J. Phys. Chem. 1995,99, 13899-13908
13899
Experimental and Theoretical Density Studies on a Nitrido- Chromium(V) Complex [CrV(bpb)N1 Chih-Chieh Wang,f Yu Wang,*vt Liang-Kuei ChouJ and Chi-Ming Che' Department of Chemistry, National Taiwan University, Taipei, Taiwan, Republic of China, and Department of Chemistry, The University of Hong Kong, Pokfulam Road, Hong Kong Received: April 25, 1995; In Final Form: July 7, 1995@
This work gives the first example of a combined experimental and theoretical electron density study of a M-Nnitrido triple bond. The electron density distribution of a chromium(V)-nitrido complex, Crv(bpb)N (bpb2- = 1,2-bis(2-pyridinecarbrboxamido)benzene), was investigated both by single-crystal X-ray diffraction measurement at 120 K and by molecular orbital calculations. The compound belongs to the space P21, Z = 2, M,= 382.32, a = 5.977(1) A, b = 13.208(2) A, c = 9.776(1) A, j3 = 90.27(1)", V = 771.7(2) A3, Mo Ka radiation ( A = 0.7107 A,$ = 0.75 mm-I), Rf= 4.1% and R, = 2.5% for 5975 observed reflections. Cr is five-coordinated in a square pyramidal fashion. There are three different Cr-N bonds in this compound, namely, CT-Nnihdo, Cr-Nmido, and Cr-Npyridinebonds. Deformation density maps were derived from the multipole model and from the theoretically calculated ones based on ab initio and DFT (density functional theory) calculations. The accumulation of deformation density along the C-H, C-C, C-N, and C - 0 bonds in the bpb ligand is clearly demonstrated for their covalent character. The agreement between the density maps obtained from the multipole model and from molecular orbital calculations is excellent in the ligand part. Some discrepancies are found near the Cr nucleus. Net atomic charges from multipole refinement are in reasonable agreement with those derived from ab initio calculations and the DFT method. Analysis of natural bonding orbitals (NBOs) reveals that the Cr-Nnit"do has a triple-bond character ( a 2 d ) and the four N of bpb behave as a-donors to Cr with Cr-Namldo a polarized covalent bond and Cr-Npyridine an essentially dative bond. d-orbital populations of Cr are derived by both experiment and theory; they are in good agreement with each other. An unpaired electron is found on the nonbonding d-orbital of the Cr atom.
Introduction
Experimental Section
Cr(V) compounds have always received considerable attention,' partly because oxochromium(V)s are active oxidants for oxidation of inorganic and organic substrates.2-8 These classes of compounds undergo a variety of reactions, for example, solvation, ligand exchange, and dimerization.' Most of the Cr(V) complexes contain at least one oxo g r ~ ~ por~similar ~ . ~u-, ~ and n-donors such as nitrido (N3-)'-6,7 or imido (RN2-) groups.I,* Among those five-coordinated Cr(V) complexes which have been structurally characterized, the geometries of the Cr(V) are always between a square pyramidal and a trigonal bipyramidal structure. The crystal structure and spectroscopic properties of the title compound have been reported previously.6 This complex is in a square pyramidal geometry with a nitrido N atom at the axial position. The chromium atom is located 0.51 8, above the equatorial plane defined by the four nitrogen atoms of bpb. The five-coordinated complex may have been a consequence of the large a-trans effect9-I0of the N3- group. This compound contains three types of Cr-N bonds: CrNnlmdo,Cr-Namldo, and Cr-Npyndlne,the bonding features of which are interesting and worth further investigation. It is necessary to clarify the true electronic charge of this high-valent Cr(V) ion. To investigate all these chemical-bonding-related properties, the title compound was reexamined with lowtemperature X-ray diffraction and with molecular orbital calculations. Because the crystal belongs to a noncentrosymmetric space group, deformation density maps are derived by the multipole expansion method."
Data Collection and Processing. The title compound was synthesized according to the literature.6 A suitable reddish orange crystal was obtained by slow diffusion of diethyl ether into a dimethylformamide solution of the crude sample. The crystal data and details of the experimental conditions are given in Table 1. Low-temperature data were measured on a CAD4 diffractometer equipped with a liquid N2 gas-flow device.'* Three reference reflections were measured every hour to check the stability of the experimental conditions; the variations in intensities are within f2%. The intensity data were first measured up to 28 = 60" for one unique set of reflections ( f h , k , f l ) , which included Friedel reflections as well. Two equivalent sets of reflections (fh,k,&l) and (&h,-k,*l) were then measured up to 28 = 50"; one and a half sets of reflections (&h,-k,&l) and (+h,+k,&l) were collected up to 28 = 80'. In addition, four measurements for each reflection of the unique set with an azimuthal angle, Y, of -15", -5", +5", and $15" were collected up to 28 = 50". These yielded a total of 20 623 reflections, which gave 8699 unique reflections after averaging the equivalents. An absorption correction was applied before the averaging according to eight measured faces. The correctness of the absorption correction was checked against the experimental Y curves for three reflections; the agreement between the measured intensities and the relative transmission coefficients was reasonable. The interset agreement between the intensities of equivalent reflections is 0.027 after the absorption correction. Data were corrected for Lorentz and polarization effects. The structure factor Fa was derived from the averaging intensity; the standard derivation of Fa was calculated from a geometric mean of all the u's of equivalents. Conventional full-matrix least-squares refinements were per-
T To whom correspondence should be addressed. ' National Taiwan University. * The University of Hong Kong. @
Abstract published in Advance ACS Absrracts, August 15, 1995.
0022-365419512099-13899$09.00/0
0 1995 American Chemical Society
Wang et al.
13900 J. Phys. Chem., Vol. 99, No. 38, 1995 TABLE 1: Crystal Data for Crv(bpb)N formula C~~ZN~CISHIZ formula weight 382.32 diffractometer used CAD4 p2 I space group a, A 5.977(1) b, A 13.208(2) c, A 9.776(1) A deg 90.27(1) v, A 3 771.7(2) Z D,,I, g cm-'
2 1.645
1(Mo Ka), 8, F(O@J) unit cell detn #; 28 range (deg)
0.710 69 390 24,30-45
scan type 28 scan width (deg) 28 range (deg) p(Mo Ka), cm-I tansmission factor crystal size (mm) temperature (K) no. total reflns no. of unique reflns no. of abs reflns ( I > 2a(I)) no. of refined params
8/28
2(0.70 + 0.35 tan 0) 80
7.5 0.842-0.963 0.2 x 0.2 x 0.15
120 20 623 8699
5975 283 0.041,0.025 0.027
RI, R I ~ "
Rmt
minimized function weighting scheme g(second ext coeff.) x lo4
XwlFo-Fcl2
I/u2(Fo)
0.068(8) 0.0044 1.7to -0.9
(Alo)max
(Ae)max.mm. e A-3
computation program a
NRCVAXI5
R1 = ~ ~ F o - F c ~ / X ~RFI ,o=~ ~XwlFo-Fc12/~wlFo12)1~; . u2(Fo)from
counting statistics. R,,, = X(Z - I ) / X I .
formed with all the positions and thermal parameters. The H atoms were relocated along the C-H vectors so as to make the C-H bond length 1.08 AI3 for the purpose of the deformation density calculation. The final refinement on 5975 observed reflections ( I 2 2a(l)) gave agreement indices of R = 0.041 and R, = 0.025. Multipole Refinement. A multipole refinement was performed, in which the atomic density is described as the sum of a core density, a spherical valence density with adjustable population Pvalence, a radial contraction-expansion parameter K, and a series of spherical harmonic terms with variable population Pimp to describe the nonspherical feature of atomic electron density according to the following expression. I = PcoreQcore
+ PvalenceK
3
Qvalence(Kr)+
I
+/
where @core and @valence are spherical core and valence densities, respectively, Kmpi s the spherical harmonic angular function in real form, R,,J is the radial part of the function where N is a normalization factor, and nl and 51 are chosen for each 1 value which was described previously.ll
R J r ) = Nr"' exp(-&r) Pcore, Pvalence, Pimp, and K are refinable parameters in addition to the atomic positional and vibrational parameters. The multipole refinement was done with a multipole expansion of the valence shell up to and including hexadecapoles for the Cr atom, up to and including octapoles for the C, N, and 0 atoms, and up to dipoles for the H atoms. Hartree-Fock functions were used for the monopoles. Scattering factor tables
for both core and valence electrons were taken from ref 14. He core electrons were used for C, N, and 0; K core electrons, for Cr. The valence electron configurations for Cr, C, N, and 0 were d5, s2p2,s2p3,and s2p4,respectively, for the valence part of the scattering factors. A C, molecular symmetry was imposed in the least-squares procedure for the multipole coefficients, Pl,,. The coefficients for all the multipole terms together with positional and anisotropic thermal parameters were obtained by a full-matrix least-squares refinement based on Fo. Electron Deformation Density. The dynamic multipole model deformation density distribution was obtained by Fourier synthesis with Fmultipole - Fsphencal as the coefficients. Both F's are in complex form including A and B parts. Fmultlpole was calculated as described earlier.' Fsphencal was calculated from the same parameters as Fmultipoleexcept that all coefficients,PI,,, were set to 0 and Pvalence was set to the neutral atom value. The static multipole deformation density distributions were calculated in direct space according to eq 1. All computations were carried out on a Micro VAX and IBM Risc 6000 computer using NRCVAX programsI5 and the programs MOLLYlIa and SALLYIlb. The contours of model deformation density were produced by a locally developed contour-plotting program.I6
'
Computational Details Basis Functions and Geometry. The Gaussian92" and DMolI8 programs were used for the ab initio and DFT calculations, respectively. The basis set used for the Cr atom was the (14,9,6)/[8,4,3]contraction (626*1/5112/41 1),19920 where the (14s,9p) primitive Gaussian functions were taken from Wachters20and (6d) basis sets were taken from Goddard.19The basis sets used for N, 0, C, and H atoms were taken from split valence level double-9 3-21G. Because of the odd electron system of the molecule, the calculation was made at the ROHF (restricted open-shell Hartree-Fock) level. The basis set used in the DFT calculation was a double numerical basis set augmented by polarization functions (DNP).18,2',22 The local density approximation was applied, in which the VWN potentia123was used. The molecular geometry was taken from the diffraction data. To reduce the computational time, a C, symmetry with the mirror plane at the bisection of the LN1Cr-N2 and passing through the C F N bond was imposed. The Cr-Npyridine and Cr-Namido bond lengths were fixed at 2.084 and 1.966 A, respectively. The internal coordinates at the Cr atom were defined so that the z-axis was along the Cr-Nnit*do and the x-axis was at the bisection of LNl-Cr-N2. Natural Bond Orbital Analysis. The natural bond orbital (NBO) a n a l y ~ i s ~ ~comprises -~' a sequence of transformations from the given basis sets to various localized sets: natural atomic orbitals (NAOs), natural hybrid orbitals25 (NHOs), natural bond orbitals26(NBOs), and natural localized molecular orbital^^^,^^ (NLMOs). The NLMOs can then be transformed to occupied MOs of ROHF functions. given basis sets
-
NAOs
-
NHOs
-
NBOs
-
NLMOs
These procedures derive their names and inspirations from the natural orbitals of Lowdin,28 which were obtained from the diagonalization of the one-particle density matrix. The given basis functions were taken from ab initio ROHF calculation. The results after NBO analysis were generally in good agreement with Lewis structure concepts and the Pauling-SlaterC o u l ~ o nconcept ~ ~ of bond hybridization and polarization. Net atomic charges, orbital populations, and bond orders are thus generated by means of NBO analysis. The charges and orbital populations obtained this way are designated as the natural
Density Studies on a Nitrido-Chromium(V) Complex
0.981 1.658
Figure 1. (a) Molecular drawing with 50% probability in thermal ellipsoids at 120K. (b) Choice of local Cartesian axes and bond order of each bond; the heavy arrows represent dative bonds. orbital population analysis (NPA), which is compared with the Mulliken population analysis (MPA). Theoretical Deformation Density. The theoretical deformation density (Agtheo)is defined as the difference between the total molecular density and the promolecular electron density. The total molecular density was calculated from ROHF molecular wave functions, each occupied molecular orbital was assigned to have two electrons, but the HOMO orbital was assigned to have only one electron. The promolecular electron density was the sum of the superposition of the spherical atomic density with atoms at the same nuclear positions as in the molecular geometry. The spherical atomic density was calculated at the ROHFIGVB level, and each valence orbital was assigned to have equal electron populations, e.g. 213, 1, and 413 for each 2p-orbital of carbon, nitrogen, and oxygen atom, respectively. All computations were performed on a CONVEX C3840 computer and an IBM RISC-6OOO computer using the Gaussian92 and DMol programs. The MOPLOT30 program was used for the deformation density calculation.
Results and Discussion Structure. The geometry of CrV(bpb)N at low temperature is the same as that at room temperature.6 The structure is
J. Phys. Chem., Vol. 99, No. 38, I995 13901 TABLE 2: Fractional Atomic Coordinates and B , Values (A2);ad’s Refer to the Last Digit Printed: (a) from Full Data Refinement; (b) from Multipole Refinement; B, = (W3)jF1L&U@i*aj*a~j atom X Y Z B, Cr a -0.11169(4) 0.0 -0.17262(3) 0.805(9) b -0.11 170(8) 0.0 -0.17260(4) 0.69(1) 0 1 a -0.2275(2) 0.2502(1) 0.0633(1) 1.60(5) b -0.2275(4) 0.2503(2) 0.0638(2) 1.56(6) 1.80(6) 02 a -0.2802(2) O.O5Oo( 1) -0.5741(1) b -0.2812(2) 0.0498(2) -0.5741(2) 1.70(7) N10 a -0.2444(3) -0.0923(1) -0.1 169(2) 1.14(6) -0.0929(2) -0.1172(2) 1.16(6) b -0.2447(4) N1 a -0.2758(2) 0.0474(1) -0.3354(2) 0.94(5) b -0.2757(3) 0.0477(1) -0.3360(2) 0.94(4) 0.1233(1) -0.1008(2) 0.96(5) N2 a -0.2530(2) b -0.2524(3) 0.1234(1) -0.1001(2) 0.90(5) N3 a 0.1026(2) 0.0333(1) -0.0 104(2) 0.99(5) b 0.1030(2) 0.0338(1) -0.0108(2) 0.93(4) N4 a 0.0836(2) -0.0617(1) -0.3276(2) 0.95(5) b 0.0840(2) -0.0614(1) -0.327l(2) 0.88(5) 0.1166(1) -0.3089(2) 0.96(6) C1 a -0.4490(3) b -0.4496(2) 0.1166(1) -0.3091(1) 0.89(4) C2 a -0.6268(3) 0.1417(1) -0.3962(2) 1.13(6) 0.1412(1) -0.3961(2) 1.20(5) b -0.6258(3) 0.2106(2) -0.3519(2) 1.25(7) C3 a -0.7877(3) b -0.7882(3) 0.2100(1) -0.3526(2) 1.30(5) C4 a -0.7712(3) 0.2555(2) -0.2255(2) 1.35(7) 0.2555(1) -0.2242(2) 1.32(5) b -0.7704(3) 0.2320(2) -0.1356(2) 1.10(6) C5 a -0.5935(3) b -0.5938(3) 0.2318(1) -0.1360(2) 1.1 l(5) C6 a -0.4352(3) 0.1608(1) -0.1774(2) 0.89(6) 0.1607(1) -0.1775(1) 0.88(4) b -0.4353(2) 0.1712(1) 0.0085(2) 1.12(6) C7 a -0.1641(3) 0.1712(1) 0.0082(2) 1.05(4) b -0.1640(3) 0.1177(1) 0.0591(2) 0.98(6) C8 a 0.0420(3) 0.1178(1) 0.0585(2) 0.99(4) b 0.0418(3) 0.1551(2) 0.1682(2) 1.30(7) C9 a 0.1668(3) 1.27(5) 0.1685(1) b 0.1551( 1) 0.1662(3) 0.1055(2) 0.2063(2) 1.27(7) C10 a 0.3616(3) b 0.1053(1) 0.2057(2) 1.30(5) 0.3621(3) 0.0173(2) 0.1366(2) 1.25(7) 0.4196(3) C11 a 0.1362(2) 1.24(5) b 0.0172(1) 0.4198(3) 0.0300(2) 1.16(6) C12 a 0.2860(3) -0.0168(1) 0.0297(2) 1.20(5) b 0.2867(3) -0.0171( 1) 0.2710(3) -0.1164(1) -0.3165(2) 1.22(7) C13 a -0.1163(1) -0.3155(2) 1.24(5) b 0.2716(3) 1.24(7) C14 a 0.3850(3) -0.1509(2) -0.4299(2) b 0.3868(3) -0.1512(1) -0.4290(2) 1.29(5) 0.3057(3) -0.1297(2) -0.5597(2) 1.3l(7) C15 a b 0.3075(3) -0.1297(1) -0.5594(2) 1.34(5) 0.1102(3) -0.0732(1) -0.5721(2) 1.13(6) C16 a b 0.1100(3) -0.0734(1) -0.5723(2) 1.17(5) 0.0038(3) -0.0412( 1) -0.4548(2) 0.91(6) C17 a b 0.0042(2) -0.0407(1) -0.4542(2) 0.93(4) 0.0237(1) -0.4618(2) 1.07(6) C18 a -0.2021(3) 1.03(5) b -0.2034(3) 0.0237(1) -0.4620(1) essentially a distorted square pyramid, where the nitrido ligand is at the axial position and the four nitrogen atoms of bpb are at equatorial positions. The bpb is not planar. The complex is best described to have C, symmetry with the mirror plane passing through the Cr-Nnihdo bond and at the bisection of the N2-Cr-N1 angle. The dihedral angle between these two halves is 38.2’. The choice of local Cartesian axes applied in the multipole terms for each atom is shown in Figure lb. The atomic coordinates obtained by full-matrix least-squares refinements based on both spherical and multipole models are given in Table 2. The thermal ellipsoids of the molecule at 120 K are shown in Figure la. The atomic thermal parameters at 120 K decrease, on average, to 30% of those at room temperature.6 Selected bond distances and angles around the chromium atom obtained from 300 and 120 K data and from multipole refinements are listed in Table 3. These structure parameters
13902 J. Phys. Chem., Vol. 99, No. 38, 1995
Wang et al.
(d)
(c)
Figure 2. Deformation density distribution in the plane of the pyridine ring: solid line, positive; dash line, zero: dotted line, negative; contour interval 0.1 e/2%-3. (a) h@M-A,static, (b)
A @ a b - , ~ ~ t l o(C) ,
A@Dm,( 4
&residual.
TABLE 3: Bond Distances (A) and Angles (deg) around the Cr Atom of [CrV(bpb)N]with esd’s in Parentheses: (a) from Conventional Refinement at 300 K; (b) from Conventional Refinement at 120 K; (c) from Multipole Refinement Cr-N10 Cr-N( 1)
a b c a b a b c a
1.560(2) N(1)-Cr-NlO 1.555(2) 1.562(2) 1.965(3) N(2)-Cr-N10 1.967(2) 1.978(2) 1.957(2) N(3)-Cr-N10 1.965(2) 1.979(2) 2.075(2) N(4)-Cr-N10
a b c a b c a b c a
b
2.080(2)
b
c a b c a b c a b c
2.080(2) 2.085(3) 2.084(2) 2.080(2) 79.29(8) 79.33(6) 79.45(6) 79.77(8) 79.43(6) 79.34(6)
c Cr-N(2) Cr-N(3) Cr-N(4) N(l)-Cr-N(4) N(2)-Cr-N(3)
N(l)-Cr-N(2) N(3)-Cr-N(4)
c a b c a b
c
106.5(2) 106.24(8) 106.31(8) 108.0(2) 107.67(8) 107.95(8) 102.1(2) 102.23(8) 102.49(8) 102.9(2) 103.68(8) 103.52(8) 79.54(9) 79.16(7) 79.18(7) 106.64(8) 107.02(6) 106.76(6)
are essentially the same; however, the Cr-N1 and Cr-N2 distances from the multipole model (1.978, 1.979 A) are somewhat longer than those from the spherical model (1.967, 1.965 A). The Cr-Nnltndodistance of 1.555 A at 120 K is very
TABLE 4: Agreement Indices of MdtiDole Refinement ~
conventional monopole octapole“
NP
Rib
RI,‘
R2d
R2we
Sf
239 259 492
0.0394 0.0374 0.0303
0.0242 0.0213 0.0151
0.0534 0.0492 0.0379
0.0258 0.0188 0.0125
1.860 1.641 1.185
Up to hexadecapole terms for the Cr atom only. RI = CIFo-Fcl/ C I F o I . RI, = ( C W ~ F O - F ~ ~ ~ / C W R2 ~ F=~CIF>-F,ZI/CF,Z. ~~)”~. e R2w - (~WIF~-F~lz/C~IFo14)1’2. f S = [&lFo-Fc12/(N0 - NP)]’”; NO (1
= number of reflections; NP = number of parameters.
short, thus consistent with that of a formal triple bond. The average Cr-NpyAdinedistance is ca. 0.1 15 8, longer than that of the Cr-Namido bond. This is expected since the amido N ligand is a better 0-donor than the pyridine N atom. The agreement indices for various refinement models are listed in Table 4. The significant improvement in agreement indices with the multipole refinements is obvious. Electron Density Distribution. Deformation densities are depicted as the static multipole model (&MI-A) and theoretical maps (@+initio and AQDR). The dynamic deformation densities calculated including the nuclear vibration motion with Fourier coefficients up to the experimental data resolution (0.90 k ’ ) show similar features but less density than the corresponding static density maps; therefore, they are not included in this text. The density distribution at the pyridine and benzene ring plane of the bpb ligand is shown in Figures 2 and 3, respectively.
Density Studies on a Nitrido-Chromium(V) Complex
J. Phys. Chem., Vol. 99, No. 38, 1995 13903
Figure 3. Deformation density distribution in the plane of the benzene ring. Contours are as in Figure 2. (a)
[email protected],c, (b) A@ab-in,t,or (c) A@Dm.
Bonding densities in C-C, C-0, C-N, and C-H bonds are observed as expected. The agreement in density between experiment (a) and theory (b and c) is excellent. The peak height in each C-C bond is roughly the same; there is no sign of altemating single-, double-bond character in either the benzene or the pyridine ring. Both bond distances and bond density indicate strongly the complete n-electron delocalization over the six-membered ring. The lone pair electrons at the 0 atom are observable in the model density map (Figure 2a), but are somewhat less pronounced than in the theoretical deforma-
(4 Figure 4. Deformation density distribution in the plane of N2-CrN1. Contours are as in Figure 2. (a) A Q M . A , ~ ~(b) , ~Aeat,.huo, ~, (c) A Q D ~ .
tion density (Figure 2b,c). This is often the case for lone pairs?' The residual map for the pyridine plane is shown in Figure 2d; it is clear that nothing much is left in the residual map. This means the multipole model nicely fits the experimental data.
Wang et al.
13904 J. Phys. Chem., Vol. 99, No. 38, I995
(4 Figure 5. Deformation density distribution in the plane of N3-CrN4. Contours are as in Figure 2. (a) A @ ~ - ~ , s r a t l c ,(b) A@ab-lnluor (c) A@Dm.
The asphericity in the electron density distribution around the Cr atom is important evidence for assessing the bonding situation of the metal atom. The bonding feature between Cr and the bpb ligand is displayed in four planes, Le. Figure 4
(c) Figure 6. Deformation density distribution in the plane of N3-CrN2. Contours are as in Figure 2. (a) A O M - A .(b) ~ ~A@ab-lruuo. ~~. (c) A Q D ~ .
(N1-Cr-N2), Figure 5 (N2-Cr-N3), Figure 6 (N3-Cr-N4), and Figure 7 (plane perpendicular to C F N at Cr); the first three are planes defined by Cr and two alternate nitrogen atoms of
J. Phys. Chem., Vol. 99, No. 38, 1995 13905
Density Studies on a Nitrido-Chomium(V) Complex
TABLE 5: Net Atomic Charges
Cr Nnitrido Namido Npyridine 01,02 C1, C6 c2, c 5 c3, c 4 C7, C18 C8, C17 C9, C16 ClO,C15 C11, C14 C12, C13 H2, H5 H3, H4 H9, H16 H10,H15 H11, H14 H12, H13
ab initio
multipole monopole
DIT
DFT
MPAb
NPAC
Hirshfeld"
MPA
+0.20(7) -0.26(4) -0.34(3) -0.13(3) -0.40(3) +0.09(2) -0.18(3) -0.23(2) +0.48(3) -0.07(3) -0.28(3) -0.15(3) -0.14(3) +0.08(3) +0.23(2) +0.21(2) +0.23(2) +0.16(2) +0.24(2) +0.22(2)
+1.56 -0.33 -1.13 -0.97 -0.66 +0.32 -0.25 -0.25 +0.91 f0.30 -0.25 -0.16 -0.33 +0.19 +0.28 f0.23 +0.31 +0.29 +0.27 +0.27
$1.18 -0.25 -0.79 -0.56 -0.66 +0.18 -0.26 -0.26 +0.75 $0.20 -0.25 -0.15 -0.30 $0.09 $0.27 $0.24 $0.29 +0.27 +0.26 +0.23
+0.45 -0.29 -0.14
+0.62 -0.42 -0.33 -0.29 -0.43 +0.18 -0.27 -0.25 $0.26 +0.18 -0.23 -0.24 -0.26 -0.02 +0.04 t0.05 +0.07 +0.08 +0.07 +0.06
-0.08 -0.25 +0.03 -0.06 -0.06 +0.11 f0.06 -0.03 -0.01 -0.04 +0.03 +0.27 f0.26 +0.32 +0.31
+0.30 +0.14
Hirshfeld partition. MPA: Mulliken population analysis. NPA: natural population analysis.
I
u,:
