Analysis of the NQR parameters in 2-nitro-5-methylimidazole derivatives by quantum chemical calculations

Abstract

The present study involves nitrogen NMR-NQR measurements and semiempirical as well as ab initio calculations at the different levels in three 2-nitro-5-methylimidazole derivatives. The NMR-NQR data were compared with the results of the quantum chemical calculations with the geometry optimization by seven semiempirical and a few ab initio methods. Since the use of a finite basis set is always a source of uncertainties in the electric field gradient (EFG) tensor components, the calculations were performed in different basis sets, and—regarding the effect of the functional—also at different levels of the theory. The results closest to experimental ones were obtained at the BLYP level of theory.

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Introduction

Imidazole and its numerous derivatives have long been the subject of interest of interdisciplinary researchers such as biophysicists or biochemists. The presence of such imidazole derivatives as histidine, histamine or polycarpine in the natural environment, together with the fact that imidazole is a component of proteins and pure nucleic bases, makes this compound fundamental for synthesis of many compounds which occur in biologically active systems. Particularly interesting medical applications are the antimycotics metronidazole, tynidazole, clotrimazole, oxykonazole, sulconazole, bifonazole, imazazlyl.^1–3 Metronidazole in appropriate doses is also one of the most frequently used radiosensibilisers, in vivo and in vitro.⁴ In recent years much attention has been devoted to the nitro derivatives of imidazole because of their anticancerous effect. So far only metronidazole from this class of compounds has been introduced to medical therapy, however, the studies on the cytostatic effect of the others are still under way. As toxicity of a given compound seems to be related to its electronic structure, it was interesting to investigate electron density distribution in the compounds of interest. In our previous paper⁵ we have found that the introduction of a substituent at 1H position of the imidazole ring leads to a redistribution of p-electron density and its delocalisation from the nitrogen atom –N[double bond, length half m-dash] onto the nitrogen –NH–. Moreover, we concluded that even very subtle substitution effects could significantly change the electron density distribution in imidazoles.

This work reports results of quantum chemical studies for the selected three derivatives of 2-nitro-5-methylimidazole (Fig. 1). The specific substituents and chemical names are given in Table 1. It is well known that 2-nitroimidazole compounds may appear in two different tautomeric forms (Fig. 2). We have performed the appropriate calculations and found that the form with the nitro group in the 2 position is more stable, however, the difference between the energies of the two forms is rather small and equal to 0.1 E_h. As a result of the substitution of a nitrogen group at position 2 and a methyl group at position 5, the quadrupole coupling constants on the nitrogen atoms in the imidazole ring increase and in the nitro group decrease.

Fig. 1 Structural formula of the studied compounds.

Table 1 The chemical names and substituents of the compounds studied

No	Compound	R1	R2	R3	R4
1	Imidazole	H	H	H	H
2	2-Nitro-5-methylimidazole	H	NO2	H	CH3
3	1-(2-Hydroxyethyl)-	CH2CH2OH	NO2	H	CH3
2-Nitro-5-methylimidazole
(metronidazole)
4	1-(2-Carboxymethyl)ethyl-2-	CH2CH2OCOCH3	NO2	H	CH[double bond, length half m-dash]CHPhCH3O
nitro-5-[2-(p-methoxy
phenyl)ethenyl]imidazole

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Fig. 2 The tautomeric forms of imidazole.

The aim of this paper is a comparison of the experimental and calculated NQR parameters. The effect of the parametrisation (in the case of semiempirical methods) as well as the basis set and the functional (in the case of ab initio methods) was analysed and the best basis set as well as the method best reproducing NQR parameters was proposed.

Calculation details

It is well known that the calculation methods of quantum chemistry can be divided into two basic groups that is the semiempirical ones and ab initio calculations. In many works semiempirical methods have been successfully applied, bringing valuable results for analysis of electron density. It is known that in the case of nitrogen these methods do not always lead to values close to experimental ones, however, the results we obtained for sulfonamides or 4N-substituted cytosine derivatives were close to the experimental values. Therefore, we applied semiempirical methods for analysis of electron density distribution in imidazole derivatives. It seemed even more justified because in the case of triasines the results were in agreement with the experimental values. Although semiempirical methods differ only in the percent of neglected diatomic differential overlap and parametrisation, we can show that the results obtained by them could lead to completely different conclusions.

The semiempirical calculations were carried out with the program package AMPAC⁶ and by seven different methods: INDO, MINDO/3, MNDO, AM1, PM3, CNDO and ZINDO/1. The ³⁵Cl-NQR frequencies were calculated from the density matrix using a program written by the authors by the method proposed in ref. 7.

The ab initio molecular calculations were carried out with the program package GAUSSIAN94⁸ in PCSS (Poznań). In non-empirical methods—the ab initio calculations—the main role is the functional chosen and the size of the basis set. We have optimized geometry at the HF and BLYP levels of theory. Two different basis sets, i.e. middle 6-31g(d,p) and extended 6-311g(2df,2pd) were used for the calculations and both were the TZ2P triple-ζ double polarized sets. The optimization of molecular geometries using the criterion of the minimum gradient of the energy relative to the nuclear coordinates was possible with all SCF wavefunctions.

The calculations of the EFG tensor components were carried on the HF, MP2 and BLYP levels of the theory. The ³⁵Cl-NQR frequencies were calculated from the principal components of electric field gradient localised on chlorine atom using a program written by the author. The quadrupole constant due to a single 2p electron (e²Qq₀h⁻¹) was taken to be 9.4 MHz.^9,10

Results and discussion

The results of NMR-NQR double resonance studies are collected in Table 2 and Table 3. Table 2 gives the frequencies while Table 3 contains the quadrupole coupling constants and asymmetry parameters. It should be pointed out, Table 2, that the introduction of NO₂ and CH₃ groups into the imidazole ring results in an increase in e²Qqh⁻¹ constants on both nitrogens of the ring and a decrease in e²Qqh⁻¹ on the nitrogen from the NO₂ group (nitro group).

Table 2 The NQR frequencies for the imidazole derivatives at 193 and 296 K

Nitrogen nucleus
–N[double bond, length half m-dash]			–NR1			–NO2
No	T/K	ν+/MHz	ν−/MHz	ν0/MHz	ν+/MHz	ν−/MHz	ν0/MHz	ν+/MHz	ν−/MHz	ν0/MHz
a Data from ref. 14. b Data from ref. 15.
1	291^a	2.511	—	0.192	1.367	0.721	0.647	—	—	—
77^b	2.556	2.345	0.21	1.417	0.719	0.698	—	—	—
2	296	2.635	2.230	0.405	1.499	0.855	0.644	1.028	0.810	0.218
193	2.639	2.235	0.404	1.499	0.820	0.679	1.045	0.821	0.224
3	296	2.598	2.350	0.248	2.046	1.655	0.391	0.792	0.613	0.179
193	2.605	2.348	0.257	2.057	1.661	0.396	0.803	0.622	0.181
4	296	2.852	2.781	0.071	2.077	1.772	0.305	0.746	0.636	0.11
193	2.871	2.797	0.074	2.076	1.771	0.305	0.753	0.644	0.109

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Table 3 The quadrupole coupling constants and asymmetry parameters (η) for imidazole derivatives

Nitrogen nucleus
–N[double bond, length half m-dash]		–NR1		–NO2
No	T/K	(e^2Qqzz/h)/ MHz	η	(e^2Qqzz/h)/ MHz	η	(e^2Qqzz/h)/ MHz	η
a Data from ref. 14.b Data from ref. 15.
1	291^a	3.222	0.119	1.391	0.93	—	—
77^b	3.253	0.135	1.418	0.997	—	—
2	296	3.243	0.250	1.569	0.821	1.225	0.356
193	3.249	0.249	1.546	0.878	1.244	0.360
3	296	3.299	0.150	2.467	0.317	0.936	0.381
193	3.302	0.156	2.479	0.320	0.950	0.381
4	296	3.755	0.038	2.566	0.238	0.921	0.239
193	3.779	0.039	2.565	0.238	0.931	0.230

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The main aim of this paper is a comparison between the experimental and calculated NQR parameters.

Since the time taken to perform calculations increases with a growing number of degrees of freedom of a molecule, we decided to perform an initial optimization of the method for pure imidazole. This compound seemed ideal as its crystal structure was well recognised. Crystallographic studies of imidazole were carried out in the years 1977–1982 by Craven et al.^11–13 It is well known that imidazole crystallises in the space group P21/c with four molecules in an elementary cell.

For an imidazole molecule we performed calculations with 7 semiempirical methods of quantum chemistry. We checked the influence of the geometry on the results. Table 4 presents the values of effective charge calculated assuming the experimental geometry at 103 and 293 K and the results obtained for the optimized geometry. As follows from these data the negative charge on the nitrogen –N[double bond, length half m-dash] is always higher than on the nitrogen NH–. This result is in qualitative agreement with the NQR data. On the other hand, the analysis of NQR parameters such as frequency, asymmetry parameters and quadrupole coupling constants calculated by the method proposed by Kaplansky and Whitehead⁷ leads to a completely different conclusion. Irrespective of whether we use the optimized or experimental geometry, the results are in contradiction to experiment. The calculated resonance frequencies and coupling constants are higher on the –NH– nitrogen than on the –N[double bond, length half m-dash] nitrogen which is in obvious contradiction to the experiments. It should be emphasised that the assignment of the experimental frequencies to particular positions does not arouse doubts. Tables 5–7 present a comparison of the measured and calculated NQR frequency. Table 5 gives the results for the optimized geometry, and Tables 6 and 7 have been obtained assuming the crystal structure at 103 and 293 K, respectively. Only the CNDO calculations and only with the experimental geometry assumed lead to the conclusions in agreement with experiment.

Table 4 Effective charges on imidazole nitrogen nucleus calculated by semiempirical methods—experimental geometry

Nucleus	CNDO	INDO	MINDO/3	MNDO	AM1	PM3	ZINDO/1	T/K^a
a T indicates crystallographic structure.
–NH–	−0.070	−0.048	0.052	−0.215	−0.189	0.319	−0.098	103
–N[double bond, length half m-dash]	−0.199	−0.248	−0.172	−0.227	−0.149	−0.099	−0.199	103
–NH–	−0.088	−0.067	0.021	−0.230	−0.204	0.322	−0.177	293
–N[double bond, length half m-dash]	−0.179	−0.228	−0.149	−0.210	−0.132	−0.072	−0.234	293
–NH–	−0.096	−0.078	0.046	−0.246	−0.208	0.311	−0.123	opt.
–N[double bond, length half m-dash]	−0.192	−0.236	−0.171	−0.229	−0.141	−0.118	−0.251	opt.

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Table 5 The results of the calculations of NQR parameters for the optimized geometry (imidazole)

Method
Quantity	INDO	CNDO	MINDO/3	MNDO	AM1	PM3	ZINDO/1
–NH–
ν+/MHz	4.000	4.010	4.020	3.940	3.580	3.970	3.600
ν−/MHz	2.880	2.830	3.250	3.810	3.480	3.920	2.880
ν0/MHz	1.120	1.170	0.770	0.130	0.100	0.050	0.720
(e^2Qq/h)/MHz	4.587	4.560	4.847	5.167	4.707	5.260	4.320
η	0.490	0.510	0.320	0.050	0.040	0.020	0.340
–N[double bond, length half m-dash]
ν+/MHz	2.290	2.170	2.170	2.230	2.070	2.820	2.340
ν−/MHz	1.600	1.740	2.020	1.660	1.550	1.720	1.570
ν0/MHz	0.690	0.430	0.150	0.570	0.530	1.090	0.780
(e^2Qq/h)/MHz	2.593	2.607	2.793	2.593	2.413	3.027	2.607
η	0.530	0.330	0.110	0.440	0.440	0.720	0.600

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Table 6 The results of the calculations of NQR parameters for the experimental geometry at 103 K (imidazole)

Method
Quantity	INDO	CNDO	MINDO/3	MNDO	AM1	PM3	ZINDO/1
–NH–
ν+/MHz	3.760	2.440	4.060	3.720	3.450	3.710	3.380
ν−/MHz	2.650	1.890	3.150	3.610	3.310	3.680	2.620
ν0/MHz	1.110	0.550	0.910	0.120	0.140	0.030	0.760
(e^2Qq/h)/MHz	4.273	2.887	4.807	4.887	4.507	4.927	4.000
η	0.520	0.380	0.380	0.050	0.070	0.010	0.380
–N[double bond, length half m-dash]
ν+/MHz	2.540	3.750	2.070	2.220	2.150	2.680	2.480
ν−/MHz	1.790	2.610	1.920	1.640	1.550	1.480	1.700
ν0/MHz	0.740	1.140	0.150	0.580	0.600	1.200	0.780
(e^2Qq/h)/MHz	2.887	4.242	2.660	2.573	2.467	2.773	2.787
η	0.510	0.540	0.110	0.450	0.490	0.860	0.560

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Table 7 The results of the calculations of NQR parameters for the experimental geometry at 293 K (imidazole)

Method
Quantity	INDO	CNDO	MINDO/3	MNDO	AM1	PM3	ZINDO/1
–NH–
ν+/MHz	3.920	2.80	4.400	3.850	3.540	3.870	3.550
ν−/MHz	2.760	2.240	3.230	3.670	3.400	3.820	2.730
ν0/MHz	1.150	0.140	0.960	0.180	0.140	0.060	0.820
(e^2Qq/h)/MHz	4.453	3.076	5.087	5.013	4.627	5.127	4.187
η	0.520	0.090	0.390	0.070	0.060	0.020	0.390
–N[double bond, length half m-dash]
ν+/MHz	2.490	3.920	2.070	2.210	2.140	2.670	2.430
ν−/MHz	2.070	2.740	1.660	1.460	1.370	1.430	1.970
ν0/MHz	0.420	1.180	0.410	0.750	0.780	1.240	0.460
(e^2Qq/h)/MHz	3.040	4.442	2.487	2.447	2.340	2.733	2.933
η	0.270	0.530	0.330	0.620	0.660	0.910	0.310

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The next problem was whether the strong hydrogen bonds (2.86 Å bond length) can play an important role. To check this we carried out ZINDO/1 calculations. This method was chosen as it is rather fast and it is a combination of CNDO and INDO methods. The results obtained for a monomer, dimer and an elementary cell containing 4 molecules of imidazole were compared, Table 8. Although a decrease in NQR frequency was obtained as expected as a result of hydrogen bond formation, the results still are not in agreement with the experimental ones. On the other hand, we obtained similar results (also in disagreement with the experimental ones) for other five-membered heterocyclic compounds like triasine. Moreover, the assumption of perpendicular orbitals did not lead to results consistent with experiment. The source of failure of the semiempirical quantum chemistry methods in these applications is in the way they force a redistribution of electron density among the nitrogen atom orbitals and the kind of parametrisation they are based on. In these circumstances it was not a surprise that the results obtained for 2-nitro-5-methylimidazole did not agree with the experimental ones. Moreover, the data on the crystal structure of this compound are not available so we were not able to verify if the results obtained by CNDO assuming the experimental geometry agree with experiment. In conclusion, the semiempirical methods have proved totally useless for investigation of electron density distribution in 2-nitroimidazole derivatives.

Table 8 The influence of the hydrogen bonds on the NQR parameters (imidazole)

ZINDO/1
Quantity	Monomer	Dimer	Elementary cell	NQR
–NH–
ν+/MHz	3.600	3.460	1.520	1.367
ν−/MHz	2.880	2.780	1.060	0.721
ν0/MHz	0.720	0.680	0.470	0.647
(e^2Qq/h)/MHz	4.320	4.160	1.720	1.391
η	0.340	0.320	0.540	0.930
–N[double bond, length half m-dash]
ν+/MHz	2.340	1.310	0.980	2.511
ν−/MHz	1.570	0.710	0.730	2.319
ν0/MHz	0.780	0.600	0.250	0.192
(e^2Qq/h)/MHz	2.607	1.347	1.140	3.222
η	0.600	0.890	0.460	0.119

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Having checked this we resorted to the non-empirical quantum chemistry methods known as the ab initio methods. Using these methods we performed analogous calculations, that is we studied the influence of geometry on the results. Since the use of a finite basis set is always a source of uncertainties in the EFG components, the calculations were performed in different basis sets, and—regarding the effect of the functional—also at different levels of the theory. The effect of different basis sets and functionals was analysed. As our earlier studies for cytosine had proved better results can be obtained using a BLYP or MP2 functional we did not carry out calculations with a HF functional. The results for imidazole are given in Table 9. As follows from these results, the best agreement is obtained using the BLYP functional in the 6-311g(2df, 2pd) basis set at fully optimized geometry, although the differences are rather small. Moreover, as indicated by the slope of the regression curves the results are in agreement with experiment. The results obtained by BLYP in the 6-311(2df, 2dp) basis set were the best. ¹⁴N-NQR frequencies, closest to the experimental ones, can be obtained by using BLYP or MP2 with full optimization methods (correlation coefficients are 0.916 and 0.905 and curve fit standard deviation 0.123 and 0.144, respectively). A comparison of the results obtained for imidazole in the experimental geometry at 103 and 293 K proves that the geometry has an essential effect on the quality of the results (Table 10)

(a)forgeometryat103K:ν(calc.)=1.023ν(NQR)+0.148;r=0.939,s=0.395 (1)

(b)forgeometryat293K:ν(calc.)=0.984ν(NQR)+0.251;r=0.929,s=0.413 (2)

(c)foroptimisedgeometry:ν(calc.)=1.039ν(NQR)+0.114;r=0.911,s=0.500 (3)

where r is a correlation coefficient and s stands for the curve fit standard error. The frequencies closest to the experimental ones were obtained at the BLYP level of theory with the application of the extended basis set.

Table 9 The results of the ab initio calculations of NQR parameters—optimized geometry (imidazole)

Method
BLYP	MP2	BLYP
Basis set
Quantity	6-31g (d,p)	6-311g (2df,2pd)	NQR
–N[double bond, length half m-dash]
ν+ MHz	2.24	2.15	2.61	2.511
ν− MHz	2.19	2.14	2.47	2.319
ν0 MHz	0.05	0.10	0.13	0.192
(e^2Qq/h) MHz	2.952	2.862	3.381	3.222
η	0.03	0.07	0.08	0.119
–NH–
ν+ MHz	1.85	1.58	1.77	1.367
ν− MHz	1.59	1.39	1.59	0.721
ν0 MHz	0.26	0.19	0.18	0.647
(e^2Qq/h) MHz	2.297	1.984	2.245	1.391
η	0.22	0.19	0.16	0.930

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Table 10 The results of the ab initio calculations of NQR parameters—experimental geometry (imidazole)

BLYP/6-311g(2df,2pd)
Temperature (T/K)
Quantity	103	293	NQR
–N[double bond, length half m-dash]
ν+ MHz	2.605	2.699	2.511
ν− MHz	2.456	2.382	2.319
ν0 MHz	0.149	0.317	0.192
(e^2Qq/h) MHz	3.375	3.388	3.222
η	0.088	0.190	0.12
–NH–
ν+ MHz	1.808	1.869	1.367
ν− MHz	1.440	1.504	0.721
ν0 MHz	0.369	0.365	0.647
(e^2Qq/h) MHz	2.165	2.249	1.391
η	0.340	0.320	0.930

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The fact that the results for imidazole were correct prompted us to perform analogous calculations for two 2-nitroimidazole derivatives: 2-nitro-5-methylimidazole and metronidazole. The results for 2-nitro-5-methylimidazole are collected in Table 11 and for metronidazole in Table 12. The influence of the basis set and the functional on the results for 2-nitro-5-methylimidazole and metronidazole illustrated by the data in Tables 11 and 12. Unfortunately, a high number of degrees of freedom and the lack of crystalline data prevented us from performing the calculations for one-third of the compounds.

Table 11 The results of the ab initio calculations of NQR parameters—optimized geometry (2-nitro-5-methylimidazole)

Method
BLYP	MP2	BLYP
Basis set
Quantity	6-31g (d,p)	6-311g (2df,2pd)	NQR
–N[double bond, length half m-dash]
ν+ MHz	2.29	2.23	2.55	2.635
ν− MHz	2.18	2.19	2.51	2.230
ν0 MHz	0.12	0.04	0.04	0.450
(e^2Qq/h) MHz	2.979	2.948	3.300	3.243
η	0.08	0.02	0.02	0.250
–NH–
ν+ MHz	1.78	1.56	1.75	1.499
ν− MHz	1.637	1.38	1.60	0.855
ν0 MHz	0.14	0.19	0.15	0.644
(e^2Qq/h) MHz	2.277	1.958	2.239	1.569
η	0.13	0.19	0.13	0.82
–NO2
ν+ MHz	0.42	0.59	0.39	1.03
ν− MHz	0.34	0.49	0.21	0.81
ν0 MHz	0.08	0.10	0.18	0.22
(e^2Qq/h) MHz	0.51	0.72	4.00	1.23
η	0.31	0.27	0.91	0.36

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Table 12 The results of the ab initio calculations of NQR parameters—optimized geometry (metronidazole)

Method
Quantity	BLYP/6-31g (d,p)	NQR
–N[double bond, length half m-dash]
ν+ MHz	2.22	2.60
ν− MHz	2.14	2.35
ν0 MHz	0.08	0.25
e^2Qq/h MHz	2.909	3.299
η	0.05	0.15
–NH–
ν+ MHz	1.88	2.05
ν− MHz	1.629	1.655
ν0 MHz	0.21	0.39
(e^2Qq/h) MHz	2.316	2.467
η	0.19	0.32
–NO2
ν+ MHz	0.41	0.79
ν− MHz	0.32	0.61
ν0 MHz	0.09	0.18
(e^2Qq/h) MHz	0.49	0.94
η	0.36	0.38

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In general, the correlation between the experimental and calculated frequencies (ν), quadrupole coupling constants (e²Qq_zzh⁻¹) and asymmetry parameters (η) is good. The following correlation dependencies were obtained between the experimental and calculated by BLYP NQR parameters:

and

where r is a correlation coefficient and s stands for the curve fit standard error.

The regression lines are shown in Figs. 3–5. A comparison of the results of our calculations shows that the electron density distribution is correctly reproduced on –NH– and the nitro group while on –N[double bond, length half m-dash] results are in disagreement with the experimental ones (Fig. 5) although the differences are rather small. The asymmetry parameters are reproduced within the error for the –N[double bond, length half m-dash] atom, i.e. in the case when the asymmetry parameters are very high.

Fig. 3 Comparison of the calculated and the experimental NQR quadrupole coupling constants for imidazole derivatives.

Fig. 4 Comparison of the calculated and the experimental frequencies for imidazole derivatives.

Fig. 5 Comparison of the calculated and the experimental asymmetry parameters for imidazole derivatives.

Conclusions

1. When using the semiempirical methods, it is possible to obtain results which do not completely match the experimental ones. The parametrisation of semiempirical methods and redistribution of the electron density between nitrogen orbitals in five-membered heterocyclic nitrogen nucleus does not lead to the adequate quantitative or qualitative results.

2. The adequacy of the calculations of effective charges on nitrogen nucleus cannot be the main criterion for a correlation between the calculations and experiment. However, the charges may be adequate in each case, the NQR frequencies may not. The ¹⁴N-NQR frequencies, closest to the experimental ones, can be obtained by using BLYP or MP2 methods starting with the experimental geometry.

3. The correlation between the experimental and calculated frequencies (ν), quadrupole coupling constants (e²Qq_zzh⁻¹) and asymmetry parameters (η) is good. However, the asymmetry parameters are reproduced with the error for the –N[double bond, length half m-dash] atom, i.e. in the case when the asymmetry parameters are very high.

4. The size of the basis set and the functional used for the calculations may radically influence the results. Much better results are obtained when the calculations are carried out in a larger basis set and for the experimental geometry.

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