J. Pkys. Chem. 1988, 92, 607-614 torus. The correlation function on the torus GAm(t)can then be evaluated by averaging the quantity A(t - to)*A(to)over different time origins to along this trajectory. Alternatively, G,,(t) can be calculated by Fourier analyzing A ( t ) along this trajectory and applying eq 13. Clearly, the quasi-classical technique cannot bring classical mechanics into complete agreement with quantum mechanics. It is not able to describe such long-time phenomena as tunneling and purely quantal wavepacket spreading. It is, however, capable of improving the short-time agreement between quantum and classical mechanics, and sometimes this improvement is very significant. The related approximation presented in eq 11 may
607
yield even better agreement with quantum behavior and deserves further study. However, the present technique is computationally simpler. It may be readily applied to a variety of different kinds of correlation functions including survival and transition probabilities that describe the evolution of nonstationary states. The quasi-classical approximation thus deserves consideration in many cases where a completely classical treatment is suspected of inaccuracy. Acknowledgment. We thank Mr. B. Ramachandran for a critical reading of the manuscript. This work was supported by National Science Foundation Grant CHE-8418 170.
Correlation between the Electron Paramagnetlc Resonance Spectra, Structure, and Bonding of the Bis(biuretato)cuprate( I I ) Dianion Saba M. Mattad Department of Chemistry, McCill University, 801 Sherbrooke St., West, Montreal, Quebec, Canada H3A 2K6 (Received: June 2, 1987)
The X a scattered wave self-consistent field method is used to investigate the electronic structure and excited states of the bis(biuretato)cuprate(II) dianion. The relationship between the spin Hamiltonian tensor components and the MO expansion coefficients for the dianion is discussed. Detailed expressions for the g tensor components are derived and are evaluated. They are also determined from the experimental solid-state electron paramagnetic resonance spectrum by simulation. The computed and experimentalvalues for the hyperfine and g tensors are found to be in good agreement. The,g and gw anisotropies are quite similar and are induced by the b2, and b3gorbitals representing the out-of-plane %-type” interactions. In contrast, the g,, anisotropies are directly linked to the coupling of the ’B,,,ground state and the excited A, states. The electronic absorption spectra and the computed electronic transitions for this complex are compared and discussed.
Introduction Alkaline media containing complexes formed by the reaction of Cu(I1) ions and biuret are characterized by their intense colors ranging from red to blue, depending on their method of preparation.’ When the biuret ligand is substituted by proteins, these solutions still retain their intense colors. This property was widely used to determine the total protein content in clinical assays.’ Another significant property of these solutions is their ability to dissolve cellulose.’ Their dissolution power is comparable to, if not greater than, standard inorganic solvent^.^ In order to understand the nature of these complexes, their mechanism of formation, and their interaction with carbohydrates, a systematic isolation and study of each individual complex under different conditions is necessary. As the first part of such a comprehensive study, the electron paramagnetic resonance (EPR) spectra and their relation to the electronic structure and bonding of bis(biuretato)cuprate(II) in solid and liquid solutions are investigated. The EPR spectra of this complex display copper nuclear hyperfine structure together with nitrogen ligand hyperfine splitting patterns very similar to those of copper(I1) porphyrins and phthalocyanins.s Due to the large number of overlapping resonance components of these spectra, a computer simulation of the spectral line shapes is necessary. With this technique the principal components of the magnetogyric (g) and copper hyperfine and nitrogen ligand hyperfine tensor components for this complex are determined. It will be demonstrated that the analysis of the EPR line shapes by simulation reveals that the fourth copper hyperfine component overlaps with the other three via its spatial perpendicular component. This phenomenon is found not to be restricted to the EPR spectra of the bis(biuretato)cuprate(II) complex alone Present address: Department of Chemistry, University of New Brunswick, Bag Service No. 45222, Fredericton, NB, Canada E3B 6E2.
0022-3654/88/2092-0607$01 .50/0
but also generally occurs in the X-band EPR spectra of copper(I1) porphyrins and copper(I1) phthalocyanins. Expressions for the components of the spin-Hamiltonian tensors are derived in terms of the molecular orbital coefficients for the ground and excited states of this dianion. These coefficients are numerically determined by using the X a scattered wave method. Most of the computed tensor components are found to be in good agreement with the experimental values determined by simulation. Experimental and Computational Details Biuret (Eastman Organic Chemicals) was recrystallized twice from water, dried at 393 K, and used in the anhydrous form (melting point 465 K). The solid dipotassium bis(biuretat0) complexes of copper and nickel were prepared by the method of McLellan and Melson.6 Cupric hydroxide was prepared by dissolving cupric sulfate pentahydrate (125 g) in distilled water and ammonium hydroxide (specific gravity 0.9) was added with constant stirring until the contents were neutral. The greenish blue precipitate formed was washed by decantation until free of sulfate ions. It was then suspended in water and a solution of sodium hydroxide (425 mL, 244 g/L) was added at 293 K. The resulting blue precipitate of cupric hydroxide was then washed and dried under vacuum at 310 K for several days. (1) Kurzer, F. Chem. Rev. 1956, 56, 95. (2) Kingsley, G. R. J . Biol. Chem. 1940, 133, 731. Cassatt, J. C. J. Biol. Chem. 1973, 284, 6129. Herbertz, G.Med. Lab. 1976, 29, 281. Later, R.; Quincy, C. J. Chromatogr. 1979, 174, 131. Kharlamov, I. P.; Popov, B. A. Zauod. Lab. 1985, 51, 13. Molnar, I. Elelmiszervizsgalati Kozl. 1982, 28, 195.
(3) Jayme, G.; Lang, F. Kolloid-2. 1957, 150, 5 . (4) Jayme, G. High Polym. 1971, 5 (Part IV), 381. ( 5 ) Lin, W. C. The Porphyrins; Dolphin, D., Ed.; Academic: New York, 1979; Vol. 4, p 235. (6) McLellan, A. W.; Melson, G. A. J. Chem. SOC.A 1967, 137.
0 1988 American Chemical Society
608
Mattar
The Journal of Physical Chemistry, Vol. 92, No. 3, I988
TABLE I: Coordinates of Unique Atoms,’ Radii, and a Values position Y
atom
X
out
0.0 0.0 -2.5789 -4.6501 -2.4249 -4.2489 0.0 0.0
Cu N1 H1 CI
01
N5 H5
0.0 0.0 2.5789 2.0587 5.0972 6.6275 6.1941 8.3296
2
radius
0.0 9.5217 0.0 2.5434 0.0 1.6000 0.0 0.9493 0.0 1.6000 0.0 1.6492 0.0 1.5985 0.0 0.9493
Norman’s radiusb
a value
9.4906 2.0747 1.6217 1.1993 1.4779 1.6181 1.5647 1.2004
0.74730 0.70697 0.75197 0.77725 0.75928 0.74447 0.75197 0.77725
nb
’The nonunique atoms are related to those listed above according to Figure 1. bThese radii obey Norman’s criteria” and were used in a separate computation for comparison purposes (see text).
210
280
290
300
Magnetlc
I H3
1
/ H2
\ 0 2
4, Figure 1. Molecular structure of the bis(biuretato)cuprate(II) dianion after Freeman et a1.I2
Solutions of the dipotassium bis(biuretato)cuprate(II) were prepared by mixing fresh cupric hydroxide and biuret in the molar ratio of 1:6. Potassium hydroxide was then added, with constant stirring, in the required concentration to yield a final solution of the appropriate pH. The total metal ion content in the copper and nickel solutions was determined electrogravimetrically. The ultraviolet and visible electronic absorption spectra were measured by means of a standard Cary 17 double beam spectrometer. The basic EPR spectrometer and accompanying apparatus used have been described previously.’ The reference part of the spectrometer cavity contained a solid sample of diphenylpicrylhydrazyl free radicals. All EPR sample tubes were checked for any interfering paramagnetic species before use. The ground and excited state electronic structures of the bis(biuretato)cuprate(II) dianion were computed by utilizing the self-consistent field X a scattered wave (Xa-SW-SCF) method.8 The computer program used was a modified version of the program available from the quantum chemistry program e ~ c h a n g e . The ~ a values for the constituent atoms of the dianion were those determined by Schwartz.Io The sphere radii of the muffin tin potential were chosen to be the same as those used in planar aromatic molecules. These radii have previously yielded excellent one-electron properties for benzene, pyridine, pyrazole, pyrazine, and imidazole.” They are tabulated in Table I. The copper and ligating nitrogen spheres were chosen to overlap by 13.6%. A second set of sphere radii, also listed in Table I, was used for comparison. This second set gave inferior results as will be discussed later. The geometry used was that determined by Freeman et al.’* and is shown in Figure 1. A Watson sphere radius of 10.37 au carrying a +2.00 charge was used. In one additional computation the Watson sphere was removed. This was found to have almost (7) Hocking, M. B.; Mattar, S . M. J. Magn. Reson. 1982, 47, 187. (8) Johnson, K.; Smith, F. C., Jr. Phys. Rev. B Solid State 1972, 5, 831. (9)Cook, M.; Case, D. QCPE 465, Indiana University, Bloomington, IN 474n5 .
(IO) Schwartz, K. Phys. Rev. B: Solid State 1972, 5 , 2466. Schwartz, K. Theor. Chim. Acta 1974, 34, 225. (1 1) Case, D. A.; Cook, M.; Karplus, M. J . Chem. Phys. 1980, 73, 3294. (12) Freeman, H. C.; Smith, J. E. W. L.; Taylor, J. C. Acta Crystallogr. 1961, 14, 407
Field
310
320
330
340
350
(MllliTesla~
Figure 2. Experimental (-) and simulated ( - - - ) spectra of dipotassium bis(biuretato)cuprate(II). Insets b and d represent a 5-fold magnification of the low field parallel components of the spectra. The spin Hamiltonian parameters used to simulate the experimental spectra are given in Table 11.
no effect on the charge distribution of the one-electron molecular orbitals. The excited-state energies were determined by the Slater transition state method.I3 For the purpose of computing the one-electron properties a reallocation of the intersphere charge to its parental spheres was done by expanding the radial wave functions beyond the sphere boundaries. This method14yields new wave functions that describe the molecular properties with the same order of accuracy as the scattered wave approximation^.'^ In the X a S W computation the Is, 2s, 2p, 3s, and 3p copper orbitals and the 1s orbitals of the carbon, nitrogen, and oxygen were treated as nonfrozen cores. The molecular potential was expanded in terms of partial waves. These terms were truncated at I = 5 for the outer sphere, 1 = 2 for the copper, I = 1 for the nitrogen, carbon, and oxygen, and I = 0 for the hydrogen centers.
Results and Discussion The EPR spectra of copper(I1)-biuret complexes in alkaline solutions have been reported by Wiersema and Windle16 and mentioned by Piesach and B1umberg.l’ Tiwari et have studied a dilute solution of bis(biuretato)cuprate(II) at a pH of 12; however no low-temperature studies were carried out. These EPR spectra yield only the average effective spin Hamiltonian tensor components. They estimated the parallel and perpendicular g tensor components from the spectrum of a magnetically concentrated sample by the method of Kne~buh1.l~Such a spectrum offers no information about the copper hyperfine and nitrogen ligand hyperfine components of this complex. Further Udupa and IndiraZocarried out EPR studies on other biuret complexes with various countercations, but only the parallel and perpendicular components of the g tensor were reported. In order to correlate the electronic structure and bonding, most of the g, hyperfine, and ligand hyperfine tensor components must be determined from (13) Slater, J. C. The Self-Consistent Field f o r Molecules and Solids; McGraw-Hill: New York, 1974; Vol. 4. (14) Case, D. A,; Karplus, M. Chem. Phys. Letr. 1976, 39, 33. (15) Cook, M.; Karplus, M. J . Chem. Phys. 1980, 72, 7. (16) Wiersema, A. K.; Windle, J. J . J . Phys. Chem. 1964, 68, 2316. (17) Piesach, J.; Blumberg, W. E. Electron Spin Resonance of Metal Complexes; Yen, T. F.,Ed.; Plenum: New York, 1969. (18) Tiwari, J. S.; Sinha, S. C.; Ghosh, P. K. Technology (Sindri, India) 1969, 6, 105. (19) Kneubuhl, F. K. J . Chem. Phys. 1960, 33, 1074. (20) Udupa, M. R.; Indira, V. J . Indian Chem. SOC.1975, 52, 585. (21) A listing of the program MONOMER is available from the author upon request.
Bis(biuretato)cuprate(II) Dianion
TABLE 11: Computed and Experimental
The Journal of Physical Chemistry, Vol. 92, No. 3, 1988 609 g, Hyperfine, and Ligand-Hyperfine Tensors'
exptl
computed
2.045 2.045 2.167 2.090d
2.0422 2.0476 2.1431 2.0776
rotation angle
Norman's radii'
0.00 gxx gYY
gzz
0.00 2.0120 2.0132 2.0478 2.0243
0.00 72.443 72.443 473.021 198.126
0.00
-55.551 -57.224 -484.567 -196.447d -23 1.985
-7 3.648 -73.954 -319.993 - 155.860 -188.979 36.67
33.814 45.664 33.814 38.023
rotation angleb,'
38.74
42.724 57.234 44.056 48.004
67.300 50.396 51.763 56.487
8 1.68
78.29 2.126 1.992 -4.218 -1.122
0.421 -3.592 -7.960 -3.710 1.12
6.87
25.831 16.790 12.773 18.464
28.539 12.852 7.567 16.320
0.00
0.00
-0.502 0.097 -0.989 -0.5166
-0.858 -0.590 -1.530 -0.993
0.00
0.00
-0.468 0.881 -0.855 -0.147
-0.041 0.7 13 -1.207 -0.178
'Calculated hyperfine values in megahertz. The sign of these tensor components cannot be determined in the present EPR experiments. Determined from the *Counterclockwise rotation angle in the xy plane. Properties computed by using sphere radii obeying Norman's criteria." EPR spectra of the complex in the liquid phase. eDetermined from the relation Ai, = (Axx Ayy A,,)/3. /Theoretical value obtained from the net spin-density at the nucleus. #Experimental ligand hyperfine splittings not resolved. The line widths along the x , y , and z molecular axes are __ 28.001, 28.001; and 19.777 MHz, respectively.
+
the experimental spectra. Since the spectra of dipotassium bis(biuretato)cuprate(II) may be a function of various parameters such as concentration, solvent, and pH, the need for a suitable reference is necessary. The corresponding nickel complex has an effective magnetic moment of 0.2 M~~ and is indicative of an almost square-planar complex. Thus the similarity in structure between the copper and nickel complexes offers a magnetically dilute sample of the Cu(I1)-biuret complex with minimal perturbation from the host nickel complex. Precipitates, from aqueous alcoholic solutions, containing small amounts of dipotassium bis(biuretato)cuprate(II) and the corresponding nickel complex yielded homogeneously dispersed microcrystals in powder form that were suitable for EPR measurements. Figure 2 represents the solid-state powder EPR spectrum at 298 K of dipotassium bis(biuretato)cuprate(II) diluted in the molar ratio of 1:200. This spectrum is very similar to the spectra of copper(I1) porphyrins and copper(I1) phthalocyanins which possess four nitrogen atoms in their equatorial plane. These complexes are also characterized by their large nitrogen Fermi contact interaction leading to observable nitrogen ligand hyperfine structure. As expected for Cu(I1) complexes of DZhsymmetry, the hyperfine tensor A is almost axially anisotropic. The A,,(Cu) component is larger than the perpendicular ones and the resonances along g,, are expected to be resolved. However the part of the spectrum around the g, and gyycomponents does not clearly represent the total theoretical number of splittings anticipated. This is because the magnitudes of the nitrogen hyperfine tensor components A(N) are about half the copper hyperfine components Axx(Cu)or Ay,,(Cu).The lines from these splittings overlap giving apparently fewer lines than the expected 36. As a result of this complication,
+
the determination of the experimental spin Hamiltonian parameters is possible only by computer simulation of the experimental spectrum. The simulated spectrum in Figure 2c is very close to the experimental one both in the position and the intensity of every transition. The "goodness" of the fit was measured by overlaying the simulated and experimental spectra and checking for both intensity and resonance field position. The effective spin Hamiltonian tensor components, determined by simulation, are listed in Table 11. The total simulated spectrum is a sum of the two spectra from the 63Cu and 65Cucomplexes. Although the Cu quadrupole tensor component, Qzz, for the main transition (AM, = r l , AmI = 0, Qzz N 3.0 X cm-') had to be considered in the simulation, it was not large enough to warrant the inclusion ) of higher order transitions ( A M , = 0, AmI = 7 1 , ~ 2 which become allowed in the presence of strong quadrupolar interactions.22 The good agreement between the experimental spectrum and theoretical simulation shown in Figure 2 enables the assessment of some of the conventions used in the interpretation of this class of ~ p e c t r a . ~The , ~ ~copper . ~ porphyrins, phthalocyanins, and biuret complexes are characterized by a set of strong "anomalous" lines at the high field end of their ~ p e c t r a .In ~ Figure 2 these lines occur around 340-350 mT. Figure 3 represents the resonance field (22) De Bolfo, J. A,; Smith, T. D.; Boas, J. F.; Pilbrow, J. R. J . Chem. SOC.,Faraday Trans. 2 1976, 481. (23) Wertz, J. E.; Bolton, J. R. Electron Spin Resonance; McGraw-Hill: New York, 1972; pp 156-157. (24) Mattar, S. M. Ph.D. Thesis, McGill University, 1982; Chapter 11.
15
I
/
0.2 -
I
‘
-
n
5
Q4-
a
Mattar
610 The Journal of Physical Chemistry, Vol. 92, No. 3, 1988
-
v)
0
0 0
0.6
-
.-
U
v)
c
4 -
a,
-5
.w
C
0.8
I
-
I I
I
294
Resonance
30 8
I
I
32 2
Field P o s i t i o n s , B , MiIliTe sla
ll
1
-15
336
in
Figure 3. Behavior of the four copper hyperfine resonance field positions as a function of cos 8.
positions, B(8), as a function of cos 8 for the simulated spectrum of the biuretato complex. The angle, 8, is the angle formed between the molecular z axis and the external applied field, B. The first 65Cuhyperfine curve, labeled “l”, is the most anisotropic followed by “2” while curves “3” and “4” have comparable and smaller anisotropies. If the resonances are assumed to have zero line widths, then the first three curves span common values of B(8). The dashed vertical line indicates that “4”does not have common B(8) values with the rest and stands out alone. Curve 4 represents the only Cu hyperfine resonance occurring in the region of 330-350 mT and is clearly responsible for the so-called “anomalous” lines. Figure 3 also shows that the closest approach between curves 3 and 4 occurs at 8 N 85’ (cos 0 = 0.09). This indicates that, due to the finite line widths of the spectrum, some overlap occurs in the perpendicular region. The overall spectral line shapes in the absence of nitrogen hyperfine splittings for the four individual lines are shown in Figure 4. They confirm that the overlap between the third and fourth copper hyperfine resonances occurs in the perpendicular region around 331 mT. A similar analysis of the third and fourth copper hyperfine lines by computer simulation, using the existing values for the effective spin Hamiltonian tensor^^^-^^ reveals that the same situation occurs for a variety of copper porphyrins and phthalocyanins at X-band frequencies. Generally for axial EPR spectra the parallel components resemble an absorption curve, while the perpendicular components resemble a derivative This is not always true for the bis(biuretato)cuprate(II) dianion. Figure 4 indicates that the fourth parallel hyperfine line resembles a distorted derivative curve while the perpendicular component resembles an absorption curve. Due to its reverse line shape behavior, the fourth perpendicular component may be mistaken for the fourth parallel component. Thus the spectral line shapes should not be related to a particular spatial component (parallel or perpendicular); rather the safest procedure is to correlate the spectral line shape with the anisotropy of the resonance field positions, B, as a function of 8 as shown in Figures 3 and 4. The dipotassium bis(biuretato)cuprate(II) single crystal belongs to the b 2 h space group.12 However, each individual molecule is considered to possess D2h symmetry. In addition the four amide (25) De Bolfo, J. A.; Smith, T. D.; Boas, J. F.; Pilbrow, J. R. J. Chem. SOC.,Dalton Trans. 1973, 1549.
(26) Manoharan, P. T.; Rogers, M. T. Electron Spin Resonance of Metal Complexes; Yen, T. F., Ed.; Plenum: New York, 1969; p 143. (27) Guzy, C . M.; Raynor, J. B.; Symons, M. C. R. J. Chem. SOC.A, 1969, 2299. (28) Lau, P. W.; Lin, W. C. J. Inorg. Nucl. Chem. 1975, 37, 2389. (29) Brown, T. G.; Hoffman, B. M. Mol. Phys. 1980, 39, 1073.
V
-25
II
I
1
I
1
I
I
Figure 5. Three-dimensional plot of the 8b,, one-electron molecular orbital in the xy plane.
nitrogen atoms surrounding the Cu atom form an almost perfect square. For D2h symmetry there is no mixing of the in-plane bonding represented by the blg, b3u, ag, and b2u orbitals and out-of-plane bonding orbitals (au, b2g,b3g,and blu). A spin-restricted computation was used to determine the molecular g tensors. However, for the determination of the Cu and ligand hyperfine tensor components, spin polarized computations were performed. The spin-polarized technique offers an easy way to determine core polarization effects that are important in the determination of the Fermi contact terms of the hyperfine tensors. In both types of computations the complex is found to have a 2Blg ground state with its singly occupied molecular orbital (SOMO) being the 8b1, one-electron molecular orbital. The three-dimensional plot in the xy plane for this spin-restricted molecular orbital is shown in Figure 5. The spin-restricted
Bis(biuretato)cuprate(II) Dianion
The Journal of Physical Chemistry, Vol. 92, No. 3, 1988 611 proximately equal to the energy between the bonding and antibonding forms of the p,(C)-p,(N') bond. The 8a, and 9a, orbitals are 95.54% and 90.87% copper in character. In both orbitals the electrons are shared almost equally -among the 3d+y(Cu) and 3d22(Cu)atomic orbitals. Because the 3d,~~z(Cu) orbital does not share its spin density with the ligating nitrogen 2p, and 2py orbitals, this indicates that the Cu-N in-plane a-type bonding must be very weak. Additional in-plane a-type bonding might also occur to a minor extent via back donation from the ligating nitrogen atoms to the empty 4p,(Cu) and 4py(Cu) components of the b2, and b3, orbitals.
l
-3
-5
Molecular g Tensor Components and Their Relation to Bonding To a first approximation, the g tensor components are given by
-7
gij =
-9
geaij
eV
- 2CCC(BIgIX(k)li(k)In) (nIlj(k?IBlg)/[E(B,g) k k' n
- E(n)I (1)
-1 1
-1 3
-15
----..lag
-l7
-19
Figure 6. Molecular orbital energy diagram for the bis(biuretat0)cuprate(I1) dianion. The one-electron orbitals of a,, blurbZg,and b3g symmetry represent the out-of-plane ?r-type bonding while the b,,, b,,, ag,and blu orbitals represent the a-type bonding. Molecular orbitals that are mainly 3d(Cu) are labeled separately.
ground-state molecular orbital energy diagram is represented in Figure 6. In accordance with ligand field theory these figures indicate that the SOMO, on the whole, is antibonding with respect to the copper and ligating nitrogen atoms. This plot, in conjunction with the computed electronic charge density distribution, reveals that the 8b,, has only 57.3% Cu character, is covalent, and is extensively delocalized. In addition, it is bonding with respect to the s(H)-s(N), S(H)-P," Py(N)-Py(C), Py(C)-P," and p,(C)-p,(N') atomic orbitals. The ligand orbitals are mainly p in character with little s contribution. The interaction of the p atomic orbitals of the ligands favor in-plane "a-type" bonding for the 8b1, one-electron molecular orbital. The one-electron orbitals of a,, blu, b2,, and b3, symmetry represent the out-of-plane a-type bonding. Because the hydrogen atoms only have occupied s atomic orbitals, it is assumed that they are not involved in the out-of-plane a-type bonding. Except for the a, representation, all the other orbitals represent the interaction of the ligand p, with the Cu atomic orbitals. The occupied la, and 2a, orbitals represent the bonding and antibonding combinations of the p,(C)-p,(O) bond. The energy difference between these bonding-antibonding combinations is -3.68 eV, indicating a strong T interaction. The lbl, and lb3, are the lowest in energy, are mainly N S and N 6 in character, and represent the bonding combinations of all the ligand p, orbitals. The 1b3, is slightly lower in energy than the 1bl, because the 3dy,(Cu) orbital is closer in energy to the ligand *-type orbitals as compared with the 4p,(Cu) atomic orbital. The 3d,,,(Cu) orbital interaction results in a molecular orbital with stronger bonding characteristics. The energy difference between the lbl, and 2blu is -3.99 eV, ap-
where the summation indexes k and k'extend over all atoms and n extends over all excited states except those of B,, symmetry.3b32 If a spin-restricted formalism is used to determine g tensor components, then the one-electron SALC orbitals may be used to determine the expressions for gi,. The detailed expressions for the one-electron SALC orbitals and the resulting equations for the gij tensor components are available as supplementary material. By use of these equations, it is found that the contribution to the g,, anisotropy arises mainly from the coupling of two B2, excited states with the 2B,, ground state. These two states, 12B2, and 22B2g,arise from the excitation of an electron from the 3b2, and 2b2, to the 8b1,, respectively. Although the 2b2, orbital is 79.6% d,(Cu), the close proximity of the 3b2, [11.7% d,,(Cu)] to the 8b1, orbital causes the 12Bzg, state to contribute significantly to the g, anisotropy. A similar situation exists for the gyytensor component. The two main states contributing to the anisotropy are the 12B3,and 32B3,. These result from the excitation of a single electron from the 4b3, and 2b3, to the SOMO. Due to DZhsymmetry of this anion, the g,, and gyycomponents should be different. However, from the almost square-planar arrangement of the ligating nitrogen atoms around the copper ion, this difference is expected to be small. The difference between the g, and gyy tensor components is computed to be 0.0054. At X-band frequencies the resonances around the g,, and gyy will differ by approximately 16.0 MHz. This is slightly less than the spectral line widths and the resonances along these two principal axes will be difficult to resolve. Consequently, the solid-state spectrum is predicted to have an almost axial appearance as is experimentally observed. In addition, the average value of the g,, and gyy components is 2.0449. This is in excellent agreement with the experimental value of 2.045 found by simulation. The contribution of the carbon, nitrogen, and oxygen ligand atoms to all the g tensor components was 2 orders of magnitude less than that of the copper. The g,, component is computed to be 2.143 as compared with the experimental value of 2.167. This g,, deviation is of comparable magnitude to that found for Cu(I1)complexes using the DVM-Xa method.32 The g,, anisotropy stems from the spin-orbit coupling of the 12B1, state with the n2Ag excited states. The excitation of an electron from the loa, orbital to the 8b1, leads to the lowest A, excited state. However, the loa, orbital is mainly p,(O) and py(0) in character with only 0.398% 3d+y2(Cu). In a spin-restricted formalism, this contributes an insignificant amount to the g,, tensor anisotropy. The main deviation of g,, from g, comes from the coupling of the 8a, and 9a, one-electron orbitals to the 8b1,. These orbitals have 49.71% and 41.84% (30) Mattar, S . M.; Ozin, G. A. J . Phys. Chem. 1986, 90, 1355. ( 3 1 ) Keijzers, C. P.; De Boer, E. J. J . Chem. Phys. 1972, 57, 1277. ( 3 2 ) Geurts, P. J. M.; Bouten, P. C. P.; van der Avoird, A. J. Chem. Phys. 1980, 73, 1306.
612
The Journal of Physical Chemistry, Vol. 92, No. 3, 1988
3dX2-,,2(Cu)character, respectively. An increase of the copper sphere radius in comparison to the radii of other centers would increase g,, to the corresponding experimental value. This procedure, however, would overestimate the g,, and gYucomponents and predict inappropriate values for the copper and nitrogen ligand hyperfine tensors. A larger copper radius would also increase the deviation of the virial ratio from the value of 2.0.*-13 In addition, the hyperfine tensors are determined from a spin-unrestricted computation while the g tensors are computed from a spin-restricted one. Thus, it is reasonable to choose the sphere radii that yield better correlation between theory and experiment for the hyperfine tensors. A spin-unrestricted formalism, in conjunction with spin projection and correlation techniques, might ultimately lead to a g,, value closer to the experimental one. Ligand and Copper Hyperfine Tensor Components For a molecule of DZhsymmetry, only the atomic center situated on the center of inversion will have the principal axes of its diagonal hyperfine tensor parallel to the g tensor axes. All other centers will generally have nondiagonal tensor components. The carbon, nitrogen, and hydrogen hyperfine tensors have been diagonalized. The angle of rotation of the principal axes for each tensor is listed in Table 11. The hyperfine tensors of the set of four hydrogen atoms (Hl, H2, H3, and H4) denoted by H are related to one another by rotations of 2 a along the molecular x and y axes. The principal tensor axes of these centers are almost coincident with the molecular axes of the molecule shown in Figure l , Table I1 represents the isotropic and anisotropic parts of the overall tensor components. These indicate that the net H hyperfine splitting is due to the transfer of a spin density via the N-H a-type bond. The components of this tensor are slightly less than the line widths of the EPR spectrum and are thus not resolved. The two H' atoms (H5 and H6) have a very small isotropic splitting of 0.15 MHz while the anisotropic components are of the same magnitude. Consequently these two hydrogen centers do not affect the shape of the EPR spectrum to any significant extent. A similar situation exists for the four I3C centers. The I3C interactions only broaden the EPR spectral line shapes and cause no observable splittings. The computed anisotropic hyperfine tensor components of the four ligating nitrogen atoms (N,, N2, N3, and N4)denoted by N are in excellent agreement with experiment. However, the computation overestimates the isotropic tensor component by 20.79%. The nitrogen hyperfine tensors are mainly isotropic with the anisotropic dipolar interactions being approximately 1 order of magnitude less than the Fermi contact interaction. The counterclockwise rotation angle of these tensors and their diagonal components indicate that the anisotropic components are almost aligned with the u-type Cu-N bonds. The most complicated hyperfine components are due to the central copper atom. In this case there exist isotropic components from core polarizations, and anisotropic ground-state dipolar interactions. In addition the anisotropic contributions from spin-orbit c o ~ p l i n gcannot ~ ~ , ~be ~ neglected. The isotropic Fermi contact term is due to a negative spin density at the Cu nucleus. This is computed to be of opposite sign and almost equal in magnitude to the anisotropic dipolar A,,(Cu) and Ayy(Cu)components. Thus, the total A,(Cu) and A,(Cu) are greatly dependent on the spin-orbit coupling terms. When these extra terms are included, the computed A,(Cu) and AJCu) components are approximately 21 .O-23.3% smaller than their experimental counterparts. The A,,(Cu) component is, on the other hand, in excellent agreement with the experimental value. In spite of the underestimation of the A,,(Cu) and A,(Cu) components, the Xa-SW technique predicts negative values for all the copper hyperfine components as is the case for copper(I1) porphyrin^^^,^^ and phthalo~yanins.~' (33) Case, D. A,; Karplus, M. J . Am. Chem. SOC.1977,99,6182. Sontum, S. F.: Case, D. A J Phys. Chem. 1982, 86, 1596.
Mattar 325 mT
Figure 7. EPR spectrum (298 K) of dipotassium bis(biuretat0)cuprate(11) in alkaline solution (pH 13.6).
The ambient temperature EPR spectrum of a 5.0 X M solution containing Cu-biuret-potassium hydroxide in the ratio 1:6:12 is shown in Figure 7. The spectrum is characteristic of a rapidly tumbling Cu(I1) complex in solution. It arises from a resonance centered around (g) = 2.090 which is further split by 198.126 MHz into four copper hyperfine lines (Icu = 3/2) from two copper isotopes. Each of the hyperfine lines should be split by 38.0 MHz into nine lines of intensity ratios 1:4:6:10:19:10:6:4:1, due to four nitrogen nuclei in the equatorial plane (IN= 1). Figure 7 shows that the Cu line at the highest field has only seven well-resolved nitrogen superhyperfine lines, the next highest has five, the next four, and the last none. The appearance of only seven lines at the highest field transition is the result of the outermost nitrogen superhyperfine lines being lost in the envelope of those of higher intensity.34 The loss of resolution with decreasing field is attributable to the dependence of the line widths on the Cu nuclear magnetic quantum number mI. The extent of variation of the line width as a function of m Idepends on the rate of tumbling of the molecule in solution, its microviscosity and anisotropy of its g and A tensor component^.^^.^^ The average g value is related to the diagonal tensor components, determined by simulation of the EPR spectra in the solid state, by the approximate relation The (g) = 2.0857 obtained from this equation is slightly different from that calculated from the liquid solution spectrum in Table 11. This is possibly due to the different host environments in the liquid and solid states. Table I1 lists the isotropic hyperfine parameters determined from experiment and computed by the Xa-SW method. Although from the present experiments one cannot determine the sign of the isotropic hyperfine coupling constants, the 65Cu and 63Cu parameters are computed to be negative while those for the ligating nitrogens are positive. Electronic Absorption Spectra The electronic spectra for the bis(biuretato)cuprate(II) dianion has been measured in the ultraviolet and visible regions. In the solid state, McLellan and Melson6 observed two broad bands centered around 20000 and 35 800 cm-'. In an alkaline solution (pH 13.6), depending on the nature of the solvent used, we determined three absorption bands in the range of 19840-20200, 29000-31280, and 35800-36000 cm-'. The energies of these bands are very similar to those found by Tiwari et al.'* The absorption bands together with those predicted by the Xa-SW method are given in Table 111. Due to the extensive delocalization of the 8b,, orbital, one cannot strictly classify the bands as d-d or charge-transfer transitions. Thus the labels in Table I11 are only of qualitative significance. (34) Roberts, E. M.; Koski, W. S. J . Am. Chem. SOC.1960, 82, 3006. (35) Kivelson, D. J . Chem. Phys. 1960, 33, 1094. (36) Wilson, R.; Kivelson, D. J . Chem. Phys. 1966, 44, 4440. (37) Norman, J. G., Jr. Mol. Phys 1976, 31, 1191.
Bis(biuretato)cuprate(II) Dianion
The Journal of Physical Chemistry, Vol. 92, No. 3, 1988 613
density on the copper atom. This results in smaller molecular g tensor components as compared with experiment and may be transition Xa-SWb type polarization exptlb rationalized as follows. The deviation of the g tensor components la, 8b,, 47965 LMCT z from the corresponding value of the free electron is directly 47 828 LMCT X 7b2, 8bl, proportional to the spin-orbit coupling constant and charge dis40962 LMCT Y 6b3, 8b,, tribution of the 8bl, orbital as shown in eq 1. The copper center 35800-36000 has the largest spin-orbit coupling constant as compared with 3b2, 4b1, 34 230 K-K* X nitrogen, carbon, and oxygen. Thus a decrease in the copper K-K* Y 4b3, 4b,, 33141 character in the 8bl, orbital will decrease the molecular g tensor 29000-31280 components. The magnetic parameters determined by using sphere 30617 d-d forbidden 2b3,-8b,, 29813 d-d forbidden radii obeying Norman's criteria are listed in Table 11. Although 2b2,- 8bl, 27226 d-d forbidden 8a,- 8b,, the A,,(Cu) and AJCu) are close to the experimental values, 26 955 LMCT X 8b2, 8b1, the A,,(Cu) component is underestimated by 32%. In addition, 9a,- 8b,, 25739 d-d forbidden A,(N) hyperfine tensor component is overestimated by 99%. This 23 994 LMCT Y 7b3, 8b1, is a direct consequence of the increased nitrogen sphere volumes. 19840-20200 From these results it is felt that the use of Norman's criteria tends 3b3, 8b1, 16729 forbidden to yield inferior results as compared with the previous computa2a,- 8b,, 16629 LMCT Z tions. 3b2, -+ 8b1, 8 164 forbidden In an attempt to improve the results using Norman's criteria, 8blg 7 076 forbidden 4b3g the effect of the Watson sphere, carrying a charge of 2.0+, on "Computed by the Slater transition state method.I3 bEnergy units in the electronic structure and the g tensor components was invescm-' . tigated. A computation without the Watson sphere resulted in the uniform destabilization of all the one-electron molecular orMcLellan and Melson have pointed out that a strong absorption bitals without any appreciable change in their charge distribution. band around 35 800 cm-' was found to occur for a variety of For example, the 8bl, SOMO was found to be 39.07% d,(Cu) metal-biuretato complexes and they assigned it to a ligand-ligand using a Watson sphere. This metal d character increased only absorption. The lowest computed ligand-ligand transitions are to 39.57% upon removal of the that sphere. When the transition mainly T-X* in character due to the excitation of an electron from state energy differences between the 8bl, and the relevant a,, b2,, the 3bZ, and 4b3, orbitals to the virtual 4b,, orbital. These and b3, orbitals in conjunction with the excited state charge transitions are allowed and induced by x and y polarized light, distributions were substituted in eq 1, no improvement in the g respectively. They are predicted to lie around 33 141 and 34230 tensor components was found. The g,, component decreased in cm-I and are assigned to the 35800-36000-cm-' band. Strictly value from 2.0845 to 2.0478. These results confirm that there speaking these transitions will be mixed with other configurations is a need for a more reliable, nonempirical, method to calculate 4b2,! 2a, 5b3,, and 3b1, 4bzn. However, of the form 2a, and partition the charge distribution of the ground and excited these extra configurations are the minor components and only states when using the muffin tin a p p r ~ x i m a t i o n .Until ~ ~ such a increase the transition energies slightly. g tensors must be interpreted in method is found, the computed The second broad absorption band lies in the region of a semiquantitative fashion only. 29000-31280 cm-l. The computed transitions that lie nearest to Solomon et al.39have encountered similar trends in the comthis band occur from 25 739 to 30617 cm-' as shown in Table puted EPR properties of copper complexes and attributed them 111. The 2b3,, 2b2,, Sa,, and 9a, orbitals are all mainly d(Cu) to the overestimation of delocalization by the Xa-SW formalism. in character. Consequently the transition of an electron from these However, they readjusted the charge distribution between the orbitals to the 8bl, orbital may be loosely termed d-d type or copper and ligands by means of a semiempirical parameter which "ligand-field" transitions. These four transitions are high in energy as compared to d-d type transitions for other Cu c o m p l e x e ~ . ~ ~ gave results that are in good agreement with experiment. This indicates that the bis(biuretat0)cuprate undergoes strong Conclusions ?r-type and in-plane a-type bonding between the copper and liThe Xa-SW is found to be a practical method to compute the gating nitrogen centers. In addition each of the Sa, and 9a, have almost equal contributions from the 3dz2(Cu) and 3 d X ~ - y ~ ( C ~ ) electronic structure of the bis(biuretat0)cuprate dianion. For a good correlation between the experimental and computed magnetic reflecting the extensive mixing of these atomic orbitals in this resonance parameters of this complex, all the components of the representation. The remaining x-polarized transition occurs copper hyperfine, ligating nitrogen hyperfine, and g tensors as well around 26955 cm-I. Since the 8b2, orbital involved in this as the relative orientation of their principal axes must be detertransition is mainly 2py(0) in character, this transition may be mined. This was accomplished by the computer simulation of its classified as a ligand to metal charge transfer transition. EPR spectra. The metal and ligand hyperfine tensor components The best candidates for the 19840-20200 cm-I band are the agree within 20% with those computed by this technique. The 8bl,, 3b3,.Sb,,, and 2a, 8bl, transitions. The 2a, 7b3, analytical expressions for the g tensor components are derived in and 3b3, orbitals are mainly composed of pz orbitals on the nitrogen terms of molecular orbital coefficients by using second-order atoms while the 7b3, orbital is mainly 2py(0). Thus, irrespective perturbation theory. The agreement between the theoretical and of being allowed or forbidden, they may be generally classified experimental g,, and gyycomponents is excellent. The g,, comas ligand-to-metal charge transfer transitions. ponent is slightly underestimated. A new, totally theoretical method to determine the sphere radii and express the spin and Relation between the Sphere Radii and Computed Properties charge density distributions in terms of the familiar Mulliken type A popular way of choosing sphere radii when constructing the population analysis is needed. This would greatly facilitate the muffin tin potential is according to a certain set of rules known determination of the g tensor components from a spin-polarized as Norman's rite ria.^' Since different sphere sizes of the muffin nonrelativistic computation. Until such a technique is developed, tin potential can lead to different results, an extra set of comthe g tensor components should be interpreted only semiquantiputations for this complex were performed with sphere sizes chosen tatively. according to these criteria. These sphere radii are also listed in From the level of agreement of the magnetic and optical Table I. In this case it is necessary to assign the copper center properties, a realistic molecular orbital picture for the structure a smaller sphere radius which, in turn, leads to a reduced charge and bonding for this dianion energies. The bis(biuretat0)TABLE 111: Spin-Restricted Electronic Excitation Energies"
-+
+
-
-
-
-
-
-
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(38) Tomlinson, A. A. G.; Hathaway, B. J.; Billing, D. E.; Nichols, P. J . Chem. Sac. A 1969, 6544. Hathaway, B. J.; Billing, D. E.; Nichols, P.; Proctor, I . M. J . Chem. Sac. A 1969, 319.
(39) Penfield, K. W.; Gewirth, A.; Solomon, E. J . Am. Chem. Sac. 1985, 107,4519.
J . Phys. Chem. 1988, 92,614-620
614
cuprate(I1) is found to have strong b,, (u-type) bonding between the copper and four ligating nitrogen atoms. The b2, and b3, out-of-plane (a-type) bonding is also strong not only for Cu-N bonds but between the biuretato ligand components as well. The in-plane a-type Cu-N bonding is found to be very weak. It manifests itself only through the interaction of the 3dX2-,,2(Cu), 4px(Cu), and 4pJCu) with the 2p,(N) and 2pJN) components of the alg, b3,, and b2" molecular orbitals. In order to judge if the Xa-SW can generally predict the electronic structure and bonding of charged transition-metal complexes, more computations of the type presented above must be performed and compared with experiment. Only then would one know what molecular properties are best predicted by this technique.
Acknowledgment. The author wishes to express his gratitude to Professor William C. Galley for his encouraging interest and valuable discussions. Financial assistance from La Direction General de L'enseignment Superieur du Quebec and the allocation of computer time by the Chemistry Department, University of Toronto, for some of the computations is acknowledged. Registry No. Bis(biuretato)cuprate(II) dianion, 61771-68-4.
Supplementary Material Available: Table of symmetry adapted one-electron orbitals for the bis(biuretato)cuprate(II) dianion and 10 equations for the molecular g tensor components in terms of molecular orbital coefficients (7 pages). Ordering information is given on any current masthead page.
Theoretical Investigation of Several Low-Lying States of trans ,trans-l,3,5Hexatriene Robert J. Cave and Ernest R. Davidson* Department of Chemistry, Indiana University, Bloomington, Indiana 47405 (Received: June 15, 1987)
Results from ab initio calculations concerning several low-lying electronic states of trans,trans-1,3,5-hexatrieneare presented and compared with experimental and previous theoretical results. The lowest excited singlet state is predicted to be the 'B, state, having essentially valencelike T a * character. The nominally doubly excited 2]A, state is found to lie approximately 0.6-0.9 eV above the 1'B, state. Results are also presented for several Rydberg states. The implications of the present results for current parametrizations of semiempirical T molecular orbital schemes are discussed.
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I. Introduction The spectroscopy of linear polyenes has been an area of intense interest for both experimentalists and theoreticians.] The study of such molecules is important to the understanding of the visual pigments2 and has also been a testing ground for theoretical models of the electronic structure of r-electron systems.'fq4 One example of the interplay between experiment and semiempirical theory in this area was the d i ~ c o v e r ythat ' ~ ~ in ~ ~longer polyenes the excited singlet state observed in fluorescence is not the ?r a * state of molecular orbital theory but is instead a state that can be described as doubly excited relative to the ground state. The understanding of this via the use of semiempirical molecular orbital and valence bond t h e o r i e ~has ~ , ~led to further consideration of the importance of electron-electron repulsions in the determination of the nature of the excited states of such compounds.' Ab initio electronic structure techniques have been applied to several of the shorter chain polyenes.*-" In the case of ethylene,*-1° a significant effort went into the description of the lowest a ?r* state. There, experimental evidence along with semiempirical molecular orbital calculations seemed to suggest a purely valencelike state. The present description based on accurate ab initio results seems to argue for a more diffuse lB,, state and for significant nonvertical excitation contributions to the spectral intensity.*-I0 Butadiene has a similar history, and only recently have ab initio methods been able to find a predominantly valencelike state near the experimentally observed intensity maximum.14 H e ~ a t r i e n e ' has ~ , ~received ~ less attention, doubtless due to the increased size of the computations and the limited success of CI results in the description of the shorter chain species. The size of the longer chain species (decapentaene, dodecahexaene) most likely prohibits application of adequate ab initio methods to the quantitative investigation of their spectroscopy in the near future, but detailed theoretical investigations of the spectroscopy of the shorter chain species can still be helpful to both experimentalist and theoretician. For example, studies of the va-
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*Author to whom correspondence should be addressed.
0022-3654/88/2092-0614$01.50/0
lence-Rydberg mixing in such species could be used for the development of more accurate semiempirical schemes. In another vein, the location of the doubly excited state (that is, the analogue of the lowest excited singlet in the long chain species) relative to the T T* excited state is still an open question for the short chain species. The development of accurate ab initio treatments for such systems may help to answer this question. In addition, the positions of the various Rydberg transitions are still very much in question for hexatriene, and a b initio results may be useful in this regard also, since current semiempirical methods are limited to the treatment of valence states. With these questions in mind, we have undertaken an investigation of the low-lying electronic states of trans,trans-1,3,5hexatriene by using ab initio C1 wave functions. The methods employed are similar to those used in our previous study of butadieneI4 and give results that are significantly different than past
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(1) Hudson, B. S.; Kohler, B. E.; Schulten, K. In Excited States; Lim, E. C., Ed.; Academic: New York, 1982, Vol. VI, p 1. (2) Biological Events Probed By Ultrafast Laser Spectroscopy; Alfano, R. R., Ed.; Academic: New York, 1982; Chapters 9-13. (3) Mulliken, R. S . J . Chem. Phys. 1939, 7 , 364. (4) Schulten, K.; Karplus, M. Chem. Phys. Lett. 1972, 14, 305. (5) Hudson, B. S.;Kohler, B. E. Chem. Phys. Lett. 1972, 14, 299. (6) Tavan, P.; Schulten, K. J . Chem. Phys. 1979, 70, 5407. (7) Schulten, K.; Ohmine, I.; Karplus, M. J . Chem. Phys. 1976, 64, 4422. (8) McMurchie, L. E.;Davidson, E. R. J . Chem. Phys. 1977, 66, 2959. ( 9 ) Brooks, B. R.; Schaefer, H. F., 111 J . Chem. Phys. 1978, 68, 4839. (10) Buenker, R. J.; Shih, S.-K.; Peyerimhoff, S . D. Chem. Phys. 1979,
36, 97. (11) Hosteney, R. P.; Dunning, T. H., Jr.; Gilman, R. R.; Pipano, A,; Shavitt, I. J . Chem. Phys. 1975, 62, 4764. (12) Buenker, R. J.; Shih, S.; Peyerimhoff, S . D. Chem. Phys. Lett. 1976, 44, 385. (13) Nascimento, M. A. C.; Goddard, W. A,, I11 Chem. Phys. 1979, 36, 147. (14) Cave, R. J.; Davidson, E. R. J . Phys. Chem. 1987, 91, 4481. (15) (a) Nascimento, M.A. C.; Goddard, W. A,, 111 Chem. Phys. Lett. 1979.60, 197. (b) Nascimento, M. A. C.; Goddard, W. A,, 111 Chem. Phys. 1980, 53, 265.
0 1988 American Chemical Society
