J. Phys. Chem. 1994,98, 1844-1850
1844
Diazasilene (Si”): A Comparative Study of Electron Density Distributions Derived from Hartree-Fock, Second-Order Mdler-Plesset Perturbation Theory, and Density Functional Methods Jian Wang, Leif A. Eriksson, Russell J. Boyd,’ and Zheng Shi Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada B3H 453
Benny G. Johnson Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 Received: August 23, 1993”
The electron densities of the 3t ground state of diazasilene (Si”) derived from density functional methods and conventional ab initio (UHF and UMP2) methods are compared and analyzed. The spin contamination is investigated at the HF, MP2, MP3, MP4, and DFT levels. The optimized geometries and vibrational frequencies obtained by using Becke-Perdew gradient corrections to the LSDA exchange and correlation functionals are also reported. The failure of the Hartree-Fock method, and other methods in which the HatreeFock singledeterminant wave function is used as the reference configuration, to predict a bound structure for Si” is attributed to the antibonding character of the spin density along the Si-N bond. The large spin contamination in the U H F and MPn calculations is shown to have no significant effect on the prediction for the equilibrium geometry of Si”. The failure of conventional ab initio methods is also attributed to their tendency to overestimate the ionic character of the Si-N bond. In contrast to ab initio methods based on a single reference configuration, DFT methods predict a tightly bound structure for Si” and a more delocalized and polarized electron distribution. The overestimation of stretching frequencies of Si” by the LSDA method can be attributed to the fact that the LSDA method overpolarizes and overdelocalizes the electrons, which leads to an overestimation of the Si-N and N-N interactions. The nonlocal corrections to the exchange and correlation potentials, however, tend to remove the overestimation by reducing the electron polarization and delocalization. Consequently, the geometries and vibrational frequencies produced at the BP and BLYP levels are in very good agreement with experimental and MRCCSD(T) results. A topological study of the LSDA and BP electron densities indicates a closed-shell interaction between Si and N , which is characteristic of the small charge transfer and large polarization of the electron density distribution observed in Si”.
Introduction Density functional theory (DFT)l,*J has emerged as a tangible and versatile computational method over the past decade. It has been employed successfully in predicting the geometries and vibrational frequencies for a number of molecular systems that require a careful treatment of electron correlation. A very interesting example is the biradical diazasilene, Si”. Electron spin resonance (ESR) and infrared resonancespectra have been obtained for SiNN in various matrices at 4 K.4 The ESR studiessuggest a linear 3 6 electronicground state for Si” in a neon matrix, which is assumed to simulate the gas phase. Since Si” may exist in the interestellar medium, its electronic structure has recently been studied in order to determine its geometry,bonding nature, and spectroscopic constants. The first ab initio theoretical study appeared in 1988, in which the selfconsistent field Hartree-Fock (HF), configuration interaction includingall single and double excitations (CISD), and complete active space self-consistent field (CASSCF) methods were employed.5 This study did not, however, successfully reproduce the experimental infrared spectrum. Instead, the theoretical results predicted that Si” is essentially unbound. Dixon and DeKock6 used the local spin density functional approximation (LSDA) to study this biradical and obtained a structure with a normal Si-N single bond length. The predicted vibrational frequencies are in qualitative agreement with the experimental results. Recently, multireference configuration interaction (MRCI) and multireferencecoupledcluster (MRCC) e Abstract
published in Advance ACS Absrracrs. January 1, 1994.
0022-365419412098-1844$04.50/0
techniques have been employed,predicting that Si” has a tightly bound structure.7.8 MRCCSD(T) calculations, in which all single, double, and connected triple excitations are included, yield vibrationalfrequenciesin close agreement with experiment.More recently, Murray et aL9reported DFT calculations for the Si” molecule with accurate quadrature and large basis sets using gradient corrected functionals, BLYP (Becke’s function for the exchange term and Lee, Yang, and Parr’s function for the correlation part). BLYP gives results which are close to the experimental frequencies and high level ab initio (MRCCSD(T)) results. The success of the DFT approach indicates that the method in this case is clearly superior to theconventionalab initio methods such as HF, CISD, and CASSCF and is qualitatively in line with multireference ab initio methods for describing the electronic structure of the Si” molecule. Therefore, an analysis and comparison of the electron densities of Si” obtained from various methods will provide insight into the essential differences between the conventionalab initio and density functionalmethods. This paper reportsa detailed analysisand comparisonof electron densities derived from density functional methods and conventional single-reference ab initio methods. The electronic structure and interatomic interactions are further discussed by means of Bader’s atoms-in-molecules theory. The spin contamination has been investigatedat the HF, MP2, MP3, MP4, and selected DFT levels. Although the optimized geometries and vibrational frequencies are not the main focus in this paper, a DFT calculation using BeckePerdew nonlocal correctionsto the LSDA exchange and correlation functionals was carried in order to compare with the BLYP results. 0 1994 American Chemical Society
Electron Density Distribution of Diazasilene
Computational Details The density functional calculations reported in this work were performed using modified versions of the Gaussian 921° program and the deMon program.11-13 Both programs employ Gaussiantype orbitals (GTO) as basis sets to solve the KohnSham (KS) equations. A polarized double-Svalence(DZVP) basis set of the form (1Os6pld)/ [3s2pl d] for N and (13s9pld)/ [4s3pld] for SiI4 is used. The form of the local spin density approximation used is that derived by Vosko, Wilk, and Nusairls while Becke's gradient-correctedexchange functional16 and Perdew's gradientcorrected correlation functional17 are used in the calculations. Throughout, we use the spin-unrestricted formalism. The unrestricted local spin density functional method will be referred to as LSDA, and thedensity functionalmethod including gradient corrections with the Becke-Perdew functionals as BP. For the modified Gaussian 92 program, fully self-consistent Kohn-Sham (KS) densities wereobtained,with no awriliaryfitting or projection techniques. The integrals involving exchange and correlation terms were calculated numerically, using the atomic partitioning scheme of Beckels (without the suggested "atomic size adjustments"). The atomic one-center integrations were handled using the SG-1 standard quadrature grid,l9 which is based on Euler-Maclaurin-Lebedev formulas.20 The geometry was optimized by both LSDA and BP methods; harmonic vibrational frequencies were then calculated analytically for LSDA and by finite difference of analytic gradients for BP. All quadrature weight derivative terms21922 were properly included in all cases. The DFT electron densities used for the comparison with the ab initio results were obtained from the deMon program. In this case, a set of auxiliary GTOs was used to fit the electron density and exchange and correlation terms. The auxiliary basis sets chosen for the fitting of the density and exchange-correlation terms are [7s2p2d] for N and [9s4p4d] for Si.14 The nonrandom extrafinegridoptionwasusedinorder tokeep the proper symmetry of the electron density. The ab initio calculations were carried out using the Gaussian 90 program.23 Since previous ab initio calculations such as HF, MP2, MCSCF, MCCI, MCCCSD(T),5*7etc. used the double-t plus polarization (DZP) basis set, and one of the first LSDA calculationsused the DZVP basis set, here we employed the DZP basis set for the ab initio calculations and the DZVP basis set for the DFT calculations to facilitate comparisons. Whereas the DZP and DZVP cover different exponent regions, the two basis sets are generally thought to have roughly the same quality. Our systematic study indicates that the conclusions of the paper will not be changed even if higher quality basis sets are used or the same basis set is used for the ab initio and DFT calculation^.^^ A modified version of the PROAIM package by Bader and his co-workers25 has been used to analyze the various densities. Although electron densities from DFT and UHF are straightforward, there are two ways to obtain electron densities from UMPZ calculations: one from the one-particle density matrix (lPDM), which is derived from the wave function corrected to the first order, and another from the Z-vector method, Le., the generalized density.26 In this work, the UMPZ oneparticle density is used. Also, it has been shown27-29 that the MP2 and CISD densities usually have very similar behavior; thus the present results will illustrate the probable trend of CISD results. In Table 1 we list the optimized geometries and vibrational frequenciesat various theoretical levels. We should note that the theoretical frequencies we used here are all harmonic while experimental ones are anharmonic. The first two LSDA calculations shown in Table 1 were performed by Dixon and DeKock6 using the D M o P and DGAUSS" programs. Compared to these results, the modified Gaussian 92 program produces a similar equilibrium structure under the local spin density functional approximation, using the
The Journal of Physical Chemistry, Vol. 98, No. 7, 1994 1845
TABLE 1: Theoretical Equilibrium Geometrical Parameters and Vibrational Frequencies in the 3E- Electronic Ground State of Si"* LSDAb 1.749 1.164 321 569 1821 LSDAc 1.737 1.167 338 605 1823 LSDAIDZVP" 1.741 1.170 335 578 1818 BPIDZVP" 1.772 1.171 321 532 1772 BLYPIDZVP" 1.774 1.179 303 511 1723 BLYPIDZPC 1.760 1.181 332 506 1725 BLYPITZZP 1.768 1.156 319 518 1775 BLYP/TZ2P+fe 1.759 1.158 330 529 1766 MRCCSD/DZPf 1.788 1.153 375 393 1825 MRCCSD(T)/DZPf 1.770 1.168 325 467 1726 MRCI/DZPg 1.899 1.149 436 2038 expth 485 1731 * Bond length in angstroms; frequencies in reciprocal centrimeters. The unrestricted Kohn-Sham equations were used in all the DFT calculationscited here. From the DMol program.M From the DGAUSS program.31 d This work, from the modified G92 program.10 e From CADPAC pa~kage.~ /Reference 7. Reference 8. * Reference 4. DZVP basis set. We observe that the LSDA/DZVP vibrational frequencies are overestimated with respect to MRCCSD(T)/ DZP and the best gradient corrected DFT methods (BLYP/ TZ2p+f). The gradient+rrected DFT methods lead to a significant improvement over the LSDA method, even using the same basis set (DZVP). The BP/DZVP harmonic frequencies are close to the BLYP/TZ2p+f frequencies. The similarity between the BLYP/DZVP and the BLYP/DZP results indicates that the DZP and DZVP basis sets have nearly the same quality. In the meanwhile, we found noticeable differences in the BP and BLYP frequencies with the DZVP basis set, which can be attributed to differences in the correlation functions employed by the two methods. We will discuss this problem in detail elsewhere. Overall, the BP/DZVP results have the same features as the BLYP results, which gives us confidence in the quality of the BP/DZVP density. Of course, we can get better results if we use a larger basis set than the DZVP basis set. But we do not expect the main features of the electron density to change if we do so. On the other hand, comparing the electron densities calculated by basis sets of similar quality can give more insight into the structure of the molecule. The MRCI/DZP calculationss predict a Si-N bond length which is 0.129 A longer than the MRCCSD(T) value. Furthermore, the vibrational frequenciesobtained at this level do not have a systematicerror, as do the MRCCSD(T) and DFT results. Its N-N stretching frequency is far above experiment and approaches the value of a N-N triple bond (2359 cm-I), relative to experimental and other theoretical results, while the Si-N stretching frequency is lower than the experimental value. The same problem can be found in the MRCCSD calculations. Since the MRCCSD(T) level predicts results in much better agreement with experiment than does the MRCCSD level, a possible explanation for the MRCI results may be due to insufficient inclusion of higher excitations in the calculations.
Spin Contamination Effect in the SiNN Molecule The spin contamination and its projection for UHFand UMPn has previously been discussed in detail elsewhere,32and therafore we list only the main features here. Since molecular orbitals (MO) of the CY and 6 electrons are not orthonormal in the unrestricted SCF formalism, the resulting total wave function is not an eigenfunction of the total spin operator S2; i.e., the wave function is spin contaminated. One can use the L6wdin spin projection operator33to project out all contaminations. In practice, only the first few spin contaminating states need to be projected out. For example, SiNN has a triplet electronic ground state, to which the S = 2-4 states contribute the major important
1846 The Journal of Physical Chemistry, Vol. 98, No. 7, 1994 0.50
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Wang et al. with results from DFT, MRCI, MRCCSD, and MRCCSD(T) calculations. It can, therefore, be concluded that spin contamination does not have any significant effect on the prediction of the equilibriumgeometry of Si”. The success of multireference ab initio methods indicates that using a single reference configurationis one of the main reasons for the failure of conventional ab initio methods in predicting the geometry and vibrational frequencies of Si”. We also calculated (S2) from DFT at fixed N-N bond length. To some extent, (S2)can be used to measure approximately the spin contamination in density functional methods. Figure 1 reports theresultsof A (Sz)= ( S 2 )-2.OOfromDFTcalculations with respect to the Si-N bond distance. We can see that the unrestricted LSDA and BP methods correspond to A (P) at least one order smaller than the UHF and UMPZ methods. The maximum A (S2)values in LSDA and BP are 0.001 and 0.014, respectively, while the UHF and UMP2 methods yield maximum A ( S2) values of O.4OOand 0.293, respectively. The much smaller A (S2)values in DFT indicate that spin contamination is not an important factor in density functional methods. This conclusion is consistent with the most recent work of Murray et al., in which the restricted open-shell Kohn-Sham results including gradient corrections are very similarto the unrestrictedKohn-Sham results with various basis sets. It is interesting to point out that the LSDA method yields slightly smaller A (S2)values in Si” than the BP method.
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contamination. Hence, only projecting out these states is sufficient. It should be pointed out that the unrestricted density functional calculations also contain spin contamination. No further effort has, however, been made to project out the spin contaminations in our DFT calculations. As experiment has shown, Si” is a biradical with a triplet ground state. The poor success of the earlier UHF study5led us to suspect that spin contamination may account for this failure. Figure 1 shows the error of (S2) in UHF and UMPZ calculations with respect to the Si-N bond length, keeping W N at the MRCCSD(T) optimizedvalue, 1.168 k7This figure shows that spin contamination is significant at these levels of theory. We thus carried out spin projection calculations. Figure 2a shows the UHF, UMP2, UMP3, and UMP4 total energieswhile Figure 2b illustrates their corresponding spin-projected energies with the N-N bond length fixed at 1.168 A. Both parts of the figure demonstrate an essentially unbound structure of Si” in the region of consideration, regardless of whether the spin contamination is included or not. These results are in sharp contrast
Electron Spin Density. As mentioned in the introduction, the only methods that seem capable of resolving the Si” problem are either DFT or multireference ab initio ones. In order to obtain insight into why DFT is able to produce an appropriate equilibrium geometry and vibrational frequencies for this molecule, whereas most ab initio methods do not, we discuss in this section the spin density distributions obtained using various methods. First of all, we address this problem by constructing spin density contour diagrams. The geometry used for these contours was taken from the MRCCSD(T) optimi~ation.~ The contour plane is chosen such that it contains the molecular axis. Figure 3a illustrates the UHF spin density contours of Si”. The two unpaired electrons populate the entire region around the molecule. The most interesting aspect of this density is that there are two nodal planes, between Si-N and N-N, respectively. The nodal plane between Si-N indicates the antibonding property of unpaired electrons between Si and N atoms. The spin density obtained at the UMPZ level remains almost identical to that of UHF, as shown in Figure 3b. This indicates that UMP2, which uses the UHF wave function as the reference configuration, will lead to results similar to those for UHF. The failure of CISD in predicting a stable bound structure of Si” may also be attributed to the similar spin density, because it employs the HF wave function as the reference determinant also. In contrast, the spin density of the LSDA calculations bears little resemblance to those obtainedat the UHF and UMPZ levels, as shown in Figure 3c. There is only one nodal plane in the LSDA spin density, situated between the two nitrogen atoms. The absence of a nodal plane between Si and N may account for its success in predicting the tightly bound structure of the Si” molecule. In the same way, the spin density distribution obtained when the Becke-Perdew gradient corrections are included is almost identical to that obtained from the LSDA calculations. Recently the density functional methods have been applied in studies of the electronicand hyperfinestructures of small radicals with considerable The advantage of DFT over the ab initio methods in terms of computational efficiency and memory requirements provides an attractive alternative in the studies of ESR spectra of radicals. The spin density at the nuclei is related
Electron Density Distribution of Diazasilene
The Journal of Physical Chemistry, Vol. 98, No. 7, 1994 1847
,---.
N
N
Si
Fipllre4. Total electron density difference contoursof the Si” molecule at the MRCCSD(T)/DZP-optimizedgeometry: (a) differencebetween LSDA/DZVP and UHF/DZP, (b) difference between LSDA/DZVP
and UMP2/DZP, and (c) difference between BP/DZVP and LSDA/ DZVP. The contour plane contains the molecular axis. The solid lines correspond to positive values while the dashed lines represent negative values.
N N
Si
Figure 3. Spin densities of the Si” molecule at the MRCCSD(T)/ DZP-optimized geometry: (a) UHF/DZP, (b) UMP2/DZP, and (c) LSDA/DZVP. The contour plane contains the molecular axis.
TABLE 2 Spin Densities at the Nuclei in the 32- Electronic Ground State of Si”*
LSDA/DZVP BP/DZVP UMP2/DZP MRCIIDZPb 0.037 0.169 0.102 QW 0.037 Q(N1)‘ -0.038 -0.028 -0.239 0.042 0.061 0.196 0.010 Q(Wd 0.054 All the results are calculated using the deMon and G90 program at theMRCCSD(T)-optimizedgeometry. Reference 8. CentralN atom. dTerminal N atom. to the isotropic coupling constants obtained in the ESR spectrum. In Table 2 we list the spin densities at the nuclei of the SiNN molecule obtained from various theoretical methods. From this table we can see that the UHF and UMPZ methods (UHF has the same spin density at nuclei as UMP2 in the SiNN molecule) generate a much higher spin density at the nuclei than the DFT methods. Total Electron Density. Figure 4 shows the total electron density differencecontoursfor thevarious methods. Thegeometry and contour planes are the same as in the preceding section. The solid lines in the contours correspond to positive values while the dashed lines represent negative ones. Figure 4a displaysthe differencebetween the LSDA and UHF calculations. The solid lines, which correspond to excess LSDA density, appear around the outer parts of the atoms and are of nonspherical symmetry. In particular, the LSDA density around Si is expanded out from the molecular axis and toward the central nitrogen relative to the UHF one. This reflects the fact that LSDA increases the electron density along the direction perpendicular to the molecular axis and that its density is more polarized than that of UHF. The UHF density, on the other
hand, mainly shows two features. One is at the N2 unit. UHF distributes more electrons at the two ends of the N2 moiety in comparison with the LSDA results. This leads to an accumulation of electron density along the Si-N bond and at the terminal N atom, as shown by the dashed lines between the N and Si atoms and at the terminal nitrogen. The other feature is that UHF densely populates the region near the nuclei, rather than the outer regions of atoms. The dashed lines near nuclei clearly illustrate that the electrons are not polarized near the nuclei in contrast to the finding at the LSDA level, even though both methods use the Si-N bond length of 1.770 A, a typical Si-N single-bond length? Thus, from the electron density difference contour, we can see that UHF leads to a more localized electron density distribution relative to the LSDA method. Because the electrons in UHF are localized around the Si atom and the N2 unit even at a normal Si-N single-bond distance, the interaction in this molecule is best described as an interaction between a “free Si atom” and a Nz unit. There is no significant electron polarization and delocalizationin UHF, and therefore there is no bonding between Si and N2. Consequently,UHFcannot predict the Si” molecule to have a tightly bound structure. Although the UMPZ method partly takes into account the effect of electron correlation, there is no big improvement of the electron density distribution compared to the case for the UHF solution, as can be seen in Figure 4b. The electron density differencecontour between LSDA and UMPZ stronglyresembles that between LSDA and UHF in that the Si atom is still like a “free atom” and that the electron density of the N2 unit can easily be recognized. Since the MP2 electron density in general has similar properties to that obtained at the CISD leve1,2*.22we can conclude that the electron density difference between LSDA and single-referenceCISD has similar features to those of Figure 4a and 4b. The BP electron density distribution, however, in which gradient corrections to the LSDA exchange and correlation potential are included, is almost identical to the LSDA results. This is illustrated in Figure 4c, where the density difference contours between BP and LSDA are shown. The main feature is that BP
1848 The Journal of Physical Chemistry, Vol. 98, No. 7, 1994
Wang et al.
TABLE 3 Positions of Bond Critical Points (au) and Electron Density and Its Laphcian at the Bond Critical Points, Net Atomic Charges, Atomic Local Moments, and Quadruple Moments in the 3Z- Electronic Ground State of SiNN at the MRCCSD(T)-Optimized Geometry UHF/DZP MP2/DZP LSDA/DZVP BP/DZVP Bond Critical Point Properties NSi 1.053 1.051 1.053 rCa 1.056 0.099 0.090 0.101 P 0.087 0.548 0.632 0.532 V2p 0.662 N-N rCa 0.636 0.627 0.610 0.609 P 0.562 0.553 0.532 0.533 Vzp -2.050 -1.893 -1.417 -1.420 Atomic Properties Si 0.644 0.660 0.691 0.671 Qb -1.592 -1.600 -1.534 -1.541 kC Qzzd 5.971 5.626 5.247 5.371 NIC -0.857 -0.734 4722 Qb -0.827 -1.031 -1.019 -1.000 MZC -1.034 2.013 2.000 1.994 Qzzd 1.984 NY 0.191 0.043 0.051 0.183 Qb 0.8 16 0.749 0.749 0.829 PZC QZZ 1.431 1.377 1.627 1.627 a The bond critical point position from the central N atom (au). The net atomic charges. Atomiclocal moment. Atomicquadruplemoment. Central N atom. /Terminal N atom. tends to pull the electrons back toward the Si atom and the NZ unit. In other words, gradient corrections seem to correct for the overestimated "covalent" feature of the LSDA method. The difference between the BP and LSDA electron densities can be used to explain the different optimized geometries and vibrational frequencies produced by the two methods. Since LSDA has a more diffuse electron distribution between the N-N and Si-N atoms than does BP, Le., LSDA overestimates the "covalent" bonding, the LSDA method leads to a shorter Si-N bond and overestimates the stretching frequencies between N-N and Si-N relative to the BP results. Although BP leads to good agreement with experimental and MRCCSD(T) results, it still overestimates the stretching frequencies in comparison with experiment, and therefore the BP electron density in SiNN is still too diffuse.
Interatomic Interactions in SiNN We now apply Bader's atoms-in-molecules the0ry35.3~to discuss the bonding properties of Si". In Table 3 we list the positions of the bond critical points, and the electron density and the Laplacian of the electron density at the critical points. For convenience of comparison, we use the MRCCSD(T) geometry in all calculations in this section. For the Si-N bond, the LSDA and BP densities have bond critical points (BCP) 1.051 and 1.053 au away from the central nitrogen with BCP electron densities of 0.101 and 0.099. UHF, on the other hand, tends to pull the bond critical points toward the Si atom, and its electron density at the BCP is smaller than those at the DFT levels. Since the positions of the BCP can be related to the atomic ele~tronegativity,3~ a shift of the BCP toward the Si atom as observed in the UHF calculations indicates that the method tends to lower the atomic electronegativity of the Si atom relative to LSDA. UMP2 gives the same BCP position between the N and Si atoms as BP, but its BCP density is lower than that from the BP calculations. Combining the electron density and its Laplacian, we can classify the interatomic interactions in SiNN according to the atoms-in-molecules theory.35.36 We first consider the N-N bond. TheLSDAelectrondensity at theBCPis 0.532, and its Laplacian
_---------
N N
.
Si
Figure 5. Contours of the Laplacian of the electron density: (a) the Laplacian of Nz at the UHF/DZP level using the experimental N-N internucleardistance (~PJN= 1.098A), (b) the Laplacian of SiNN using LSDA/DZVP density at the MRCCSD(T)/DZP-optimizedgeometry, and (c) the Laplacian of SiNN using UMP2/DZP density at the MRCCSD(T)/DZP-optimized geometry. The contour plane contains the molecular axis. The solid lines correspond to negative values while the dashed lines represent pitive values.
is -1.417. The large values of p and -Vzp indicate that the electrons are accumulated at the bond critical point, leading to a shared interaction between N-N. The Si-N interaction, however, has low values of p a t the BCP, and its Laplacian is positive. This corresponds to an electron depletion at the BCP. The values of p and Vzp at the BCP between Si and N are characteristic of a closed-shell interatomic interaction. Relative to the DFT results, UHF and UMPZ predict larger magnitudes of p and Vzpbetween the two nitrogens, which indicates a stronger shared interaction between them. The smaller p and larger V2p in the UHF and UMPZ results indicate a weaker interaction between the N and Si atoms than what is predicted at the DFT levels. The interatomic interactionsin SiNN can be further illustrated by the contours of V2p. For convenience of comparison, we first discuss the contours of Vzp of N2, obtained at the MP2 level using the experimental N-N bond length of 1.098 A.21 Figure 5a shows the contours of V2pfor the N2 molecule, where the solid lines correspond to negative values while dashed lines represent positive values. This contour plot is typical of a shared interaction between two nitrogen atoms.36 The region of space over which Vzp is negative, and which contains the interatomic critical point, is contiguous over the valence regions of both atoms and the valenceshellofthe chargeconcentration. Whena SiNN molecule
Electron Density Distribution of Diazasilene is formed, the main feature of V z p between the nitrogen atoms remains similar to that of Nz, as is demonstrated by Figure Sb, where the contoursof V 2 pof Si” were obtained from the LSDA calculations. Hence, the N-N interaction in SiNN is a shared interaction, as previously mentioned. In contrast to the N-N interaction, the Laplacian of p is positive over entire regions between Si and N (cf. Figure Sb), and therefore the Si-N interaction can be classified as a closed-shell interaction. Although the LSDA results indicate that the Si-N interaction in LSDA is a closed-shell interaction between a Si atom and a NZunit, it is not a simple interaction between a free Si atom and a NZ unit. Instead, it involves substantial polarization of the electron distribution. Comparison of the Laplacian of p derived from the LSDA calculations with that obtained from UMPZ (Figure Sb and Sc) shows that the LSDA V 2 pdistribution is more polarized than that of UMP2. V 2 p on the Si atom (solid lines near Si), as obtained from LSDA calculations, is distorted along the direction perpendicular to the molecular axis, and Vzp on the central N atom is deformed toward the Si atom more than what is observed using the UMPZ density. The degree of electron polarization can be measured by the atomic local moment and quadruple moment in the corresponding atomic basin~.~S.36 Table 3 reports the atomic propertiescalculated using the UHF, UMP2, LSDA, and BP densities. When the molecular axis of SiNN is aligned along the z axis, the LSDA and BP derived local moments (pz) and quadruple moments Qzz in the Si basin are smaller in magnitude than those obtained at the UHF and UMP2 levels. The small positive Qzz value corresponds to a larger value of Qxx and Qyy,which is a measure of the degree of electron polarization along the x and y directions, Le., the direction perpendicular to the SiNN molecular axis. Therefore, the smallervalues of pz and Qzz from the LSDA results indicate that the electron density distribution obtained in the LSDA calculations is less polarized along the molecular axis in the Si basin but more polarized perpendicular to the axis as compared to the UHF and UMP2 results. The BP calculations show the same features as that of LSDA, but in general the BP results tend to be more shifted toward those obtained from the UHF and UMPZ calculations. We also note that the larger electron transfer from Si into the Nz unit in the LSDA and BP calculations is a contributing factor to the large polarization of the electron distribution relative to the case for UHF and UMP2.
Conclusions The electron density distribution, equilibriumgeometries, and vibrational frequencies of the 3 2 - ground state of diazasilene have been investigated using DFT, UHF, and UMPZ methods. The comparison of electron densities derived from density functional and conventional single-reference ab initio methods providesvaluable insight into theelectronicstructure oftheSiNN molecule. The wave function derived from HartreeFock calculations is found to be unsuitable for describing the SiNN molecule. Due to the antibonding property of the spin density along the Si-N bond, UHF cannot predict a tightly bound structure of Si”. The MP2, MP3, MP4, CISD, and CASSCFmethods also cannot reproduce the correct structure, if the H F single-determinant wave function is used as the reference configuration. The spin contamination in UHF and UMPn, although large, has no significant effect on the prediction for the equilibrium geometry of Si”. The antibonding nature of the spin density along the Si-N bond, as observed in the H F calculations, is not the only reason for the failure of conventionalab initio methods. The H F method inherently overestimates the ionicity of a molecule, which results in the electron density becoming localized on the Si atom and the
The Journal of Physical Chemistry, Vol. 98, No. 7 , 1994 1849
NZunit without allowing for large polarization of the electron cloud. As a result, the SiNN molecule at the HF level displays a simple interaction between a free Si atom and a Nz unit, Although the UMPZ method incorporates some of the effects of electron correlation, its electron density is still localized on the Siatomand theNzunit. Thisoverestimationoftheioniccharacter of SiNN is not properly corrected by the CISD and CASSCF methods. The overestimation of the Si-N bond length and N-N stretching frequenciesand the underestimation of the N-N bond length and Si-N stretching frequencies by the MRCI and MRCCSD methods suggest that the overestimation of the ionic character is not completely corrected at these levels of theory. In contrast to single-referenceab initio results, DFT predicts a tightly bound structure for Si”. The LSDA method leads to a bonding spin density between the Si and N atoms and to large delocalization and polarization of the electrons of SiNN relative to the UHF and UMP2 methods. The ability of the LSDA method to describe the polarization of the electrons in molecules such as SiNN is closely related to its treatment of the electron exchange and correlation terms. The local spin density approximationcorrespondsto a homogeneous electron gas model, and therefore it allows for large delocalization and polarization of the electrons. The overestimation of stretching frequencies of SiNN by the LSDA method can be attributed to the fact that the LSDA method overpolarizes and overdelocalizes the electrons, which leads to an overestimation of the Si-N and N-N interactions. The gradient corrections to the exchange and correlationpotentials, however, tend to remove the overestimation by reducing the electron polarization and delocalization. This overestimation is, however, still not completely corrected in the BP method. On the basis of the topological study of the LSDA and BP electron densities, the interaction between Si and N is found to be a closed-shell interaction, which is characteristic of the small charge transfer and large polarization of the electron density distribution observed in Si”.
Acknowledgment. We thank the Natural Sciences and Engineering Research Council of Canada for financial support and Professor R. F. W. Bader for a copy of the PROAIM package of programs. The financial support from the Swedish National Science Research Council and the Killam Trust is gratefully acknowledged (L.A.E). J.W. thanks the Killam Trust for a Predoctoral scholarship. B.G.J. thanks the Mellon College of Science for a Graduate Fellowship. We thank Dr. N. Burford and Mr. J. Clyburne for helpful discussions.
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