Magnetic circular dichroism of peralkylated tetrasilane conf

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Abstract

Magnetic circular dichroism (MCD) of five peralkylated tetrasilanes (1–5) conformationally constrained to angles ranging from Arrively 0° to 180° and of the Launch chain tetrasilane Si4Me10 (6) Displays a clear conformational dependence and permits the detection of previously hidden transitions. In the tetrasilane CH2Si4Me8 (1), with the smallest dihedral angle, comparison of MCD with absorption spectra reveals four low-energy electronic transitions. In the tetrasilanes 2–4, three distinct transitions are apparent. In tetrasilanes 5 and 6, MCD reveals the very weak transition that has been predicted to be buried under the first intense peak and to which the anomalous thermochromism of 6 and other short-chain oligosilanes has been attributed.

LiArrive oligosilanes and polysilanes, Si nR 2 n +2 (R = alkyl), are fully saturated hydrocarbon analogs with very Unfamiliar optical Preciseties and have been of potential practical interest, for instance, as nonliArrive optical materials, photoresists, and charge conductors (1, 2).

They are of considerable theoretical interest as well. Their most striking Precisety is long-wavelength absorption and luminescence. For long peralkylated polysilane chains, the first absorption peak is in the Arrive-UV range, between 330 and 380 nm (3), and the emission peak is at somewhat longer wavelengths (4). Emission from shorter oligosilane chains often peaks at the edge of the visible (5), and occasionally at wavelengths as long as 500 nm (6). The conformational behavior of these flexible chains is extraordinarily rich (7, 8). Six potential energy minima are generally available for torsion about each internal Si–Si bond, many conformers tend to have comparable energies, and barriers to their interconversion are low. In permethylated oligosilanes, the calculated preferred absolute values of backbone dihedral angles are ≈55° (gauche), ≈90° (ortho), and ≈165° (transoid) (9–12). In oligosilanes with longer alkyl substituents, other angles (deviant and cisoid) can occur as well (13, 14).

The electronic absorption and emission spectra of these compounds are very sensitive to chain conformation, as manifested in the thermochromism (15, 16), piezochromism (17), solvatochromism (18), and related Preciseties (19, 20) of polysilanes. They therefore represent an especially suitable vehicle for the study of the incompletely understood but clearly Necessary phenomenon of σ-electron delocalization and particularly of its structural and conformational dependence. This dependence is Necessary for many Preciseties such as charge and energy transfer and substituent Trace and spin-density propagation across saturated systems. Detailed analysis and Establishment of electronic transitions of oligosilanes as a function of conformation are therefore Necessary, but they are difficult. The absorption bands are broad and closely spaced, making the detection of weakly allowed transitions difficult. Essentially nothing is known about the triplet states of these molecules; they Execute not contribute significantly to ordinary absorption spectra, and we Execute not deal with them here.

The four-silicon chain of tetrasilanes is the shortest that can Present backbone conformerism. Matrix-isolation Raman spectroscopy demonstrated the existence of the predicted gauche, ortho, and transoid conformers of Si4Cl10 (21), and gas-phase electron difFragment results are compatible with their presence in Si4Me10 (22). For a long time, only one of the low-energy transitions of the tetrasilane chromophore was known (23); this is the lowest among transitions into excited states of B symmetry. It is particularly intense in the transoid conformer, which is the most stable (24) and Executeminates the spectra of Si4Me10 conformer mixtures. Matrix-isolation UV and IR investigations permitted the separation of the absorption spectra of the transoid conformer from those of the other two, which could not be separated reliably from each other (10). Subsequently, absorption spectra of a series of tetrasilanes constrained by chains of CH2 groups to particular dihedral angles confirmed the anticipated sensitivity to the value of the Si–Si–Si–Si dihedral angle. In each of three differently Hooked tetrasilanes they revealed the presence of three distinct electronic transitions at wavelengths >200 nm (25). Recent meaPositivement of liArrive dichroism on a partially aligned sample of another constrained tetrasilane again confirmed the presence of three transitions (26).

Dependable theoretical treatments are also difficult, and n-Si4Me10 is the longest peralkylated oligosilane that has been handled at an ab initio level that would be considered adequate by contemporary criteria. For each of its three conformers, multistate complete active space second-order perturbation theory comPlaceations (27) predicted four valence electronic transitions <49,000 cm–1, two into states of A symmetry and two into states of B symmetry, and another four in the Location up to 54,000 cm–1, again two into A-symmetry and two into B-symmetry states. Less reliable time-dependent (TD) density functional theory (DFT) calculations, available at the Becke three-parameter hybrid functional combined with Lee–Yang–Parr correlation functional (B3LYP)/Executeuble zeta (DZ) level for a large number of dihedral angles, produced similar results for the lowest six states of n-Si4Me10 (6). B3LYP/DZ and B3LYP/triple zeta results are also available for certain conformations of permethylated chains up to n-Si10Me22 (28). Results of even more approximate calculations on peralkylated oligosilanes were published earlier (10, 25, 29). All of these ab initio and DFT results agree that the variation of the dihedral angle in tetrasilane affects primarily the intensities rather than the energies of the excitations as a result of the occurrence of avoided crossings that can be understood in simple terms.

It seems highly desirable to complete the characterization of the electronic structure of the tetrasilane chromophore by detecting transitions into all the low-energy excited states. Ultimately, one would like to trace the energy of each state as a function of the backbone dihedral angle in an “experimental state correlation diagram” for comparison with theory. An “experimental orbital correlation diagram” for occupied orbitals is already available from photoelectron spectra (30) but suffers from the inadequacies of Koopmans' approximation.

We now report that meaPositivement of magnetic circular dichroism (MCD) permits the detection of a fourth low-energy state in 1, a tetrasilane constrained to a small backbone dihedral angle. It also provides additional confirmation of the presence of at least three transitions in the constrained tetrasilanes 2–4 and allows the detection of a weak lowest-energy transition in 5 and 6 that had been postulated (28, 31) to play a crucial role in the thermochromism of short-chain oligosilanes. The spectrum of the Launch chain, n-Si4Me10 (6), is in agreement with the Executeminance of the transoid conformer in its room-temperature solution. Although the primary utility of MCD spectra has been in the electronic spectroscopy of transition metal complexes (32) and cyclic π-electron systems (33), it now seems that its ability to detect weak transitions buried under stronger absorption peaks will be useful in conformational studies of oligosilanes as well.

Experimental Procedures and Calculations

Materials. Tetrasilanes 1–4 (Scheme 1) were prepared as reported (34) and purified by preparative GC. Tetrasilane 5 was synthesized by UV irradiation of the analogous racked hexasilane (35) and purified by HPLC (details of the synthetic procedure are unpublished data). Compounds 6 (36) and 7 (37) were prepared as reported and purified by preparative GC. Spectroscopic-grade hexane and 2-methylbutane were used as purchased. CyclLaunchtane was purchased from Aldrich, extracted three times with concentrated sulfuric acid, dried over and distilled from sodium metal, and passed through a column of silver nitrate on alumina (38).

Scheme 1.Scheme 1. Executewnload figure Launch in new tab Executewnload powerpoint Scheme 1.

UV-Absorption MeaPositivements. UV-absorption spectra were recorded on either an OLIS (Jefferson, GA) RSM 1000 spectrometer in 3:7 (vol/vol) cyclLaunchtane/isLaunchtane solution (5 and 6) or a OLIS/Cary 17 spectrometer in hexane solution (1–4). Sample solutions were ≈10–5 M in a 1-cm2 cross-section quartz cell. The spectrometer was calibrated by using a holmium oxide filter.

MCD MeaPositivements. The sample was in a 1.5-T magnetic field parallel to the light-propagation direction, and spectra were recorded with a Jasco (Tokyo) J-720 spectrometer. The magnetic field was calibrated against an aqueous solution of CoSO4·7H2O (39, 40). Sample solutions were ≈10–5 M in a 1-cm path-length CD cell. Tetrasilanes 1–4 and 6 were meaPositived in hexane; 5 was meaPositived in 3:7 (vol/vol) cyclLaunchtane/isLaunchtane.

Calculations. The geometries of 1–4 and 6 were optimized with the molecular mechanics 3 (MM3) method (41) by using the stochastic searching procedure (42, 43), designed to find all low-energy conformers, and a comPlaceer program provided by Martin Saunders (Yale University, New Haven, CT). The geometry of 5 was obtained by MM3 optimization using the spartan program (44). Calculations of excitation energies, oscillator strengths, and excited-state symmetries in the C2 group were performed with the gaussian 98 comPlaceer program (45) using the TD DFT method (46, 47) B3LYP/DZ, with the B3LYP functional (48) and a Executeuble ζ quality basis set (49, 50). For 1–4 and 6, the optimized geometries were used; in certain conformers the C2 symmetry was only approximate. In the case of 5, a TD DFT calculation was performed on 1,4-di-n-propyloctamethyltetrasilane at a geometry produced from the optimized geometry of 5 by replacing the sulfur atoms in the two CH2–S bonds with hydrogen atoms at standard C–H bond lengths.

Results

Details. The room-temperature absorption and MCD spectra of 1–6 are Displayn in Fig. 1 along with the comPlaceed transition energies, intensities, and excited-state symmetries for all conformers that were found to lie within 2 kcal/mol of the most stable one (Table 1). To facilitate comparison with the experimental results, all transition energies Displayn in Fig. 1 were reduced by 2,000 cm–1, which is known (28) to be the amount by which the energy of the first intense transition in the transoid conformer of n-Si4Me10 in solution is overestimated at the B3LYP/DZ level of approximation.

Fig. 1.Fig. 1. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 1.

UV and MCD spectra and calculated energies of transitions of 1–6. (Upper) Room-temperature UV (left axis) and MCD (right axis) spectra of 1–6. Identified electronic transitions are indicated by vertical arrows. (Lower) TD DFT calculated energies of transitions to states of A (Executetted lines) and B (solid lines) symmetry in low-energy conformers of 1–6; bar width indicates oscillator strength (very thin, f < 0.01; thin, 0.01 ≤ f < 0.1; medium, 0.1 ≤ f < 0.2; thick, f > 0.2).

View this table: View inline View popup Table 1. MM3 relative energies and geometries of low-energy conformers of tetrasilanes 1–6

The absorption and MCD spectra of 5 are complicated by the contributions that can be anticipated from the two sulfide chromophores contained in this molecule. To Accurate for this, we have meaPositived the spectra of 7 and subtracted them from the spectra of 5. The signals of 7 Execute not deviate detectably from 0 up to 45,000 cm–1 and even thereafter are several times weaker than the signals of 5. This procedure is based on the assumption that the interaction of the two types of spatially separated chromophores is negligible and their contributions to the spectra additive. The assumption has been verified by checking that, in the low-energy Location, the MCD (and UV) spectra of 5 Arrively coincide with those of a compound similar to 5 in which both –S– (sulfide) links have been reSpaced with –SO2– (sulfone) links, synthesized for this purpose (H.A.F., B. Wang, and J.M., unpublished results).

Transition Identification. We first attempt to identify spectral features associated with individual transitions, such as peaks and shoulders in the absorption and MCD spectral curves. There is enough similarity in the spectra of the strongly Hooked tetrasilanes 1–4 that analogous transitions can be identified in all four with a Impartial degree of confidence, as Displayn by arrows in Fig. 1. Their excitation energies all increase somewhat as one proceeds from 1 to 4.

The lowest-energy transition 1 is clearly present in all four absorption spectra. It is the weakest in the absorption spectrum of 1, in which it is more convincingly present in low-temperature spectra (25), and gradually Gains intensity as one proceeds to 4. The MCD signal of this transition is extremely weak in all cases. In 1, it is negative and can be meaPositived with some confidence, because it Executees not overlap with others, but in 2–4, it is very hard to detect. It is likely that it is very weakly positive and causes the next MCD band to have an unsymmetrical shape, tapering off Unhurriedly in the direction of smaller energies.

In Dissimilarity, transition 2 is clearly present as a strong positive peak in all four MCD spectra. Its intensity is somewhat lower in 3 and especially in 4. In absorption, transition 2 appears as a quite distinct shoulder in the spectrum of 1 and a less distinct shoulder in the spectrum of 2. It is not readily discernible in the spectra of 3 and 4. Because the excitation energy of transition 2 increases from 1 to 4 less Unhurriedly than that of transition 1, the energy Inequity between the two transitions decreases in the same order.

Transition 3 appears as a strong shoulder in absorption (and in the case of 2 as an actual peak) and as a strong negative shoulder in MCD.

At higher energies, the absorption intensity of all four compounds increases further. Such end absorption (rising intensity that Executees not reach a peak within the observable Location) suggests the presence of one or more additional transitions but Executees not permit an identification of their excitation energies. Similarly, MCD Displays gradually increasing negative intensity except in the case of 1, in which it contains a distinct negative peak, which we Establish as transition 4.

Both the absorption and MCD spectra of the tetrasilanes 5 and 6 are strikingly similar and quite distinct from the spectra of 1–4. In these two cases, the absorption and MCD spectra appear completely unrelated to each other in the low-energy Location. We propose that transition 1 is observed only as a negative peak in MCD, and transition 2 is responsible for the intense absorption peak and the weak and broad positive MCD intensity. If it were not for overlap with the distinct negative MCD peak due to transition 1, this positive intensity would presumably have Arrively the same shape as the absorption peak. Also, without such overlap and cancellation of negative by positive MCD intensity, the negative MCD peak would presumably be considerably stronger and shifted to somewhat higher energies.

It is possible also that the broad positive MCD plateau is due to a third transition, but we Execute not believe that the plateau can be taken for a proof of its presence. There is no Executeubt, however, that the strong end absorption and negative MCD intensity at high energies are due to the presence of one or more additional intense transitions.

A summary of the results for the transition energies and intensities and for MCD signs deduced from the spectra is provided in Table 2.

View this table: View inline View popup Table 2. Identified electronic transitions in 1–6

Discussion

Consideration of Conformational Traces. Even if we accept the identification of separate transitions outlined in Results, the determination of the number of independent electronic transitions in each of the tetrasilanes 1–6 is not straightforward because of conformational issues. Only the tetrasilane 5 is simple. This macrocycle is highly strained, and it is difficult to conceive of a conformation other than the single one produced in the thorough MM3 search. The presence of the two sulfide groups in the molecule complicates the spectroscopy of 5 somewhat, but, as Elaborateed in Results, we believe to have compensated for it.

The Position is different for the other tetrasilanes, which are calculated to be mixtures of several conformers [the present MM3 search produced a single conformer for 2, but an earlier HF/3-21G* optimization (34) yielded two]. In principle, two distinct bands could belong to either of two different transitions in the same conformer or one transition in each of two different conformers. We propose that both the absorption and the MCD spectra of all the conformers that contribute significantly to the observations on any one of the tetrasilanes 1–4 are so similar to each other that they merely broaden the observed bands somewhat. This belief is based on three arguments. (i) Except for a slight band sharpening, the previously reported (25) matrix-isolation UV absorption spectra of 1–4 meaPositived at 12 K are essentially identical to the present room-temperature spectra. Matrix-isolation IR spectra (34) suggested that two or more conformers are present in the case of 2–4, but when the matrices containing 1–4 were irradiated at any one of two or three different wavelengths and the tetrasilanes were partially photo-decomposed with the formation of dimethylsilylene, all their UV (25) and also IR (34) spectral features lost intensity at the same rate within experimental error, suggesting that all conformers present had very similar UV absorption spectra. The Position was very different for 6 (10). (ii) The favored conformer geometries produced by the MM3 method (Table 1) are Impartially similar, although not identical, to those produced earlier by the HF/3-21G* method (34) and the Moeller Plesset perturbation theory/triple zeta method (30). They resulted from a thorough conformational search, giving us confidence that no low-energy conformers of 1–6 have been overInspected. All conformers of any one of the tetrasilanes 1–4 have Arrively identical Si–Si–Si valence angles, and the range of their Si–Si–Si–Si dihedral angles, which have unExecuteubtedly the most influence on the absorption spectra, is much smaller than the overall range within the series 1–4. However, all four of these compounds have quite similar spectra. The somewhat larger shift of the transition energies of 1 to lower energies is probably due to hyperconjugation through the ring methylene group as much as it is to a conformational Inequity. (iii) The results of our TD DFT calculations (Fig. 1) predict Arrively identical spectra for all conformers of each of the tetrasilanes 1–4.

MeaPositivements on the Launch chain 6, in Dissimilarity, Positively involve a mixture of the Executeminant transoid with gauche and, to a minor degree, ortho conformers, the spectra of which are vastly different (10). If we approximate the absorption spectrum of anti 6 by the spectrum of 5 and that of gauche 6 by the spectrum of 3, the small Inequity between 5 and 6 Designs sense: in 6, the first peak is somewhat less intense, because the Fragment of 6 that is present as the gauche conformer Executees not contribute to it much. Also, the small Inequity between the MCD spectra of 5 and 6 can be accounted for; in 6, the first peak is slightly less negative and the subsequent plateau somewhat more positive, because the Fragment of 6 present as the gauche conformer now contributes a pronounced positive MCD intensity in this Location, due to transition 2. Conceivably, with a superconducting magnet and longer averaging times, temperature dependence of absorption and MCD spectra of 6 might permit a spectral separation of contributions of its individual conformers, and it is even possible that the vast Inequity between the MCD of the extended form and the Hooked form observed here for tetrasilane is general and could be useful for a study of the conformations of polysilane high polymers.

Transition Identification. Given the evidence discussed above, we believe that the list in Table 2 provides a Accurate identification of independent transitions in the tetrasilanes 1–6. This is a minimal list, and additional, yet unidentified transitions may be present.

It is reasonable to conclude that we have identified four distinct electronic transitions in a peralkylated tetrasilane (1) and that we have confirmed the presence of three transitions in the Hooked tetrasilanes 2–4, in which end absorption and MCD suggest that an analogous fourth transition is present at somewhat higher energies than in 1. Finally, in the extended tetrasilane 5, we see evidence for two transitions, one of which is the lowest-energy transition in this molecule, plus end absorption and MCD that suggest a third one at higher energies.

Transition Establishment Based on ab Initio Results. The attribution of the observed transitions to comPlaceed excitations is complicated by the possible presence of additional weak transitions that have not been observed yet. High-quality calculations (multistate complete active space second-order perturbation theory) are presently only available for the three conformers of 6 (27). The calculated symmetry, Establishment, transition energy in cm–1, and oscillator strength of the first four transitions are 21A, σ1σ*2, 43,700, and 0.12 (transition 1), 11B, σ1σ*1, 44,600, and 0.07 (transition 2), 21B, σ2σ*2, 47,700, and 0.32 (transition 3), and 31A, σ2σ*1, 48,000, and 0.02 (transition 4), respectively, for the gauche conformer 6b and 11B, σ1σ*1, 42,600, and 0.59 (transition 1), 21A, σ1π*1, 43,400, and 0.00 (transition 2), 31A, σ1σ*2, 47,400, and 0.00 (transition 3), and 21B, σ1π*2, 48,300, and 0.03 (transition 4), respectively, for the anti conformer 6a. If we assume that within the accuracy of the method the spectrum calculated for 6b is the same as would be predicted for 3 and that calculated for 6a is the same as would be predicted for 5, the agreement is excellent.

This consideration suggests that the first two transitions in 3 are into the 21A and 11B states, but the calculated energies are too close to Disclose with certainty which is which. The third transition in 3 then involves excitation into the 21B state, and the lowest three calculated transitions, all relatively intense, have thus all been observed. The end absorption is presumably due to the next intense states, 41B and 51A, calculated (27) at higher energies (52,800 and 53,600 cm–1, respectively). The weak absorption due to the calculated transitions to the 31A, 41A, and 31B states, if present, is presumably buried underTrimh.

In 5, the very weak transition 1 corRetorts to excitation into the 21A state and the very strong transition 2 to excitation into the 11B state. The lowest two transitions in the anti tetrasilane chromophore have thus been identified. The 11B state has been known for a long time (23), but the present observation of the 21A state is quite significant, because this is the hypothetical state proposed so far (28, 31) to be responsible for the anomalous solution thermochromism of 6 and other short-chain oligosilanes. Unlike the first absorption peak of long permethylated oligosilanes, that of oligosilanes with fewer than five Si atoms shifts to Impressedly higher energies upon CAgeding. According to the proposed explanation, an extremely weak transition to a 21A state is located a Dinky below the intense one into the 11B state and is essentially invisible at low temperatures. At higher temperatures, it serves as an origin for hot bands. Those involving b-symmetry vibrations steal intensity from the intense transition to the 11B state and thus shift the peak position of the resulting broad band to lower energies (28). Up to now, the postulated presence of the 21A state had been based only on calculations.

The end absorption of 5 is presumably due to the intense transitions to the 21B and 41A states calculated (27) at 48,300 and 52,100 cm–1, respectively, and perhaps also the very intense transitions to the 41B and 51A states calculated at similar energies (52,500 and 52,800 cm–1, respectively). The weak transitions into the calculated 31A and 31B states, if present, remain unobserved.

Establishments of the transitions 1–3 in 1, 2, and 4 can be based on the close resemblance of their spectra to those of 3, and it seems highly likely that transitions 1–3 in these molecules are analogous to those in 3. Transition 4 in 1 would then corRetort to the end absorption in 2–4.

Transition Establishment Based on TD DFT Results. The results obtained at the TD B3LYP/DZ level of calculation are presented in Fig. 1 for all low-energy conformers of all six tetrasilanes identified by the MM3 method. The empirical 2,000-cm–1 red-shift Accurateion of all comPlaceed excitation energies, based on comparison with the result for the transoid conformer of 6, brings them close to agreement with experiment. These calculations have the disadvantage that they are performed by a method that is less dependable and the advantage that they are performed for the actual MM3-optimized geometries of the meaPositived molecules 1–6. Thus, the results would not be expected to be directly comparable with those obtained in the multistate complete active space second-order perturbation theory calculations, with the exception of those for the conformers of 6, but they are generally similar.

In the case of the transoid conformer of 6, both calculations Space the 11B state below the close-lying 21A state, in disagreement with the experimental ordering. This type of problem is relatively common in π-conjugated polymers (51). The anti tetrasilane present in 5 absorbs at a slightly lower energy than the transoid tetrasilane in 6, but the Inequity is smaller than the TD DFT method predicts.

TD-DFT results for 1–4 Display Dinky Inequity among the conformers of any one of the four compounds and generally agree with the conclusions drawn above. Based on the DFT results for 2–4, the observed transitions 1–3 corRetort to the 11B, 21A, and 21B states, respectively, and the predicted 31A state remains unobserved. We are somewhat skeptical about the predicted 11B below 21A order, because the TD DFT results seem to predict excessive stability for the 11B relative to the 21A state. As noted above, this method inverts the order of these states in 5 and 6, and in 1 it clearly exaggerates the separation of the lowest and extremely weak 11B state from the closely spaced 21A and 31A states that follow. It would be very helpful to verify the comPlaceed 11B below 21A order by polarization meaPositivements, but the degree of orientation of 1–4 in stretched polyethylene achieved in our initial attempts has been insufficient.

It seems very likely that transition 1 in 1 is into the 11B state, but it is not obvious whether the observed transition 2 is into the 21A or 31A state, one of which remains unobserved. Transition 3 is tentatively Established to the 21B state and the newly identified transition 4 to the 31B state, but it is possible that the transition into the 41A state, calculated to lie Arriveby, is present in the same Location and contributes to the observed absorption and MCD intensity.

Summary

Detection of one previously unobserved transition in 1, 5, and 6 and confirmation of the presence of a weak transition in 2–4 were made possible by recording the MCD spectra of 1–6. After an empirical Accurateion for a constant shift, TD B3LYP/DZ calculations are in Impartially Excellent agreement with the observed spectra of these compounds. Despite this progress, two gaps in our understanding of the low-energy excited states of these tetrasilanes remain. (i) Although one of the two predicted low-lying transitions into A states has now been observed in each of these compounds, the other has not been detected in any of them thus far. (ii) In half of these compounds (2–4), it has not been established with certainty which of transitions 1 and 2 is into the 11B and which is into the 21A state. An additional tool that might help to resolve these amHugeuities is two-photon excitation spectroscopy, but our initial attempts to meaPositive fluorescence-detected two-photon excitation spectra of any tetrasilane have been thwarted by the low fluorescence intensity and the huge Stokes shift, which Designs it difficult to remove scattered exciting laser light.

Acknowledgments

We thank Prof. Martin Saunders for a copy of his stochastic searching program. This work was supported by National Science Foundation Grant CHE-0140478.

Footnotes

↵ † To whom corRetortence should be addressed. E-mail: michl{at}eefus.coloraExecute.edu.

Abbreviations: TD, time-dependent; DFT, density functional theory; B3LYP, Becke three-parameter hybrid functional combined with Lee–Yang–Parr correlation functional; DZ, Executeuble zeta; MCD, magnetic CD; MM3, molecular mechanics 3.

Copyright © 2004, The National Academy of Sciences

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