the HHLYP result, and the corresponding interaction energy was found to

12270 J. Phys. Chem., Vol. 100, No. 30, 1996

Ruiz et al.

TABLE 2: Optimized Geometrical Parameters, Harmonic F-F Stretching Frequencies, Total and Interaction Energies and Mulliken Population Analysis for the C2H4‚‚‚F2 Complex Calculated with Different Methodologies and the Available Experimental Datac VWN d(C-H) d(C-C) d(F-F) d(F...plane)

1.096 (1.094) 1.344 (1.335) 1.606 (1.428) 1.922

PP

PW

Distances (Å) 1.090 (1.094) 1.367 (1.336) 1.738 (1.445) 1.891

1.076 (1.081) 1.367 (1.329) 1.669 (1.411) 1.836

C-C-H plane (C-C)-H

121.2 (121.8) 1.3 (0.0)

121.3 (121.7) 1.1 (0.0)

Angles (deg) 121.3 (121.8) 121.3 (121.7) 1.1 (0.0) 1.1 (0.0)

F-F

486 (1056)

471 (991)

Frequency (cm-1) 511 (982) 492 (1042)

-276.210 277

-278.237 421

Total Energy (au) -278.497 035 -278.132 769

BSSE corrected BSSE noncorrected BSSE


1.094 (1.097) 1.367 (1.326) 1.679 (1.397) 1.798

BP

F1 F2 C H

-38.4 -38.4

-25.7 -25.8

0.0

0.1

-0.117 -0.289 -0.177 (-0.286) +0.189 (+0.143)


-0.132 -0.253 -0.123 (-0.233) +0.158 (+0.116)

0.5

Mulliken Analysis -0.143 -0.098 -0.274 -0.269 -0.102 (-0.226) -0.184 (-0.296) 0.157 (+0.113) +0.182 (+0.148)

HHLYP 1.077 (1.077) 1.318 (1.317) 1.374 (1.367) 2.945

MP2 1.085 (1.085) 1.338 (1.337) 1.421 (1.412) 2.894

expt .(1.085)a .(1.339)a .(1.412)b

121.4 (121.4) 0.1 (0.0)

.(121.1)a .(0.0)a

1051 (1095)

873 (918)

.(917)b

-278.034 453

-277.502 296

121.7 (121.7) 2.8 (0.0)

-0.5 -1.1

-0.4 -1.2

0.6

0.8

+0.012 -0.016 -0.228 (-0.224) +0.115 (+0.112)

+0.019 -0.022 -0.224 (-0.222) +0.113 (+0.111)

a Reference 90. b Reference 91. cThe values for the free molecules are indicated in parentheses. The Mulliken population analyses in the MP2 column were calculated at the HF level.

TABLE 3: Optimized Geometrical Parameters, Harmonic Br-Br Stretching Frequencies, Total and Interaction Energies, and Mulliken Population Analysis for the C2H4‚‚‚Br2 Complex Calculated with Different Methodologies and the Available Experimental Datac VWN d(C-H) d(C-C) d(Br-Br) d(Br‚‚‚plane)

1.095 (1.097) 1.347 (1.325) 2.392 (2.299) 2.496

BP 1.091 (1.094) 1.350 (1.335) 2.408 (2.334) 2.712

PP

PW

Distances (Å) 1.092 (1.094) 1.347 (1.336) 2.416 (2.355) 2.842

1.079 (1.081) 1.349 (1.329) 2.423 (2.333) 2.536

HHLYP 1.077 (1.077) 1.323 (1.317) 2.324 (2.304) 3.081

MP2 1.085 (1.085) 1.343 (1.337) 2.347 (2.322) 2.966

expt .(1.085)a .(1.339)a .(2.281)b

C-C-H plane (C-C)-H

121.5 (121.8) 1.6 (0.0)

121.6 (121.7) 0.5 (0.0)

Angles (deg) 121.6 (121.8) 121.6 (121.7) 2.1 (0.0) 1.1 (0.0)

121.6 (121.7) 0.3 (0.0)

121.3 (121.4) 0.3 (0.0)

.(121.1)a .(0.0)a

Br-Br

260 (338)

256 (319)

Frequency (cm-1) 253 (305) 252 (322)

320 (344)

303 (330)

.(325)b

-5218.210 430

-5226.601 675

Total Energy (au) -5226.683 078 -5226.267 812

-5225.819 391

-5222.321 130

BSSE corrected BSSE noncorrected BSSE Br1 Br2 C H

-14.0 -14.4

-6.0 -6.1

0.4

0.1

+0.043 -0.177 -0.312 (-0.286) +0.189 (+0.143)

+0.001 -0.135 -0.290 (-0.233) +0.152 (+0.116)


0.3

Mulliken Analysis +0.003 +0.021 -0.113 -0.167 -0.229 (-0.226) -0.298 (-0.296) +0.141 (+0.113) +0.186 (+0.148)

-2.6 -3.0

-2.5 -4.9

0.4

2.4

+0.008 -0.062 -0.237 (-0.224) +0.131 (+0.112)

+0.021 -0.071 -0.240 (-0.222) +0.133 (+0.111)

a Reference 90. b Reference 91. c The values for the free molecules are indicated in parentheses. The Mulliken population analyses in the MP2 column were calculated at the HF level.

be -4.33 kcal/mol, which is very close to the corresponding MP2 value.Overall, for the ethylene-halogen molecule complexes, as the size of the halogen atom increases, the role played by the HF exchange decreases and the spread of values obtained with different methods is narrower. B. Ammonia-Halogen Molecule Complexes. In this section we present results for the family of complexes of ammonia with a halogen molecule (NH3‚‚‚X2, X ) F, Cl, Br, and I). These complexes were chosen in order to study a different type of charge-transfer interaction. In this case the orbitals involved in the interaction are the ammonia lone pair

and the σ antibonding orbital of the corresponding halogen molecule. This family of charge-transfer systems may be classified as n-σ type complexes. Owing to the enhanced donor capabilities of the ammonia lone pair in comparison with the π system, one expects that the intermolecular interaction for the ammonia complexes would be stronger than in the ethylene complexes. The geometry studied in this case corresponds to the parallel orientation of the halogen molecule with respect to the ammonia lone pair (3). As in the ethylene case, the complex with chlorine has been the most widely studied, and thus, it will be presented first and in more detail.

+0.024 -0.122 -0.258 (-0.233) +0.153 (+0.116) +0.057 -0.156 -0.326 (-0.286) +0.187 (+0.143) I1 I2 C H

Reference 90. b Reference 91. c The values for the free molecules are indicated in parentheses. The Mulliken population analyses in the MP2 column were calculated at the HF level.

-4.3 -4.8 0.5 -11.2 -12.1 0.9

-139 19.603 666 -13 906.055 051


184 (213) 188 (227) I-I

121.7 (121.7) 1.1 (0.0) 121.6 (121.8) 1.3 (0.0) C-C-H plane (C-C)-H

a

+0.037 -0.088 -0.244 (-0.222) +0.135 (+0.111) +0.014 -0.064 -0.239 (-0.224) +0.132 (+0.112)

-2.9 -4.7 1.8 -2.3 -2.8 0.5

-13 918.275 881

-13 913.285 391

.(214)b 208 (222) 214 (224)

.(121.1)a .(0.0)a 121.3 (121.4) 0.4 (0.0) 121.6 (121.7) 0.4 (0.0)

.(1.085)a .(1.339)a .(2.666)b 1.085 (1.085) 1.343 (1.337) 2.757 (2.743) 3.171 1.077 (1.077) 1.323 (1.317) 2.729 (2.612) 3.340

J. Phys. Chem., Vol. 100, No. 30, 1996 12271

Distances (Å) 1.093 (1.094) 1.109 (1.081) 1.347 (1.336) 1.344 (1.329) 2.771 (2.722) 2.799 (2.733) 3.036 2.821 Angles (deg) 121.7 (121.8) 121.6 (121.7) 1.1 (0.0) 1.1 (0.0) Frequency (cm-1) 191 (220) 184 (214) Total Energy (au) -139 18.832 568 -13 919.118 327 Interaction Energy (kcal/mol) -5.4 -5.7 -5.4 -6.7 0.0 1.0 Mulliken Analysis +0.026 +0.024 -0.100 -0.134 -0.229 (-0.226) -0.309 (-0.296) +0.141 (+0.113) +0.182 (+0.148) 1.092 (1.094) 1.347 (1.335) 2.785 (2.727) 2.995 1.095 (1.097) 1.343 (1.326) 2.766 (2.694) 2.765 d(C-H) d(C-C) d(I-I) d(I‚‚‚plane)

expt MP2 HHLYP PW PP BP VWN

TABLE 4: Optimized Geometrical Parameters, Harmonic I-I Stretching Frequencies, Total and Interaction Energies and Mulliken Population Analysis for the C2H4‚‚‚I2 Complex Calculated with Different Methodologies and the Experimental Available Datac



1. Ammonia-Chlorine Molecule Complex. For this complex, experimental data for the intermolecular distance87,100 and the vibrational spectra101,102 are available. Unfortunately, to our knowledge the interaction energy has not been determined experimentally. The results for this complex are presented in Table 5. At all levels of theory, the N-H bond distance remains unaffected by the interaction. The electron transfer to the ClCl σ* orbital is reflected in the increase of this bond distance. The analysis of the intermolecular distances shows, as in the case of ethylene, that the VWN and GGA methods overestimate the interaction, and thus the Cl‚‚‚N distance is shorter than in the HHLYP and MP2 calculations. For this reason, the changes in the Cl-Cl bond distance and in the Cl‚‚‚N-H angle are more pronounced in the VWN and GGA methods. Nevertheless, the experimental intermolecular distance is larger than that provided by all theoretical methods, in a similar fashion as in the ethylene complex. The HF calculations performed by Lucchese et al.62 and Umeyama et al.,39 using a double-zeta basis set in both cases, yield 2.93 Å for the intermolecular distance. More recently, Matsuzawa et al.61 also at the HF level but with a 6-31+G* basis set found 2.890 Å. Roeggen and Dahl,50 using an extended geminal model, obtained 2.57 Å for the same distance. Trends for the Cl-Cl vibrational frequency were found to be similar to those discussed above for the C2H4‚‚‚Cl2 complexes. The complete set of harmonic vibrational frequencies for the NH3‚‚‚Cl2 complex and those corresponding to the isolated molecules are gathered in Table IIIS in Supporting Information. Turning to the energy, one can see, as in the ethylene complexes, that the absence of the HF exchange tends to overestimate this interaction. The previously reported HF interaction energies are -2.39 kcal/mol by Lucchese el al.,62 -2.90 kcal/mol by Umeyama et al.,39 and -2.48 kcal/mol by Matsuzawa et al.61 The reason for the differences is not only associated with the distinct basis but also that in Umeyama’s results, the dispersion contribution has been added perturbatively. The only reported case that contains electronic correlation energy is the work of Roeggen et al.50 These authors reported an interaction energy of -5.89 kcal/mol, in very good agreement with our MP2 value. Even though there are no experimental interaction energies available, we can use the reported experimental values of the quadratic intermolecular stretching force constant to gauge the strength of the interaction.87 For the ethylene complex with a chlorine molecule, the value is 7.1 N m-1, while for the ammonia complex it is 12.7 N m-1 indicating that the interaction with ammonia is stronger than with ethylene, in agreement with our calculated interaction energies. 2. NH3‚‚‚X2 (X ) F, Br, and I) Complexes. The results for the fluorine complex are displayed in Table 6. The trends observed in the optimized F-F bond and the intermolecular distances and in the harmonic F-F stretching frequency and the interaction energies are very similar to those obtained in the ethylene complex. In comparison with the ethylene complex at HHLYP and MP2 levels, all the parameters related to the strength of the interaction are consistent with the fact that the interaction in the ammonia complex is stronger. However, in the VWN and GGA methods the interactions in both complexes are very similar and do not reflect the well-known trend that they are stronger for the ammonia complexes in comparison with the ethylene ones. We found this behavior only for the fluorine complexes, and it is probably due to the faster decay of the effective potential in the intermolecular bond region of

12272 J. Phys. Chem., Vol. 100, No. 30, 1996

Ruiz et al.

TABLE 5: Optimized Geometrical Parameters, Harmonic Cl-Cl Stretching Frequencies, Total and Interaction Energies, and Mulliken Population Analysis for the NH3‚‚‚Cl2 Complex Calculated with Different Methodologies and the Available Experimental Datae VWN d(N-H) d(Cl-Cl) d(Cl‚‚‚N)

1.023 (1.023) 2.146 (2.023) 2.283

1.021 (1.023) 2.167 (2.058) 2.382

PP

PW

HHLYP

Distances (Å) 1.022 (1.025) 1.012 (1.017) 2.171 (2.043) 2.166 (2.048) 2.371 2.238

MP2

1.005 (1.006) 2.075 (2.021) 2.498

108.4 (111.6)

109.6 (112.4)

Angles (deg) 109.7 (112.7) 109.6 (113.4)

110.1 (111.7)

111.2 (112.8)

Cl-Cl

396 (541)

379 (519)

Frequency (cm-1) 374 (520) 392 (528)

464 (550)

450 (539)

-973.521 577

-977.052 019

Total Energy (au) -977.375 410 -976.896 136

-976.918 514

-975.656 096

Cl1 Cl2 N H

-0.023 -0.191 -0.670 (-0.700) +0.295 (+0.233)

Interaction Energy (kcal/mol) -13.8 -13.2 -14.1 -13.1

-12.7 -13.0 0.3

0.3

-0.021 -0.173 -0.600 (-0.632) +0.265 (+0.211)

0.1


expt .(1.012)a .(1.988)b 2.724c

1.014 (1.014) 2.080 (2.028) 2.518

Cl‚‚‚N-H

BSSE corrected -20.0 BSSE -20.1 noncorrected BSSE 0.1


BP

-8.1 -9.2

-5.8 -7.8

1.1

2.0

+0.026 -0.151 -0.564 (-0.576) +0.229 (+0.192)

.(112.4)a 460d (559)b

+0.070 -0.148 -0.570 (-0.556) +0.217 (+0.185)

a Reference 90. b Reference 91. c Reference 87. d Reference 102. e The values for the free molecules are indicated in parentheses. The Mulliken population analyses in the MP2 column were calculated at the HF level.

TABLE 6: Optimized Geometrical Parameters, Harmonic F-F Stretching Frequencies, Total and Interaction Energies, and Mulliken Population Analysis for the NH3‚‚‚F2 Complex Calculated with Different Methodologies and the Available Experimental Datac VWN d(N-H) d(F-F) d(F...N)

1.020 (1.023) 1.613 (1.397) 1.883

BP 1.018 (1.023) 1.633 (1.428) 1.955

PP

PW

Distances (Å) 1.019 (1.025) 1.006 (1.017) 1.693 (1.445) 1.617 (1.411) 1.905 1.866

HHLYP 1.006 (1.006) 1.385 (1.367) 2.529

MP2 1.014 (1.014) 1.431 (1.412) 2.563

expt .(1.012)a .(1.412)b

F‚‚‚N-H

103.6 (111.6)

104.4 (112.4)

Angles (deg) 104.2 (112.7) 104.3 (113.4)

112.2 (111.7)

112.5 (112.8)

.(112.4)a

F-F

583 (1056)

553 (991)

Frequency (cm-1) 545 (982) 575 (1042)

985 (1096)

834 (918)

.(917)b

-254.463 642

-256.214 495

Total Energy (au) -256.433 808 -256.122 902

-256.017 276

-255.568 189

BSSE corrected BSSE noncorrected BSSE F1 F2 N H

-35.0

-25.8

Interaction Energy (kcal/mol) -32.6 -25.0

-35.8

-26.9

-33.4

-26.0

-2.4

-2.2

0.8

1.1

0.8

1.0

0.7

0.9

-0.127 -0.257 -0.517 (-0.700) +0.301 (+0.233)

-0.118 -0.238 -0.465 (-0.632) +0.273 (+0.211)


-1.7

-1.3

+0.028 -0.051 -0.574 (-0.576) +0.200 (+0.192)

+0.047 -0.056 -0.563 (-0.556) +0.191 (+0.185)


the VWN and GGA methods compared with those that incorporate the HF exchange term. For the bromine and iodine complexes (Tables 7 and 8), the analysis of the geometrical parameters shows that at HHLYP and MP2 levels there is an important displacement of the hydrogen atoms that produces an enlargement of the N-H bond and a flatness of the pyramidal geometry of NH3. This flattening results in a loss of the s character of the lone pair orbital and, consequently, an increase in the HOMO eigenvalue that favors the electron transfer. There is an overall better agreement among the results provided by the different theoretical models, except for the values of the intermolecular distances with the VWN and PW methods and the interaction energies calculated at the VWN level. The results obtained by Kollman et al.44 using the HF method and a 4-31G basis set for the iodine-

ammonia complex show a very short intermolecular distance, 2.64 Å, and 7.4 kcal/mol for the BSSE corrected interaction energy. Surprisingly, this is the only case where the interaction calculated at the HF level is stronger than our MP2 results. We attribute this fact to the different basis sets employed. Our results show that for the same halogen molecule, as the interaction gets larger, one finds a smaller discrepancy among the different calculations in comparison with the ethylene complexes. A plausible explanation would be that the description of the exchange potential in the region of the intermolecular bond is better in the ammonia complexes because of the shortening of the intermolecular distances. C. General Remarks about the Interaction Energy in the Charge-Transfer Complexes. Our aim in this section is to provide some insight into the underlying factors that govern


J. Phys. Chem., Vol. 100, No. 30, 1996 12273

TABLE 7: Optimized Geometrical Parameters, Harmonic Br-Br Stretching Frequencies, Total and Interaction Energies, and Mulliken Population Analysis for the NH3‚‚‚Br2 Complex Calculated with Different Methodologies and the Available Experimental Datac VWN d(N-H) d(Br-Br) d(Br‚‚‚N)

1.022 (1.023) 2.423 (2.334) 2.498

PP

PW

Distances (Å) 1.024 (1.026) 1.013 (1.017) 2.446 (2.355) 2.421 (2.333) 2.522 2.362

HHLYP 1.070 (1.006) 2.355 (2.304) 2.629

MP2 1.081 (1.014) 2.378 (2.322) 2.570

expt .(1.012)a .(2.281)b

Br‚‚‚N-H

108.6 (111.6)

109.2 (112.4)

Angles (deg) 109.4 (112.7) 110.7 (113.4)

101.0 (111.7)

101.9 (112.8)

.(112.4)a

Br-Br

271 (338)

257 (319)

Frequency (cm-1) 266 (305) 261 (323)

294 (344)

281 (330)

.(325)b

-5 196.467 897

-5 204.581 205

Total Energy (au) -5 204.622 096 -5 204.262 206

-5 203.658 923

-5 200.247 525



1.024 (1.023) 2.396 (2.299) 2.396

BP

Br1 Br2 N H

-20.3

-12.9

Interaction Energy (kcal/mol) -14.0 -13.6

-21.3

-13.2

-14.5

0.8

0.3

0.5

+0.010 -0.208 -0.689 (-0.700) +0.295 (+0.233)

+0.006 -0.183 -0.623 (-0.632) +0.266 (+0.211)

-8.1

-6.4

-14.7

-10.1

-11.0

1.1

2.0

4.6

Mulliken Analysis +0.014 +0.007 -0.181 -0.212 -0.595 (-0.600) -0.601 (-0.626) +0.253 (+0.200) +0.269 (+0.209)

+ 0.012 -0.147 -0.505 (-0.576) +0.212 (+0.192)

+0.063 -0.163 -0.549 (-0.556) +0.215 (+0.185)


the strength of these intermolecular interactions. In Figure 3 we depict the corrected BSSE interaction energy for the C2H4X2 complexes along the halogen series for three of the methods that we have used in this work. The methods selected are BP, as a representative example of a GGA functional, the hybrid method HHLYP, and MP2. The role of the Hartree-Fock exchange is clear from this figure; it not only provides results in very good agreement with those from MP2, but more important, it modifies dramatically the trend of the interaction energy. The most noticeable change is that produced on the fluorine complex. It is also worth noting that the agreement between the GGA functionals and the hybrid and MP2 methods improves systematically on going from fluorine to iodine. For iodine, the interaction energies provided by the three methods are practically the same. The BSSE only modifies the numerical values of the interaction energies. The trends are preserved. For the NH3-X2 complexes, the situation is completely analogous.The BSSE corrected interaction energies of the BP and HHLYP functionals as a function of the difference between the donor orbital (HOMO) of the isolated molecule and the acceptor (LUMO) of the isolated halogen molecule for the two types of complexes considered in the present work are presented in Figure 4. The straight lines are least squares fits. The first aspect to be noted from this figure is the effect that the inclusion of the Hartree-Fock exchange has on the resulting interaction energies. As is well-known, the lack of the correct asymptotic behavior on the exchange and correlation functional produces smaller gaps.79 In the charge-transfer complexes, this fact results in a larger interaction energy. As noted previously, the most important effects are on the fluorine complexes. For a pure charge-transfer interaction one would expect that the interaction energy is essentially determined by the energy difference between the donor and acceptor orbitals. Even though this fact seems to be true in the GGA results, the HHLYP produces a different picture. In the latter case, the energy differences between the donor and acceptor orbitals of both types of complexes are practically the same, but the interaction energies for the σ-π complexes are considerably less than those corresponding to the σ lone pair energies. A plausible explanation can be given using the analysis for the ethylene-halogen

complexes presented by Prissete et al.42 through a partitioning of the intermolecular interaction. This analysis shows that the dispersion and charge-transfer terms increase in going from fluorine to iodine, but there is a substantial cancellation with the electrostatic term, breaking down the tendency along the halogen group. Our results for the ammonia complexes seem to confirm that this behavior is more general. The presence of the Hartree-Fock exchange in the exchange and correlation functional affects all the Kohn-Sham orbitals of the system. Since in a charge-transfer process the frontier orbitals of the interacting species are expected to play the major role in the description of the interaction, we have thoroughly examined their behavior in the C2H4-X2 and NH3-X2 complexes. In Figure 5 we depict the behavior of the BSSE corrected interaction energies corresponding to the ammonia complexes, in conjunction with the HOMO orbital energies of the isolated acceptors (Figure 5a), LUMO orbital energies of the isolated acceptors (Figure 5b), and the differences of the HOMO of the donor and the LUMO of the acceptor (Figure 5c). As can be seen from these figures, the interaction energies go almost parallel with the LUMO of the isolated halogen molecules. Another interesting feature that emerges from these plots is the effect that HF exchange (i.e., the inclusion of the correct asymptotic behavior) has on the frontier orbitals of the isolated halogen molecules. Both, HOMO and LUMO, are numerically affected, but in the latter orbital energies, HF exchange has a dramatic effect on the trends. A very similar behavior is found for the ethylene complexes. IV. Conclusions In this work we have presented a density functional study on charge-transfer complexes belonging to two different families: C2H4‚‚‚X2 and NH3‚‚‚X2 (X ) F, Cl, Br, and I). The local spin density method provides a large overestimation of the intermolecular interaction that is partially corrected by the generalized gradient approximations. Within this latter approximation, the Becke-Perdew and Perdew-Perdew functionals provide a better description than the local spin density approximation. The agreement among all methods considered

Reference 90. b Reference 91. c The values for the free molecules are indicated in parentheses. The Mulliken population analyses in the MP2 column were calculated at the HF level. a

+0.077 -0.177 -0.552 (-0.556) +0.217 (+0.185) +0.025 -0.158 -0.484 (-0.576) +0.261 (+0.192) +0.012 -0.205 -0.613 (-0.626) +0.268 (+0.209) Mulliken Analysis +0.033 -0.175 -0.621 (-0.600) +0.254 (+0.200) +0.022 -0.171 -0.650 (-0.632) +0.266 (+0.211) +0.021 -0.199 -0.708 (-0.700) +0.295 (+0.233)

-11.0 -13.0 2.0 BSSE corrected BSSE noncorrected BSSE

Ruiz et al.

I1 I2 N H

-6.9 -11.6 4.7 -7.3 -10.2 2.9

-13 890.781 514 -13 896.103 682

-17.9 -18.0 0.1

Interaction Energy (kcal/mol) -11.7 -10.5 -13.7 -11.3 2.0 0.8

-13 897.586 239 -13 884.311 065

Total Energy (au) -13 896.775 172 -13 897.108 562

.(214)b 197 (222) 205 (224) 186 (213) 191 (227) I-I

Frequency (cm-1) 186 (220)

188 (214)

.(112.4)a 102.5 (112.8) 101.6 (111.7) 112.5 (113.4) Angles (deg) 110.2 (112.7) 110.0 (112.4) 109.4 (111.6) I‚‚‚N-H

.(1.012)a .(2.666)b 1.081 (1.014) 2.785 (2.743) 2.743 1.071 (1.006) 2.764 (2.612) 2.783 1.014 (1.017) 2.800 (2.733) 2.542 Distances (Å) 1.024 (1.026) 2.793 (2.722) 2.713 1.023 (1.023) 2.800 (2.727) 2.717 1.024 (1.023) 2.774 (2.694) 2.591 d(N-H) d(I-I) d(I‚‚‚N)

expt MP2 HHLYP PW PP BP VWN

TABLE 8: Optimized Geometrical Parameters, Harmonic I-I Stretching Frequencies, Total and Interaction Energies, and Mulliken Population Analysis for the NH3‚‚‚I2 Complex Calculated with Different Methodologies and the Available Experimental Data


12274 J. Phys. Chem., Vol. 100, No. 30, 1996

Figure 3. BSSE corrected intermolecular interaction energy for C2H4‚‚‚X2 (X ) F, Cl, Br, and I) complexes.

Figure 4. BSSE corrected intermolecular interaction energy for C2H4‚‚‚X2 and NH3‚‚‚X2 (X ) F, Cl, Br, and I) as a function of the difference between the donor orbital (HOMO) of the isolated (C2H4 and NH3) molecule and the acceptor orbital (LUMO) of the isolated halogen molecule.

here improves when one moves from fluorine to iodine. In contrast to the charge-transfer complexes, another weak interaction, the hydrogen bond, has been reasonably described by the generalized gradient approximation. However, a closer inspection of the results shows that, analogous to the charge-transfer interaction, the intermolecular distances are underestimated. The hydrogen bond is probably better described by DFT because of its more electrostatic nature.4,5 The inclusion of HF exchange through the hybrid method (half-and-half) proposed by Becke52 yields a description very similar to that obtained with the secondorder Møller-Plesset method, for the intermolecular distances, vibrational spectra, rotational constants, and interaction energies, and in very good agreement with available experimental data. The basis set superposition errors calculated in these complexes for the pure density functional methods are relatively small, in a fashion similar to those reported for hydrogen-bonded systems.4,5 The hybrid nature of the half-and-half method is also reflected in the basis set superposition error, and the values are between those provided by pure density functionals and Hartree-Fock related methods. All results reproduce the well-known fact that ammonia is a stronger donor than ethylene, showing the enhancement of the donor capabilities of the lone pair compared with the π system of ethylene. The interaction energy in going from chlorine to iodine is practically constant, in agreement with previous work.42 Dispersion and charge-transfer terms increase on going to iodine, but there is a compensation with electrostatic terms. The interaction energy is not directly related to the energy difference between the donor-acceptor orbitals as one expects in a pure charge-transfer interaction. The trends observed for the interaction energies go practically parallel with the behavior of the



Figure 5. BSSE corrected intermolecular interaction energy and (a) HOMO orbital energy of the isolated halogen molecule, (b) LUMO orbital energy of the isolated halogen molecule, and (c) the difference between the donor orbital (HOMO) of the isolated NH3 molecule and the acceptor orbital (LUMO) of the isolated halogen molecule for NH3‚‚‚X2 (X ) F, Cl, Br, and I).

LUMO of the isolated halogen molecule. The Hartree-Fock exchange produces a dramatic change in the LUMO orbitals. However, the interaction is not solely determined by this orbital, since the values of the interaction energies for the σ-π and the lone pair-π complexes are quite different. The results presented in this work show that charge-transfer complexes are a stringent and important testing ground for new functionals. This must encourage the search for new exchangecorrelation functionals, aiming to find a pure density functional capable of competing with the hybrid methods. Researchers using molecular modeling techniques involving density functional theory should be aware of the overestimation of chargetransfer interactions when one uses the local spin density or the generalized gradient aproximations. Acknowledgment. One of us (E.R.) acknowledges the CIRIT for providing a postdoctoral fellowship. We thank Dr. D. Fox and Professor J. J. Novoa for providing very valuable information. We also acknowledge DGSCA/UNAM-Me´xico and CESCA (Centre de Supercomputacio´ de Catalunya) for grants of computer time on their Cray-YMP machines. Supporting Information Available: Comparison between deMon and Gaussian92/DFT (Table IS) and calculated harmonic vibrational frequencies for C2H4‚‚‚Cl2 (Table IIS) and NH3‚‚‚Cl2 (4 pages). Ordering information is given on any current masthead page. References and Notes (1) Salahub, D. R.; Castro, M. E.; Proynov, E. I. In RelatiVistic and Electron Correlation Effects in Molecules and Solids; Malli, G. L., Ed.; Plenum Press: New York, 1994; Vol. 318. (2) Salahub, D. R.; Fournier, R.; Mlynarski, P.; Papai, I.; St-Amant, A. In Density Functional Methods in Chemistry; Labanowski, J., Andzelm, J., Eds.; Springer: New York, 1991. (3) Ziegler, T. Chem. ReV. 1991, 91, 651.

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Charge-Transfer Complexes: Stringent Tests for Widely Used Density

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