81
J . Phys. Chem. 1994, 98, 81-87
Ab Initio Study of the Structures, Energetics, and Bonding of the Isomers BeNH and HBeN Orlando Roberto-Netot and Fernando R. Ornellas' Instituto de Qujmica, Universidade de SBo Paulo, Caixa Postal 20780, Siio Paulo, SP 01 498-970, Brazil
Received: May 5, 1993'
The structures, energetics, spectra, and bonding of the isomers BeNH and HBeN are described theoretically at the a b initio Hartree-Fock and configuration interaction levels. The species HBeN is still unknown experimentally, and the results reported in this paper represent the first theoretical prediction of its existence. For the molecule BeNH, vibrational frequencies with an unequivocal assignment of the N H stretching are the only experimental data found in the literature. In contrast with the scarceness of experimental information, and complementing previous studies on BeB, BeC, BeN, and BeF, this paper reports detailed results on geometries, vibrational frequencies, relative stabilities, excited electronic states, and electronic rearrangements leading to the bonding in the molecules BeNH and HBeN. The molecule BeNH is 10.5 kcal/mol more stable than HBeN, and the favorite route for dissociation involves breaking the Be-N bond in both BeNH and HBeN. The three lowest electronic states in BeNH are very closely spaced with the first excited singlet state ('II)only about 1500 cm-I higher than the ground state (IF) in; contrast, for HBeN the first 311 is about 8000 cm-l higher than the 3 2 - ground state. Their vibrational frequencies are quite distinct, and the predicted values for HBeN will certainly allow an unequivocal identification of this species. As to the bonding in the molecule BeNH, an unexpected 2s* 2pX12pY1electronic promotion leads to a *-type bond between the beryllium and nitrogen atoms which is not found in the isomer HBeN. In both molecules a significant ionic character also contributes to the bonding between these two atoms.
-
1. Introduction In recent investigationswe have characterized the lowest-lying electronic states of new beryllium-containingdiatomicslike BeN,I BeC,ZBeB,3 BeF2+,4 and BeH2+,5as well as reported detailed spectroscopic data for the experimentally known and several unknown electronicstates of other beryllium compounds like BeF, BeF+,6and BeH+.7 As a step further in this study of beryllium-derivedmolecules, this paper reports theoretical results on the structures, bonding, energetics, and spectra of the isomers BeNH and HBeN that formally can be viewed as generated from either BeN, BeH, or NH. In the case of the species HBeN, as far as we know, it is still an unknown molecule both theoretically and experimentally. They are also isoelectronicto BCH,8 C2H+,9LiOH,IO BeO," and C2,1z whose electronic states have shown an alternation between singlets and triplets. The BeNH molecule is known experimentally to be obtained from the pyrolysis of beryllium amide, Be(NH2)2,I3but neither a single geometrical parameter nor any discussion about the assignment of the electronic states was found in the literature. Besides its preparation, the only information available refers to its IR spectrum where a sharp band at 3330 cm-I is attributed to the N-H ~tretching.'~ Theoretically, an early semiempirical calculation on BeNH has been reported by Dewar and Rzepa15and contains structural parameters and the enthalpy of formation for the molecule in the states 3 I l and IZ+.Dill et a1.16 approached the same system at the self-consistent-field(SCF) level with the STO-3G and 6-3 1G basis sets and found, in disagreement with Dewar, that the ground state is a with the state l2+ lying 11 577 cm-I (33 kcalfmol) higher in energy. In a more recent study of geometries and enthalpies of formation of a series of lithium and beryllium derivatives, Sana and Leroy17 also found a 1Z+ground state with the 311 3299 cm-I (9.4 kcal/mol) higher in energy; this study was t Permanent address: Instituto de Estudos Avanpdos, DivisHo de Lasers, Centro T&nico Aeroespacial, Caixa Postal 6044. SHo Jose dos Campos, SP 12231-297, Brazil. Abstract published in Aduance ACS Absrraers, December 1, 1993.
0022-3654/94/2098-008 1$04.50/0
carried out at the SCF and Mdler-Plesset (MP2 and MP4) levels with a basis set of the type 6-31+G(2df,p). From the chemical point of view, beryllium compounds have an electron-deficientnature which is manifested by a high degree of association.18 Their chemical properties are basically dominated by the possibility of an electronic promotion of the type 2 9 2s12p1which permits the existence of a vast set of bond types: multicenter, electron-deficient,coordinate, ionic, covalent, and also the formation of polymeric associations like HBeH ... BeH2.19 The nonexistence of any information in the literature characterizing the HBeN species, the limited studies of BeNH, and the still relatively unexplored theoretical electronic description of beryllium compounds are per se indicators of the need of a global characterization of these molecules. To achieve this goal, they have been approached by the ab initio SCF andconfiguration interaction (CI) methodologies by making use of extended basis sets with a main focus on the determination of equilibrium geometries, the calculation of relative stabilities and harmonic frequencies, an analysis of the allowed dissociation channels and the associated dissociationenergies, an identification of the lowestlying electronicstates and computation of their vertical excitation energies, and finally a description of the role played by the beryllium orbitals in the electronic rearrangements leading to the chemical bonds in these compounds.
-
2. Theoretical Methods Since earlier studies have been too limited, a first step toward the planning of the calculation has been the determination of the manifold of possible electronic states of the isomers BeNH and HBeN. Guided by the generalized Wigner-Witmer rules,"Table I shows the first few molecular electronic states which correlate with the fragments Be NH, BeN H, and HBe + N. The electronic structure calculation has been carried out using the SCF, SDCI (singles and doubles CI), and MR-SDCI (multireference singles and doubles CI) methodologies. Account for higher order excitations has been considered using Davidson's correction (DC) to the SDCI results. At the SCF level, geometries were optimized and harmonic frequencies were calculated using
+
0 1994 American Chemical Society
+
Roberto-Net0 and Ornellas
82 The Journal of Physical Chemistry, Vol. 98, No. I, 1994
TABLE I: Electronic States of BeNH and HBeN and Their Correlation with the Possible Molecular Fragments According to the Generalized Wiper-Witmer Rules states of Be + NH
molecular states
IS, + 3 1 IS, + IA IS, + 11+
+ 31IS, + 3n
3P.
3c-
states of BeN + H
molecular states
+ 2s, + 2s, 2n + IS, 4n + 2s, 2c++ 2s,
'1In, 3n 3n, Jn l1+,3 c + 3z-,
4E2c-
1A
I1+ I,3,5z-, I.33n 3n
IZ-,31-
states of HBe
+N
+ 4s. 2n + 4s. 2n + 2P, 2 z + + 4s. 2z+
molecular states 3z-,
21+ + 2Du
sz-
L3z-, L3n, I.3A
3n, 'n
lJz+, IJz-, I.3n
3z-,
sz-
TABLE II: HF-SCF, HF-SDCI, and HF-SDCI plus Davidson's Correction Energies (au), Relative Energies (A& cm-I), and Mwle Moments (D) for the Lowest Electronic States of the Molecule BeNH' ~~
HF-SCFb state
l1+ 3n
In
1A
electronic configuration
...4u21d
...4u25u1lr3
...4u25u11r3
...4u25u21r2
SDCI
E
AE
E
AE
-69.583 65 -69.627 60 -69.623 12
9645 0.0 983
-69.819 07 -69.82299 -69.818 46 -69.712 20
860 0.0 995 24 315
SDCI E -69.841 07 -69.838 53 -69.834 30 -69.715 91
+ DCC
P
AE
SCF
CI
0.0 558 1 485 25 274
4.903 0.998
4.875 1.113 1.174
a Optimized geometries for the two lowest states are given in Table 111. SCF(6-31G') results of ref 16: =69.542 06 au (lz+)and -69.594 81 au (3II); AE 5 -1 1 577 cm-1 (-33.10 kcal/mol). e MP4 results of ref 17: -69.8355 58 au (lz+)and -69.820 55 au (311);AE = 3299 cm-1 (9.43 kcal/mol).
TABLE III: Optimized Bond Distances (au) of BeNH and Schlegel's gradient algorithm as implemented in the GAMESS HBeN at the SCF and SDCI (in Parentheses) Levels code.2' The optimization was considered complete for changes BeNH HBeN in theenergygradient smaller than 10-4hartreelao. At theSDCI level, geometries were obtained as the minimum in the potential distance 3n IZ+ 3z3n diatomics energy surfaceconstructed by varying the B e N , N-H, and B e H BeN 2.790 2.516 2.992 2.837 3.045 (4z-p internuclear distances. SDCI and MR-SDCI results have been (2.805) (2.550) 3.020 (2.853) computed with the MELD code developed by Davidson and 2.8Olb 2.521b 2.806E 2.577c collaborators.22 N-H 1.871 1.860 1.962 (3z-)d The starting sets of atomic functions employed were the (13s,(1.885) (1.887) Sp), (13s,8p),and (8s) setsof primitiveGaussiansof DuijveneldtZ3 1.873b 1.861b contracted to [5s,3p], [7s,4p], and [Ss] for beryllium, nitrogen, 1.894c 1.887c and hydrogen, respectively. These basis sets were augmented Be-H 2.502 2.487 2.538 (2z+)d with s- and p-type diffuse functions (Be, a, = 0.015 and ap = a Theoretical, ref 1 . Theoretical SCF, ref 17. Theoretical MP2, ref 0.010; N, a,= 0.028 and ap= 0.025) as recommended by Dunning 17. Experimental, ref 32. and Hay.z4 Also included are two d-type functions ( a d = 0.20 and 0.60) in the beryllium set?' three d-type functions ( a d = a 983 cm-I (2.81 kcal/mol) high lII is calculated to be the first 0.335,0.968, and 2.837) in the nitrogen set,26 and three p- and excited state at the SCF level, whereas a 860 cm-l (2.46 kcal/ one d-type functions (H, ap= 1.8,0.60, and 0.20, a d = 0.70) in mol) high lZ+ is obtained as the first excited state in the SDCI the hydrogen ~ e t . 2The ~ final basis sets (14~,5~,2d)/[9~,5~,2d], calculation. The inclusion of Davidson's correction30changes (14~,8~,3d)/[9sSp,3d], and (8sJ3p,1d)/[5s,3p,ld] for beryllium, the order of the states with the IZ+being now the ground state, nitrogen, and hydrogen, respectively, comprised a total of 94 in agreement with the results of Dewar and Rzepals and Sana contracted functions. and Leroy17 and with the 311state 558 cm-1 (1.60 kcal/mol) In the CI calculations the population of the two innermost higher in energy followed by the at 1485 cm-I (4.25 kcal/ canonical molecular orbitals, which correspond to the 1s orbitals mol). The effect of the use of a more extended basis set than that of nitrogen and beryllium, was kept frozen. This study was carried of ref 16 is also clearly seen in the SCF results of Table 11.Another out in both the C , and C,point group symmetries, and secondpoint to emphasize is the dominant role played by the Hartreeorder perturbation theory with an energy threshold of 1 X 1od Fock configuration and the relative closeness of all these states. au was used to keep the final CI wave function within a tractable In comparing the data of this work with those of Sana and size. The nature of the bonding in BeNH and HBeN in their Leroy,17 it is important to keep in mind that their geometrical ground states was investigated using both Mulliken's28 and natural parameters result from an optimization at the MP2 level with the population analyses (NPA).29 These calculationswere performed 6-31G** basis set, while more accurate energies values were on a CONVEX C220 computer. obtained as single point calculations at full fourth-order perturbation theory employing the 6-3 l+G(Zdf,p) basis set. 3. Results and Discussion The importance of electronic correlation is clearly reflected in the energy difference between the 311 and l2+states. It shifts 3.1. Electronic and Structural Properties of BeNH. Explorfrom about 9645 and 860 cm-1 (27.6 and 2.5 kcal/mol) at the atory calculations at the SCF level for the electronic states of SCF and SDCI levels, with the 3lT always lower in energy, to BeNH predicted by the Wigner-Witmer rules (Table I) indicate -558 and-3299cm-l(-1.6and-9.4 kcal/mol) at theSDCI+DC the states lZ-,SZ-, and 3Z- as unbound and the states 32+and and MP4 levels with the order of the states now reversed. This SlT as very high energetically. Table I1 collects the energies at type of behavior, observed3' in the study of molecules containing the SCF, SDCI, and SDCI plus Davidson's correction for the multiple bonds, reflects the importance of the inclusion of higher four lowest electronic states of BeNH (3n, lZ+,32-,and In) as than single and double excitations in the calculation to better well as the electronic configurations characterizing each of them account for electronic correlation effects. In this respect, the and their dipole moments. Optimized geometrical parameters inclusion of Davidson's corrections in the SDCI energies comfor the molecule in the states 311 and 1Z+ are summarized in pensates for the quadruple excitations included in the MP4 Table 111. approach. The first striking difference to note is that all three levels of calculation predict a different energetic ordering. At the SCF The relatively small energy separation between the singlet and and SDCI levels, the 311 state is found to be the ground state, but triplet states in BeNH can be contrasted with that for the
The Journal of Physical Chemistry, Vol. 98, No. 1, 1994 83
Ab Initio Study of Isomers BeNH and HBeN
TABLE IV Harmonic Frequencies (cm-I) for BeNH. and HBeN Calculated at the SCF Level BeNH HBeN BeN mode 3n 1E+ 3E3n 4z3894 1221 155
e(0) 40)
44
3970 1710 652
2238 994 586
2253 1094 553
931b
BeH -
NH -
2z+
3z-
2049
3 3 w
a Experimental values, ref 14: 3330 (st), 1570 (Sch), 1510 (st), and 1200-500 cm-I (large band). b Theoretical (MR-SDCI),ref 1. e Experimental, ref 32.
TABLE V HF-SCF,HF-SDCI, and HF-SDCIplus Davidson's Correction Energies (au), Relative Energies (A& cm-I), and Dipole Moments (D)for the Lowest Electronic States of the Molecule HBeN' HF-SCF SDCI SDCI + DC Ir state electronic configuration E AE E AE E AE SCF CI
...4&
-69.624 78 0.0 -69.80899 0.0 -69.583 43 9 074 -69.769 98 8 562 1z-69.564 86 13 151 -69.753 68 12 139 -69.531 24 20 528 (-69.73275)b 16 732 1E+ In -69.515 13 24065 -69.707 13 22 356 0 Optimized geometries for the two lowest stat- are given in Table 111. MR-SDCI.
3z3n
0 2 1 r2
...4u25a11r3 ...4a25d1r2 ...4u25d1 r2 ...4u25d1 r3
isoelectronic BCH molecule,*where the l2+state is 14 000 cm-' (40.1 kcal/mol) higher than the 3rI. Concerning the structural parameters, the data in Table I11 show a much shorter beryllium-nitrogen internuclear distance in BeNH ('2+:2 . 5 1 6 ~ (HF) 0 and2.550~0 (CI)) than that predicted for thespecies BeN (3.045 ao).I This fact, indicative of a stronger bond between these atoms in the triatomics, is also reflected in the vibrational frequencies and dissociation energies discussed latter. The correlated value for the nitrogen-hydrogen distance (1 -887 Q) is very close to that observed in N H (1.962 ao).32Also, correlation effects do not seem to affect very significantly these distances when the molecule is in the excited 311 state. Overall, thevalues calculated in this work are quite concordant with those of ref 17. Harmonic frequencies calculatedat the SCF level for the states 3 r I and 12+ are shown in Table IV together with available experimental results. It is worth recalling that an IR spectrum was recorded for a sample in the crystalline state at -196 'C and that the only unequivocally assigned band is the N-H stretching frequency at 3330 cm-l; a stretching was also assigned for the band at 1510 cm-l, and the large and very intense band in the region 500-1 200 cm-I remained unassigned. Additional analyses of the IR spectrum and X-ray data did not indicate the existence of any reagent Be(NH2)Z left in the sample. Considering the SCF calculations tend to overestimate the frequencies relative to the experimentalones,33 the data in Table IV corroborate the identification of the ground state as a l2+. The calculated harmonic frequencies of 3970, 1710, and 652 cm-1 (Table IV) can be associated with the stretchings u(N-H) and u(Be-N) and with the bending mode, respectively. The smaller harmonic frequency reported for thediatomics BeN (93 1 cm-1) again atests for the stronger binding in BeNH. Another interesting result also listed in Table IV is the too low value of the bending frequency (155 cm-1) in the 3 r I state. This value is suggestiveof a weakly linear conformation or a flat bending motion potential surface. To check this possibility additional SCF and SDCI calculationswere carried out for structures with the Be-N-H anglevarying from 0 to 50'; surprisingly,the energies of these structures differed by no more than 0.3 kcal/mol. On the basis of this behavior we judge it more cautious to classify the BeNH molecule in the 311state as a quasi-linear or weaklylinear molecule34 Another point examined was the reliability of the basis set used in this work to predict conformational geometries of molecules with flat potential energy surfaces. Additional calculations at the SCF level on the molecule NHz in the A 2 A ~ state, which is also classified as quasi-linear, were also carried out. Our calculation predicts an angle of 142.5' versus an
-69.82428 -69.78703 -69.769 17 (-69.75273)* -69.723 99
0.0 8 176 12 096 15 703 22 01 1
1.336 0.515
1.192 0.061 0.422 0.319 0.053
experimental value of 144O,35 a result that certainly gives us confidence in the predicted structure for BeNH. 3.2. Electronic and Structural Properties of HBeN. The energies of the lowest five electronic states of HBeN are listed in Table V. Exploratory calculations also pointed out that the electronic states 32+,%-,and 5rI are too high in energy. In contrast with the energetic order calculated for BeNH, the three levels of calculation predict the same ordering for the electronic states of HBeN. In fact, the SCF energy differences between these states are only about 10% off the results predicted at the configuration interaction level. Inclusion of Davidson's correctiondoes not alter the SDCI results significantlyas was the case for BeNH, where there was an inversion in the order of the electronic states. Distinctively, the lowest excited states of HBeN are not so closely spaced as the ones for BeNH. At theSDCI+DC level, a 311 is predicted to be 8 176 cm-' higher in energy than the 32-ground state and is followed by a '2- at 12 096 cm-I, a IZ+ at 15 703 cm-', and a at 22 01 1 cm-l. With the exception of the 12+, these states are dominated by the Hartree-Fock configuration. Note also that the 32-ground state correlates with the lowest dissociation channel of either the fragments HBe N or H BeN. The prediction of a 3 2 - ground state agrees with that for the isoelectronic HBC molecule.* Whereas HBC is calculated to be 1364 cm-1 (3.9 kcal/mol) less stable than BCH? HBeN is estimated in this work to be 3684 cm-I (10.5 kcal/mol) higher in energy than BeNH. The harmonic frequencies of HBeN in the states 3 2 - and 3 r I calculated at the SCF level are listed in Table IV and compared with the corresponding frequencies of BeN and BeH since no experimental work is known for HBeN. In contrast with the stretching frequency associated with the Be-N bond in the BeNH molecule, which indicatesa stronger bond than that in the parent structure BeN, the corresponding frequency in HBeN (994 cm-l) is very close to that calculated for BeN (931 cm-l).l Similarly, the frequency estimated for the BeH stretching (2238 cm-') is within 10% of theexperimentalvalue(2045 ~ m - ~ ) ~ * o f t h e d i a t o d c BeH. This frequency behavior finds its counterpart in the internuclear distances. The Be-N separation in HBeN (3.020 ao) is very close to that in BeN (3.045 U O ) , ~and the BeH distance in the triatomics (2.487 ao) isslighly shorter than theexperimental distance in BeH (2.538 a0).32 The sets of calculated frequencies for both BeNH and HBeN presented in Table IV show quite distinct values, a fact which turns out to be of practical relevance in the search for the identification of the species HBeN, which is still unknown experimentally, so far as we know. 3.3. Relative Stabilities and Dissociative ch.nwb of BeNH and HBeN. In accordancewith the Walsh r ~ l e , which 3 ~ says that
+
+
84
Roberto-Net0 and Ornellas
The Journal of Physical Chemistry, Vol. 98, No. 1 , 1994
Be+NH
BeNH
B8N+H
HBeN
HBe+N
Figure 1. Dissociation channels and relative energies (cm-I) for the molecules BeNH and HBeN.
TABLE VI: Energies (au) of the Dissociation Fragments of the Molecules BeNH and HBeN' fragment energy fragment energy fragment energy Be (IS,) -14.623 08b H (49,) -0.499 99 N ( 'S.) -54.513 99 Be (3Pu) -14.517 546 BeN ('E-) -69.176 12 N (2D,) -54.418 07 NH ()E-) -55.141 44 BeN (2z-) -69.167 65 N (2P,) -54.377 30 NH (Izt) -55.038 01 BeN (2n) -69.169 14* BeH (2zt) -15.197 46 NH ('A) -55.077 666 BeN ( 2 z t ) -69.126 96 BeH (211) -15.106 34 0 With the exceptionof hydrogen, these values refer to CI energies and the basis sets of the fragmentsincludeasghostfunctionsthe basis functions for the missing atom@)in the triatomics. Equilibriumgeometries were used for the diatomics. b MR-SDCI results. HAB molecules with 10 or less valence electrons should be linear in their ground states, this study predicts linear structuresfor the ground states of both isomers BeNH and HBeN with the latter one 3684 cm-1 (10.5 kcal/mol) higher in energy, a behavior very similar to that of the isoelectronic BCH and HBC. On the other hand, these results do not follow the general tendency noted by Bruna and Peyerimhoff)' that, in a series of ABH molecules containing atoms of the first row of the periodic table, the favored isomer has the more electronegatigve atom at the terminal position. A global view of the energy levels of the lowest electronic states and the associated dissociation channels of both isomers in their linear geometries is shown in Figure 1, and the calculated energies of the fragments are collected in Table VI. These fragment energies were obtained at the SDCI and MR-SDCI levels with the inclusion of Davidson's corrections and with the counterpoise procedure to correct for eventual basis set superposition errors.38 Consider first the dissociation of BeNH via the fragments Be N H as shown in the left-hand side of Figure 1. The combined data of Tables I1 and VI predict an energetic order of these fragments as shown in that diagram with the lowest channel about 16 800 cm-1 higher than the ground state of BeNH. Clearly the molecular ground state (12+) and the first five lowest excited states ('II and In) correlate with high lying (- 40 000 cm-I) dissociation channels, so a less energetic dissociation could only happen via a crossing of the surfaces involving the ground state and the fragments correlating with it and the surface connecting the first dissociation channel with a very high lying molecular state. This dissociation route would be unlikely to occur for an
+
energy transfer less than 17 000 cm-l (-49 kcal/mol). A comparison of the fragments' theoretical energies relative to the first channel (14 000,22 702, and 23 162 cm-1) and the experimental values (12 566, 21 202, and 29 807) are indicative that the levelof correlation included in this work can give safe estimates of the proper order of these levels. The other alternative for dissociation of BeNH involves breaking the nitrogen-hydrogen bond, and as shown in the central section of Figure 1, this process would involve more than double the energy needed to break the beryllium-nitrogen bond. Notice also that, although for BeN there is a small discrepancy between theorder ofthestates predictedin thiscalculationand theextensive one in ref 1, it does not affect the general conclusion that BeNH would preferentially dissociate into Be + NH. To quantify this discrepancy, we recall that the relative spacings between the states 42-,22-, *II,and SF in BeNl are 0,2426,2532, and 11 119cm-I, while this calculation predicts 0, 1858, 1532, and 10 768 cm-1, with the first channel 36 203 cm-I higher than the BeNH ground state. One particular difference between HBeN and BeNH, besides the energy spacing between their excited states, is that in the case of HBeN its ground state correlates with the first dissociation channels of the two possible alternatives for bond breaking. Considering now the isomer HBeN, cleavage of the hydrogenberyllium bond leads to the same fragments as discussed above for BeNH and clearly represents a highly energetic route, even considering that HBeN is 3684 cm-l less stable than BeNH. The other channel, represented in the right-hand side of Figure 1 and leading to BeH (22+)+ N (4S,), is 24 762 cm-I higher than the ground state of the parent molecule and is likely to be a favored path for molecular dissociation. Experimentally, the relative energies of the first four dissociation channels are found to be 0, 19 220,20 033, and 28 841 cm-I, whereas this study predicts 0, 21 052,20 000, and 30 000cm-1, with thesecondchannel slightly higher than it should be. This order reversal between two states very close in energy, although reflecting a 10% error in the description of the nitrogen 4S-2D energy separation, certainly does not invalidate the general conclusions reached so far for the order of the electronic states of HBeN. 3.4. Nature of the Bonding in BeNH and HBeN. An approximate picture of the electronic rearrangement leading to the bonding of the atoms of beryllium, nitrogen, and hydrogen
Ab Initio Study of Isomers BeNH and HBeN
The Journal of Physical Chemistry, Vol. 98, No. 1, 1994 85
TABLE VII: Natural and Mulliken Population Analyses (e) and Atomic Charges for BeNH (1Z+) and HBeN (%-)a Be N H A0 NPA Mu1 NPA Mu1 NPA Mu1
TABLE VIII: Valence Natural Bond Orbitals of BeNH (X %+) and HBeN (X 3E-) BeNH hybrid (% p) coefficients NO POP. h& hN hH ce. CN CH nN 1.931 SpO.sg(41) 1.Ooo
1s 2s 2pa 2py 2pa 3d
1.987 0.252 0.391 0.391 0.210 -0.020
1.987 0.052 0.118 0.118 0.018 0.007
2.000 1.691 1.873 1.873 1.590 0.012
H
2.010 1.760 1.544 1.544 0.978 -0.080
0.654
0.970
0.002 0.002 0.003
0.035 0.035 0.001 -0.018
Be
NPA
Mu1
NPA
Mu1
NPA
Mu1
1s 2s 2Pa 2PY 2p, 3d
1.595
1.226
2.000 0.516 0.009 0.009 0.082 0.022
1.905 0.787 0.050 0.050 0.563 -0.014
2.000 1.948 0.988 0.988 1.819 0.007
2.000 1.903 0.944 0.944 1.583 0.057
4
0.002
Naturalchargesfor BeNH, HBeN, and BeH2, with Mullikencharges
in parentheses, are as follows. BeNH: q& = 1.700 (0.789), q N = -2.039 (4.757), qH 0.339 (-0.033). HBeN: q H -0.618 (-0.228), q h = 1.362 (0.659), q N
1.995 sp1.u (59) 1.998 ~ ( 1 0 0 ) ~ ( 1 0 0 ) 1.998 ~ ( 1 0 0 ) ~ ( 1 0 0 )
-0.744 (-0.431). BeH2: q&
e
1.238, q H =-0.619.
in BeNH and HBeN was provided by both Mulliken and natural population analyses. Table VI1 summarizes both types of population results. Note first that Mulliken’s analysis predicts a physically meaningless slightly negative population for the 3d orbitals. This result generaly occurs with population analysis methodologies that employ nonorthogonal orbitals and reflects the nonconservation of the probability density in the method. This fact has led the proponents of the natural population analysis (NPA) to view it as a more balanced procedure than Mulliken’s. Despite these differences, it is evident in Table VI1 that a very significant charge migration from the beryllium 2s to the nitrogen 2p orbitals is taking place in the BeNH molecule. The very low population of the 2s and 2p orbitals in beryllium suggests the existence of a very ionic core leading to a strong ionic-type bond similar to the one observed for the isoelectronic molecule B e 0 ( p = 5.866 D).39 The large dipole moment of BeNH (4.903 D) corroborates this conjecture. A visualization of the xz section of the l?r molecular orbital displayed in Figure 2 provides additional insight into the electronic rearrangement taking place in the molecule. Populated with four electrons, this orbital, as shown in Figure 2b, has a large component of the nitrogen 2p, orbital in its composition. However, the significant distortion toward the beryllium atom indicates an uncommon participation of the beryllium pxb)orbitals in a ?r-type bond. To strengthen the role played by these orbitals, we recall that in BeN (c W )a bond shortening to 2.588 a0 (ground state 3.045 ao) occurs with a four-electron occupation of the ?r orbital. A similar role played by the beryllium pxb) orbitals in making ?r bonds and whence contributing to strengthen the Be-Be bond has also been discussed by Bruna et al.41in the context of Be2H,q (q = -1, 0, 1,2) compound. A comparison with the corresponding 1 r molecular orbital of BeN, shown in Figure 2a, reveals a much less distorted density in this case, which is certainly one of the factors responsible for the larger internuclear distance and the smaller harmonic frequency calculated for this molecule. The valence natural bond orbitals (NBO)29 of BeNH are summarized in Table VIII. Notice first that the electronic population over all the natural bonds adds up to 11.922 electrons and corresponds to the minimal basis occupation in the jargon of the NBO methodology. The remaining 0.078 electrons are distributed over Rydberg-type orbitals and are not shown in this table. The NBO analysis distributes the eight valence electrons in a nitrogen lone pair (nN), in a covalent nitrogen-hydrogen
s (100)
NO
pop.
1.000 1.000 nplN 1.000 U&H 1.000 nN‘ 0.882 U * ~ H 0.067 1.000 K ! (&H 1.000 0.882 !rL ,,ehH 0.067
hes
hH
nN
?!hN
-
s (100) ,Po’” (9.7)
0.824 0.969 0.969
0.246 0.246
HBeN hybrid (% p)
N
A0
0.023
UNH T&N T&N
coefficients CH
hN
~ p o(26) .~~ h (100) !+ (100)
Ce.
SPOJ’
CN 1.ooo 1.ooo 1.OOo
0.892
0.452
sp2.84 (74)
s (100)
0.566
1.000 0.452 4 . 8 9 2
(9.7)
~
p(26)~
s (100) spOJ1 (9.7)
, 0.892
~
~
1.000
0.452
1.ooo
sp2.84 (74) 0.452 -0.892
s (100) sp0,l1(9.7)
bond (UNH), and in two *-type orbitals. The lone pair orbital is mainly a hybrid type SPO.~* (41% p) constituted approximately by 41% and 59% of nitrogen 2p, and 2s orbitals, respectively. The bond orbital (UNH) written in the form (uNH)
0.824[~~’.~’(59% p)]N
+ 0.566[~]H
represents a bond polarized toward the nitrogen atom where the nitrogen hybrid contribution is of the type ~ ~ 1 . 4with ’ 59% due to the 2p,orbital and the hydrogen hybrid is 100%s-type. Finally, the T&N bond orbital written in the form rBeN = 0.246[2pxb,Be]
+ 0.969[2pxb)N]
also predicts an electronic density predominantly centered on the nitrogen, as implied by the high value of the polarization coefficient but with a non-negligible contribution of the beryllium pX@) orbitals. Notice that this type of analysis has also predicted an a priori, not imagined ?r-type bond between the beryllium and nitrogen atoms. Application of the NBO methodology to the isoelectronic BCH (*E+) molecule predicts the existence of two *-type and one a-type bonds between carbon and nitrogen with the latter one showing a hybridization of the type spl,94(66% p) and ~ ~ 0(44% . ~ 8 p) for the carbon and nitrogen atoms, respectively. A classical picture of a triple bond can thus be visualized for BCH whereas in BeNH the third bond is essentially of the ionic type. With attention now focused on the bonding in the molecule HBeN (X32-), Table VI1 collects Mulliken’s and natural values for atomic populations resulting from both analyses. Notice first that the two approaches predict only one isolated electron in each of the nitrogen p, and pyorbitals. This point is further illustrated in Figure 2d, which represents the x(y)z section of either the lx, or l?ryorbitals and clearly reveals the dominant nitrogen 2px@) orbital character. The distortion toward the beryllium atom is much less than that observed for the molecule BeNH and very similar to that of the 1?rorbital in BeN (Figure 2a). In fact, the beryllium-nitrogen equilibrium distance (3.020 ao) and the harmonic frequency (994 cm-1) in HBeN are very similar to those of BeN (3.045 a0 and 931 cm-I). We recall that the BeN results come from a large-scale CI calculation. In contrast with BeNH, both analyses predict an excess of negative charge on the hydrogen atom mainly from a migration from the beryllium 2s orbital. Although part of the original
lif
\ \
....- .--_- _- -_- -._
,
-
\
.
,
HBeN
I' 4u
-
I
\ \
/ /
- d
I " " '
C
,
/ . - - _ #
------c'
BeN
i
...
\
\ /
I
- a
-
IT
BeNH
- t
'
'
'
a
I'
I
I
I
I
I
I I
I
'
'
'
'
'
-
' 5u
-
HBeN
-
Ab Initio Study of Isomers BeNH and HBeN
The Journal of Physical Chemistry, Vol. 98, No. 1, 1994 87
in HBeN. This charge rearrangement is reflected in a lower dipole moment ( ~ S C F= 1.336D) for HBeN than for BeNH (I.(SCF = 4.903 D). Additional insight is also provided by the xz sections of the 4u and Su orbitals (Figure 2, parts e and f, respectively) doubly occupied in the Hartree-Fock configuration. The 4u orbital can be associated with a hydrogen-beryllium bond, but with a significant negative polarization toward the hydrogen atom. The Suorbital, on theother hand, reflectsa mixing mainly of beryllium and nitrogen 2p, orbitals with a major contribution from the nitrogen atom. These orbitals together with data on the atomic populations disclose a positive core in the beryllium atom and are indicative of an ionic contribution in the binding between the hydrogen and nitrogen atoms with beryllium. Note also the similarity of the charge distribution found in this molecule to that of the BeHz species, which is known to form polymeric associations.lg Complementing this picture, Table VI11 also lists data on the composition and population of the valence natural bond orbitals. Note first that a distinction is made here between orbitals with CY and @ electrons, and that according to the NPA terminology a total of 0.102electrons is distributed over Rydberg orbitals and is not shown in that table. In contrast with BeNH, there is a lone pair ( n ~ , with a hybridization of the type sp0.35(26% p), reflecting a larger contribution of the nitrogen 2s than in BeNH. , singly occupied, Also there are two lone orbitals (npp, n b ~ )each representing pure hybrids 100% p-type on the nitrogen atom. It is worth pointingout that, similar to Mulliken’s analysis, no *-type bond is predicted for this molecule. Concerning the bonding between the hydrogen and the beryllium atoms, the natural orbitals UH& and are essentially a contribution of the hybrids ~ ~ 0 (9.7% p) on beryllium and s (100%)on hydrogen with polarization coefficients0.452and 0.892,respectively, therefore pointing out the charge concentration toward the hydrogen atom. Next, the two nonbonding orbitals (nk,
