Calculation of 15N and 31P NMR Chemical Shifts of Azoles

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry 15

31

Calculation of N and P NMR Chemical Shifts of Azoles, Phospholes and Phosphazoles: A Gateway to Higher Accuracy at Less Computational Cost Yuriy Yu. Rusakov, Irina L. Rusakova, Valentin A. Semenov, Dmitry O. Samultsev, Sergey V. Fedorov, and Leonid B. Krivdin J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b05161 • Publication Date (Web): 25 Jul 2018 Downloaded from http://pubs.acs.org on July 26, 2018

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The Journal of Physical Chemistry

Calculation of 15N and 31P NMR Chemical Shifts of Azoles, Phospholes and Phosphazoles: A Gateway to Higher Accuracy at Less Computational Cost Yury Yu. Rusakov, Irina L. Rusakova, Valentin A. Semenov, Dmitry O. Samultsev, Sergei V. Fedorov and Leonid B. Krivdin*

A. E. Favorsky Irkutsk Institute of Chemistry, Siberian Branch of the Russian Academy of Sciences, Favorsky St. 1, 664033 Irkutsk, Russia. E-mail: [email protected]

Abstract A number of computational schemes for the calculation of 15N and 31P NMR chemical shifts and shielding constants in a series of azoles, phospholes and phosphazoles was examined. A very good correlation between calculated at the CCSD(T) level and experimental 15N and 31P NMR chemical shifts was observed. It was found that basically solvent, vibrational and relativistic corrections are of the same order of magnitude and alternate in sign being in average of about 2-3 ppm in absolute value, however, being much larger (up to 14 ppm) in the case of solvent molecules explicitly introduced into computational space. At the DFT level, the performance of nine exchange-correlation functionals including six conventional gradient functionals and three hybrid functionals was studied. The most accurate results were reached at with OLYP and Keal-Tozer's family of functionals, KT1, KT2 and KT3, while most popular B3LYP and PBE0 functionals showed most unreliable results. Based on these data, we highly recommend OLYP and KT2 functionals for the computation of 15N and 31P NMR chemical shifts at the DFT level in the diverse series of nitrogen and phosphorous containing heterocycles. Benchmark calculations of 15N and 31P NMR chemical shifts in a series of larger nitrogen and phosphorous containing heterocycles were performed at the DFT level in comparison with experiment and revealed the OLYP functional in combination with aug-pcS-3/aug-pcS-2 locally dense basis set scheme as the most effective computational scheme. ACS Paragon Plus Environment

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1. Introduction Since the early days of NMR till present, much attention has been focused on 15N NMR chemical shifts, both on their experimental and computational aspects. Indeed, computation of 15N NMR chemical shifts provides a powerful tool in the structural elucidation of the nitrogen-containing organic and biological molecules and gives a deeper insight into vitally important biochemical phenomena such as self-association, molecular recognition and base-pairing. Complimentary,

15

N

NMR of nucleoside bases can serve as a direct probe for the studies of nitrogen environment in oligomeric fragments of nucleic acids and nucleosides resulting in a deeper insight in the vitally important biochemical phenomena. Calculation of 15

N NMR chemical shifts provides a powerful tool in a structural elucidation of the

nitrogen-containing organic and biological molecules, coordination complexes with nitrogen-containing ligands and intermolecular complexes together with biological species including nucleotides, nucleosides, peptides and even small proteins. On the other hand,

31

P NMR plays a major role in the identification and

structural elucidation of diverse organophosphorus compounds and related biological species. Basically,

31

P NMR chemical shifts provide a straightforward

structural information on the mechanisms of the fundamental enzymatic reactions, elucidation of biochemical transformation and many other bioorganic and biochemical aspects. As an example, 31P NMR chemical shifts are widely used in the studies of asymmetric metal complex catalysis and represent a promising structural tool for the oxidative catalysis. A number of phosphorus heterocycles are well known to be biologically active compounds possessing antibacterial, antitumor and hepatotoxic activity and are used as building blocks in modern organic synthesis. In the present communication, in continuation of our previous studies (see review[1] for references), we performed a high-level

15

N and

31

computational study of the series of azoles, phospholes and phosphazoles. ACS Paragon Plus Environment

P NMR

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2. Computational Details Geometry optimizations of all compounds were performed with GAUSSIAN 9.0 code[2] at the MP2/ATZP//ADZP level. Cartesian coordinates of all optimized structures in gas phase and in solution (where applicable) are given in Supporting Information.

For

five

benchmark

CCSD/ATZP//ADZP calculations of

compounds,

15

N and

31

all

non-relativistic

P NMR isotropic magnetic

shielding constants were carried out in gas phase with CFOUR package[3] while all four-component relativistic GIAO-DFT(KT2) calculations were performed with DIRAC code.[4] Vibrational corrections were calculated at the MP2/ADZP level of theory using CFOUR package. Solvent corrections were calculated within the IEFPCM approach at the MP2/ATZP level using GAUSSIAN 9.0 code. All calculated 15

N and 31P shielding constants were converted into chemical shift scale based on

chemical shifts of neat nitromethane (for 15N) and 85 % H3PO4 (for 31P) used as the standards. All calculated

15

N and 31P NMR chemical shifts were evaluated based

on the calculated chemical shifts of the title reference compounds using the same functionals and basis sets. Further computational details can be requested directly from the authors.

3. Results Reported herewith are the results of benchmark CCSD(T) (Coupled Cluster Singles and Doubles with Perturbative Triples Corrections) calculations of 15N and 31

P MMR chemical shifts in the series of five representative azoles, phospholes and

phosphazoles with available most reliable experimental data. Further on we examined the performance of diverse DFT computational schemes for the calculation of

15

N and

31

P NMR chemical shifts in a much wider series of

compounds including such aspects as most reliable functionals and basis sets, ACS Paragon Plus Environment


solvent effects, vibrational corrections and relativistic effects. To test the reliability of the proposed computational schemes, we performed benchmark calculations of 15

N and

31

P NMR chemical shifts in comparison with experiment in a series of

larger nitrogen and phosphorous heterocycles representing different bonding situations involving nitrogen and phosphorous atoms.

3.1 Benchmark CCSD(T) calculations A Coupled Cluster (CC) theory5,6 for systems that are described primarily by a single Slater determinant is now well elaborated for the calculation of molecular electronic structures as well as for different molecular properties. It makes use of the exponential representation of the cluster excitation operator, exp( Tˆ ), operating on a reference wave function, which results in the exact solution of the Schrödinger equation. Within the CC theory a cluster operator represents a sum of single ( Tˆ1 ), double ( Tˆ2 ), triple ( Tˆ3 ) and etc. cluster excitation operators. These operators are expanded in a series of second quantized operators with the expansion coefficients called as cluster amplitudes, which are needed to be found. The equations for the cluster amplitudes are derived algebraically, namely by projecting the Schrödinger equation onto a set of excited determinants, including the non-excited reference wave function. As a result, one obtains the coupled equations for the cluster amplitudes, which can be solved iteratively. Different approximate schemes of CC method are obtained by truncating the expansion of cluster operator Tˆ . One of the most widespread schemes is the CCSD model,6 which involves no more coefficients than the configuration interaction single and double excitation model, called as CISD.7 The cluster operator within the CCSD approach is expressed as the sum of single and double excitation operators, Tˆ = Tˆ1 + Tˆ2 . However, apart from these, CCSD treats the contributions of triple and quadruple excitations, the latter being disconnected products of single and double excitations, such as Tˆ1Tˆ2 , Tˆ13 , Tˆ22 , Tˆ12Tˆ2 , and so on. The number of operations in CCSD model ACS Paragon Plus Environment

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increases no more rapidly than the sixth power of the basis set functions, N6(see ref.6). The CCSD method is correct through the third order in Møller-Plesset (MP) perturbation theory,8,9 but it also includes infinitely higher order terms of the restricted type. During last years, this model has received a lot of attention in NMR quantum chemical field due to a number of advantages, such as size extensivity,10,11 reasonable scaling (N6), and taking into account higher disconnected excitations, which are occurred to be sufficient for the simple closedshell molecules at their minimum energy geometries. Despite of the obvious advantages of the CCSD model, it appears that in some difficult cases this model is not sufficient. In particular, to achieve the correctness through the fourth order in perturbation theory, one must include the connected triple excitations Tˆ3 . In addition, as was stated by Purvis,6 when HartreeFock orbitals are used, perturbation treatment indicates that the dominant contribution to CI triple excitation operator Cˆ 3 usually comes from Tˆ3 , which is not included in the CCSD method. The most straightforward remedy is to resort to CCSDT approach,12,13 which has received a significant attention due to coupled iterative treatment of the triple connected excitations Tˆ3 . Nonetheless, these calculations are impractical for the time being as the straightforward inclusion of connected triples invariably leads to a dramatic growth of operations, so that the CCSDT scheme scales as N8. This problem resulted in a variety of approximate triple excitation methods, which can be divided in two distinct classes, namely the iterative and noniterative approximations. In the iterative approximations, the equations for Tˆ1 , Tˆ2 and Tˆ3 are coupled, but Tˆ3 equation is truncated, guided by perturbational consideration to reduce computational cost. Among those are the CCSDT-n models of Bartlett and co-workers.14 The noniterative class implies that the equations for Tˆ3 are decoupled from the ones for Tˆ1 and Tˆ2 . The initial approximations to Tˆ3 cluster amplitudes are estimated from the terms taken from the Tˆ1 and Tˆ2 CCSDT-1 iterative method, but Tˆ3 is not allowed to alter Tˆ1 or Tˆ2 . In this respect, the simplest examples are the ACS Paragon Plus Environment


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CCSD+T(CCSD) and CCSD(T) methods, the latter used in the present study. Both methods are noniterative approximations to the CCSDT-1 method that are correct through the fourth order in perturbation theory, differing only in the fifth-order energy term. It is known that CCSD(T) requires iterative solutions of the CCSD equations with N6 operation scale, followed by a non-iterative N7 step to obtain the triples corrections. This is a significant achievement compared to the iterative N8 steps for CCSDT. Moreover, approximated connected triple cluster amplitudes in CCSD(T) do not required to be stored explicitly on disc, they are simply evaluated from the double excitations CCSD amplitudes and the fluctuation potential when they are needed. The CCSD(T) model has already been proven to provide very accurate prediction of NMR chemical shifts, especially in the complex electronic systems with strong electron correlation effects which are the objects of the present study. For such complex electronic systems, CCSD(T) model could be regarded as a proper standard. However, CCSD(T) calculations of 15N and 31P NMR chemical shifts of the real-life compounds considered herewith with using augmented penta-zeta quality basis sets are beyond the current computational capacity. In that way, in this study we employed the scheme of the Composite Method Approximation (CMA),15 as described by eqn. (1).

CCSD(T)/aug-pcS-4 ≈ HF/aug-pcS-4 + [CCSD(T)/aug-pcS-2 – HF/aug-pcS-2]

(1)

The CCSD(T)/aug-pcS-4 values are thus approximated by the sum of the HF values, calculated using large penta-zeta quality aug-pcS-4 basis set and the correlation contribution, evaluated as the difference between the CCSD(T) and HF values, obtained using a smaller basis set of triple-zeta quality, namely aug-pcS-2. In the virtue of the fact that CCSD(T) results, which are to be used throughout the paper as the reference (calibration) data, could hardly be received within the ACS Paragon Plus Environment

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reasonable computational limits, we have to resort to CMA of CCSD(T). So, starting from this point under the CCSD(T) approach we would imply the composite approximation of CCSD(T), namely CMA CCSD(T). Herewith, we performed a series of benchmark CCSD(T) calculations of and

31

15

N

P NMR chemical shifts of five representative azoles, phospholes and

phosphazoles, see Table 1. Solvent and vibrational corrections to 15N and 31P NMR chemical shifts of five compounds given in Table 1 were evaluated as described in the corresponding sections of the paper, namely in Section 3.3 (solvent effects) and Section 3.4 (vibrational corrections).

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TABLE 1: Calculated 15N and 31P NMR Chemical Shifts of Five Salient Azoles, Phospholes and Phosphazoles Including Solvent, Vibrational and Relativistic Correctionsa

Calculated chemical shiftc Structure

Atom

Shielding constantb

Gas Phase (δGP)

N

Solvent Vibrational correction correction

Relativistic correction

(∆δsolv)

(∆δvibr)

(∆δrel)

Exp.d Total (δcalc)

(δexp)

N

112.6

-236.6

2.0

-4.0

0.3

-238.3

-235.2

P

411.9

-54.4

0.8

-1.3

0.2

-54.7

-49.2

P

366.3

-8.8

1.1

-2.2

0.4

-9.5

-8.7

Me

P H

P Me



Page 10 of 59

N-1

32.7

-156.7

2.8

-7.9

0.8

-161.0

-154.1

N-2

-87.2

-36.8

-2.3

-1.1

0.3

-39.9

-35.4

P

275.1

82.4

-3.0

0.7

1.3

81.4

93.8

N-1

28.4

-152.4

2.9

-5.6

0.7

-154.4

-150.9

N-2

-116.4

-7.3

-4.4

1.9

-0.4

-10.2

-20.9

P

124.8

232.7

-3.0

-1.5

1.9

230.1

223.0

a

All shielding constants, chemical shifts and their contributions are in ppm. Calculated at the CCSD(T) level within the Composite Method Approximation in gas phase. c Evaluated as δ = δst + σst – σ (δ - calculated chemical shift, δst - experimental chemical shift of a standard, σst and σ - shielding constants of a standard and a compound under study). d Experimental values (solutions in: CDCl3 for pyrrole and phospholes and C6D6 for phosphazoles) are taken from different sources, see text for references. b


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As one can see in Table 1, a good correlation between calculated 15N and 31

P NMR chemical shifts and their experimental values (taken from refs.16,17,18,19) is

observed, which is also illustrated in Figure 1. It is seen that solvent, vibrational and relativistic corrections are of the same order of magnitude and alternate in sign being in average of about 2-3 ppm in absolute value. The origin and substituent trends of these three accuracy factors are discussed in more details in the subsequent sections of the paper.

Figure 1. Correlation plot of theoretical 15N (blue circles) and 31P (green diamonds) NMR chemical shifts of five salient azoles, phospholes and phosphazoles calculated at the CCSD(T)/aug-pcS-4 level with taking into account solvent, vibrational and relativistic corrections versus experiment. ACS Paragon Plus Environment


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Results presented in Table 1 and Figure 1 demonstrate the potential of CCSD(T) method with taking into account solvent, vibrational and relativistic corrections in calculation of 15N and 31P NMR chemical shifts. However, CCSD(T) calculations are extremely computationally demanding, so that in the present study we have examined the performance of various DFT schemes for the calculation of 15

N and

31

P NMR chemical shifts in a much more wider series of compounds

including ten azoles 1-10, and thirteen phosphazoles 11-23. N

3 N

N

3

4

N

N 2

2

N

N 1

N

Me

Me

Me

Me

Me

1

2

3

4

5

1

N

1


N

1

N

1

2

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3.2 Functionals and basis sets In the present study we have examined the performance of nine exchangecorrelation functionals including six conventional GGA (Generalized Gradient Approximation)

functionals,

namely

KT1,

KT2,

KT3,20,21

OPBE,22,23

OLYP,24,25,26,27 OPW91,26,27,28 and three hybrid functionals (that are those containing a fraction of an exact orbital exchange), namely B3LYP,24,29 PBE0,30,31 and B97-2.32 It is worth mentioning that KT1, KT2 and KT3 functionals by Keal and Tozer20,21 have been designed specifically for NMR shielding constants. All KealTozer exchange-correlation functionals contain modified (with internal parameter) exchange gradient correction, which is the key issue for the high quality theoretical shieldings. The key parameters of that correction were determined primarily by fitting to the experimental shielding constant data for a series of challenging molecules with the first- and second-row nuclei, while the rest of parameters were fitted to atomization energies, ionization energies, total energies and other physical properties. It should be also recalled that in some of our previous papers51,33,34 the Keal-Tozer exchange-correlation functionals have been shown to give the best reliable data for the phosphorous and nitrogen chemical shifts calculated within the DFT approach. The OPBE, OLYP and OPW91 functionals might also be promising for the calculation of phosphorous and nitrogen NMR chemical shifts. They include correspondingly popular PBE,31 LYP24 and PW9128 correlation functionals and, on the other hand, OPTX26,27 exchange functional, which, according to results of ACS Paragon Plus Environment


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Zhang et al.,22 show a remarkably good performance for NMR chemical shifts. Wu

et al.35 have also performed the DFT calculations using 21 exchange-correlation functionals of NMR chemical shifts of several heteroatoms, including nitrogen in particular. The OPBE and OPW91 functionals have been proven to give the best agreement with the experimental data along the whole set of systems studied there, giving even better results as compared to the standard wave-function based MP2 method. The OLYP and O3LYP (the latter one has not been taken into consideration here) were also shown to provide sufficient accuracy, being slightly inferior to OPBE and OPW91. Three hybrid functionals B3LYP, PBE0 and B97-2 have also been chosen for comparison as the commonly used functionals. However, one should not expect them to give the optimal NMR properties because they were introduced without any relation to the calculation of NMR shielding constants. The performance of nine examined functionals in combination with Jensen's quadruple quality aug-pcS-3 basis set for the calculation of

15

N and

31

P

NMR chemical shifts in the series of about two dozens of mostly representative compounds, namely 1-23, is illustrated in Figures 2 and 3 with the corresponding numerical data compiled in Table 2. Along with the mean absolute errors (MAE) shown in Figure 2, we also analyzed their normalized values (NMAE), i.e. the percentages of MAE in respect to the total range of shielding constants (chemical shifts) which are presented in Figure 3. MAE (ppm) and NMAE (%) were evaluated as the deviations of calculated DFT values in respect to the highest achievable results of CCSD(T) calculations (used here as the most reliable accuracy reference).


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TABLE 2: Chemical shieldings of 1-23 calculated at different levels of theory



Cmpd

1

Formula a

Page 16 of 59

Atom

CMA CCSD(T)

B3LYP

OLYP

B97

OPW91

OPBE

PBE0

KT1

KT2

KT3

N

112.2

75.6

82.5

83.7

87.3

87.9

81.9

91.0

89.6

90.3

N-1

54.8

17.1

29.0

27.0

35.0

35.8

24.2

38.1

35.9

37.1

N-2

-54.7

-104.3

-81.2

-90.9

-74.0

-73.0

-96.9

-67.3

-71.1

-69.8

N-1

103.9

67.7

74.4

75.5

78.8

79.5

73.9

84.3

82.5

82.6

N-3

-16.0

-65.3

-46.9

-52.4

-40.6

-39.7

-58.1

-32.4

-35.0

-33.8

N-1

23.5

-16.0

-0.5

-5.8

5.5

6.4

-8.9

11.5

8.2

8.6

N-2

-122.4

-176.4

-143.7

-161.0

-134.8

-133.6

-168.4

-126.6

-131.9

-130.9

N-3

-114.8

-169.3

-138.0

-154.0

-129.6

-128.4

-161.4

-119.5

-124.4

-123.6

2

3

4


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5


N-1

50.9

13.3

24.2

23.1

29.9

30.6

20.5

34.6

32.1

32.7

N-2

-39.5

-88.6

-69.7

-76.0

-63.6

-62.6

-81.4

-54.9

-58.9

-58.2

N-4

2.7

-43.4

-28.6

-32.0

-23.8

-23.0

-36.9

-13.2

-16.3

-15.8



Page 18 of 59

N-1

1.6

-37.0

-19.2

-26.0

-12.3

-11.4

-29.4

-9.6

-12.9

-11.6

N-2,5

-76.4

-126.3

-99.9

-114.0

-93.9

-92.9

-119.9

-83.6

-89.2

-88.9

N-1

104.0

68.7

74.4

76.3

78.6

79.2

74.8

85.2

83.2

83.1

N-3,4

-82.3

-139.0

-115.2

-123.7

-107.3

-106.2

-130.5

-97.5

-101.1

-99.9

N-1

35.0

-3.8

9.0

6.1

14.7

15.6

3.4

21.8

18.6

18.7

N-2

-123.0

-177.0

-146.6

-162.5

-138.8

-137.5

-169.3

-127.6

-133.7

-133.8

1

N-3

-164.9

-223.6

-186.6

-206.7

-177.2

-175.8

-214.9

-165.7

-171.8

-171.3

Me

N-4

-82.3

-135.6

-112.7

-121.5

-106.0

-104.9

-127.8

-93.0

-97.8

-97.6

N-1

-24.1

-64.9

-44.9

-53.6

-37.9

-36.8

-57.2

-32.3

-36.6

-36.0

N-2

-134.3

-189.0

-154.9

-174.7

-147.2

-145.9

-181.7

-135.3

-142.1

-142.4

N-3

-89.6

-142.4

-116.6

-128.2

-109.5

-108.4

-134.7

-98.0

-102.9

-102.4

N-5

-51.7

-100.3

-77.5

-88.3

-72.0

-71.0

-93.7

-61.3

-66.6

-66.4

6

7

3

4 N

N N2

8 N

9


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10


N-1

-27.6

-68.8

-49.4

-57.5

-42.5

-41.5

-60.9

-35.1

-39.7

-39.7

N-2,5

-115.9

-167.9

-137.5

-154.5

-130.6

-129.3

-160.6

-117.6

-124.5

-125.2

N-3,4

-149.3

-204.6

-172.8

-189.1

-164.6

-163.3

-196.3

-150.9

-157.5

-157.8

P

161.2

62.1

108.1

96.1

128.7

131.2

87.2

139.5

135.2

142.2

N

79.1

37.7

48.1

46.8

53.3

54.1

44.2

56.8

55.2

56.7

P

108.8

5.3

57.4

38.6

77.1

79.8

28.9

92.4

88.0

94.7

N-1

25.9

-12.5

1.4

2.8

7.0

7.8

-5.8

9.3

7.0

8.6

N-2

-113.3

-175.4

-141.1

-160.9

-133.0

-131.7

-167.9

-124.4

-130.1

-129.4

P

276.3

182.2

218.5

213.0

235.3

237.6

205.3

254.4

250.8

255.1

N-1

32.5

-4.9

8.0

4.8

13.5

14.3

1.8

16.1

13.9

15.4

N-5

-86.3

-137.4

-112.3

-123.9

-105.8

-104.8

-130.8

-97.9

-101.8

-100.3

11

12

13



P

14

N

5

Page 20 of 59

P

135.0

28.2

78.5

59.5

95.2

97.8

50.7

115.3

109.1

114.1

N-1

9.6

-36.5

-18.8

-25.7

-12.2

-11.2

-29.3

-8.9

-11.8

-10.3

N-5

-118.4

-175.2

-146.4

-161.1

-139.4

-138.2

-168.3

-132.2

-136.5

-134.8

P

117.8

19.6

65.5

50.9

83.8

86.3

41.9

96.1

91.8

98.7

N-1

47.4

5.5

18.2

14.9

23.5

24.3

11.9

28.0

26.0

27.2

N-3

-76.5

-133.3

-104.8

-119.3

-97.3

-96.1

-125.9

-89.3

-93.4

-92.2

N 1

Me

15


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16

17


P

151.3

51.5

96.8

85.4

116.5

119.0

75.7

129.4

126.9

134.8

N-1

83.6

47.4

54.4

55.6

58.7

59.3

53.5

63.3

61.6

62.2

N-4

-34.1

-90.4

-67.8

-76.2

-60.4

-59.3

-82.3

-51.1

-54.3

-53.2

P

169.1

67.1

109.1

99.7

127.3

129.7

91.0

144.5

140.0

145.4

N-1

81.9

41.3

49.5

50.1

54.2

54.9

47.8

59.5

57.5

58.2

N-4

-36.1

-86.7

-68.9

-73.7

-63.4

-62.5

-79.8

-54.3

-56.7

-55.1

P

139.8

37.3

80.7

69.2

97.3

99.8

59.9

119.1

114.9

120.7

N-1

0.8

-38.9

-23.1

-28.4

-17.1

-16.2

-31.9

-11.6

-14.9

-14.3

N-4

-169.7

-235.8

-193.3

-218.5

-183.3

-181.7

-227.2

-170.1

-176.0

-176.5

N-5

-168.4

-226.1

-188.2

-210.0

-179.7

-178.4

-218.7

-169.5

-175.5

-174.4

P

62.3

-40.5

9.0

-9.5

26.4

29.1

-19.3

44.0

39.2

45.1

N-1

30.4

-8.3

3.5

1.4

8.9

9.7

-1.4

12.7

10.2

11.2

N-2

-121.2

-184.8

-153.9

-170.9

-146.9

-145.6

-177.6

-136.9

-142.9

-142.5

N-4

-47.7

-103.1

-82.5

-89.6

-76.3

-75.3

-95.5

-66.2

-69.7

-68.6

18

19



Page 22 of 59

1 2 3 P 74.3 -39.1 4.2 -9.5 19.3 21.8 -18.5 44.7 39.0 42.7 4 5 N-1 65.9 25.3 34.7 34.3 39.4 40.2 31.8 45.1 42.8 43.7 6 7 20 N-3 -190.2 -266.0 -226.1 -248.2 -216.3 -214.7 -257.2 -203.5 -209.2 -208.8 8 9 10 N-4 -127.9 -192.6 -166.4 -176.4 -159.1 -157.9 -184.3 -147.7 -150.9 -149.2 11 12 P 100.1 -12.2 32.8 16.0 46.5 49.2 7.7 76.3 69.3 71.0 13 14 N-1 -13.1 -59.4 -40.5 -48.3 -33.9 -32.9 -51.8 -27.9 -32.0 -31.4 15 16 N-3 -177.5 -229.0 -195.3 -212.5 -186.8 -185.3 -219.9 -173.5 -180.0 -180.1 17 21 18 19 N-4 -193.7 -255.8 -216.9 -238.2 -207.7 -206.3 -247.3 -195.7 -201.3 -200.4 20 21 N-5 -150.3 -224.8 -191.5 -210.1 -184.1 -182.8 -217.6 -173.3 -180.0 -179.6 22 23 P 202.4 127.7 159.6 157.3 177.2 179.4 151.2 183.4 180.9 189.3 24 25 22 26 27 N-2,5 -143.3 -211.3 -178.5 -195.0 -172.1 -171.0 -206.0 -155.4 -159.0 -157.5 28 29 30 31 P 360.4 284.0 309.0 313.0 327.3 329.4 309.2 338.8 334.9 337.9 32 33 23 34 35 N-3,4 -161.0 -227.8 -199.8 -212.2 -194.4 -193.3 -221.6 -180.3 -184.5 -182.7 36 37 38 a All geometry optimizations are performed at the MP2/aug-cc-pVTZ level. In all DFT calculations aug-pcS-3 basis set was employed 39 40 on all atoms. In all CMA CCSD(T) calculations aug-pcS-4 was used on all atoms at the HF level and ATZP at the CCSD(T) level. 41 42 43 44 ACS Paragon Plus Environment 45 46 47

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Figure 2. Mean absolute errors of different functionals employed in the DFT calculations of 15N (yellow bars) and 31P (blue bars) NMR shielding constants and chemical shifts in the representative series of compounds 1-23. All values are given in ppm in respect to the CMA CCSD(T) results.



Figure 3. Normalized mean absolute errors of different functionals employed in the DFT calculations of 15N (yellow bars) and 31P (blue bars) NMR shielding constants and chemical shifts in the representative series of compounds 1-23. All normalized mean absolute errors represent a percentage of the CMA CCSD(T) values.

As one can see from these data, the best performance is demonstrated by OLYP and Keal-Tozer's family of functionals, KT1, KT2 and KT3. On the other hand, most popular B3LYP and PBE0 functionals showed most unreliable results. As an example, NMAEs of the calculated 15N NMR chemical shifts are 7.9 and 7.5 % for PBE0 and B3LYP while they are only 2.6 and 1.4 % for KT2 and OLYP functionals; for the calculated 31P NMR chemical shifts, NMAEs are 11.9 and 9.2 ACS Paragon Plus Environment

Page 24 of 59

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% for PBE0 and B3LYP while they are as small as 1.4 and 2.4 % for KT2 and OLYP functionals. Based on these results, we highly recommend OLYP and KT2 functionals for the computation of

15

N and

31

P NMR chemical shifts in the diverse series of

nitrogen and phosphorous containing heterocycles at the DFT level.

3.3 Solvent effects Solvent effects may play an important role in the accurate prediction of 15N and 31P NMR chemical shifts. At the stage of benchmark calculations, we used the Integral Equation Formulation of Polarizable Continuum Model (IEF-PCM)36,37,38,39 It is known that IEF-PCM simulates the environmental effects of different nature and complexity within a solvation continuum formalism,40 without taking into account any specific solute-solvent interactions. Within this formalism, the isotropic solutions are represented by a homogeneous dielectric medium which is polarized by the molecular solute placed in an arbitrary cavity. The total electrostatic potential can thus be presented as the sum of the molecular (solute) electrostatic potential and the so-called reaction potential, representing the potential of the induced electric charge on the cavity surface due to the dielectric medium response. The reaction potential is expressed in terms of an Apparent Surface Charge (known as ASC model) distribution over the cavity boundary which is expressed in terms of the complicated space integral functional of the electron density. The latter can be found by the double numerical integration over the cavity surface. For this purpose, the whole cavity surface is partitioned into the so-called curvilinear triangles, called tesserae. Eventually, the polarization energy functional is included into the Hamiltonian and then the problem reduces to the unified theoretical treatment depending on the method being used. Shown in Figure 4 are the solvent corrections of nonpolar cyclohexane (ε 2.0), polar aprotic acetone (ε 21.0) and polar protic water (ε 80.0) to 15N and 31P NMR shielding constants while the full set of solvent corrections for the studied ACS Paragon Plus Environment


Page 26 of 59

series of compounds calculated at the DFT level using OLYP and KT2 functionals employing aug-pcS-3/aug-pcS-2 locally dense basis set (LDBS) scheme are compiled in Table 3.

TABLE 3: Solvent corrections (absolute values, ppm) to NMR shielding constants of 1-23 calculated at the DFT level using OLYP and KT2 functionals with employing aug-pcS-3/aug-pcS-2 locally dense basis set scheme

Cyclohexane

Acetone

Water

Cmpd. Atom OLYP 1 2 3 4

5 6 7

8

9

10

N-1 N-1 N-2 N-1 N-3 N-1 N-2 N-3 N-1 N-2 N-4 N-1 N-2,5 N-1 N-3,4 N-1 N-2 N-3 N-4 N-1 N-2 N-3 N-5 N-1 N-2,5 N-3,4

1.2 0.2 7.0 2.5 10.7 2.0 7.0 10.1 1.2 5.4 8.1 0.4 5.5 3.2 13.0 2.7 3.9 10.1 8.2 1.4 5.7 8.3 4.0 2.3 3.5 7.0

KT2 1.9 0.7 6.1 3.2 9.4 2.7 6.1 8.7 1.7 4.5 6.9 0.1 4.7 3.9 11.4 3.4 3.1 8.9 6.7 1.9 4.8 7.1 3.3 2.8 2.8 5.9

OLYP 5.9 3.1 14.0 8.9 22.6 7.9 14.0 20.9 5.4 9.4 15.7 1.8 9.6 10.7 28.1 9.5 5.6 20.9 15.7 6.3 9.9 16.0 5.5 8.6 4.1 13.0


KT2 6.6 3.7 12.9 9.6 20.7 8.8 12.6 18.6 5.9 8.5 14.1 2.3 8.6 11.4 25.5 10.3 4.5 18.6 13.5 6.9 8.6 14.1 4.7 9.3 3.3 11.2

OLYP 6.5 3.4 14.8 9.6 23.9 8.6 14.9 22.1 5.8 9.8 16.6 2.0 10.0 11.6 29.9 10.2 5.8 22.2 16.6 6.8 10.3 16.9 5.6 9.2 4.1 13.7

KT2 7.1 4.0 13.7 10.3 21.9 9.4 13.4 19.7 6.3 8.9 14.8 2.5 9.0 12.3 27.1 11.0 4.7 19.7 14.2 7.5 9.1 14.8 4.8 9.9 3.3 11.8

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11 12

13

14

15

16

17

18

19

20

21

22

P N P N-1 N-2 P N-1 N-2 P N-1 N-2 P N-1 N-3 P N-1 N-3 P N-1 N-3 P N-1 N-4 N-5 P N-1 N-2 N-4 P N-1 N-3 N-4 P N-1 N-3 N-4 N-5 P N-2,5

4.4 0.8 4.3 1.6 6.8 5.6 1.4 5.5 1.3 0.2 6.7 1.9 2.5 10.4 6.8 3.0 10.5 3.2 1.3 8.9 1.4 2.2 10.1 5.4 2.1 1.6 5.1 7.9 3.5 3.0 16.3 12.5 2.0 2.4 8.9 10.1 7.6 0.8 9.5

0.3 1.7 0.0 2.1 5.8 1.4 1.8 4.6 2.7 0.6 5.8 2.3 3.4 8.7 2.3 3.7 8.9 0.9 2.3 7.6 2.8 3.0 4.9 7.9 2.3 2.2 4.0 6.3 1.2 4.0 13.9 10.7 2.5 3.3 4.4 8.7 9.4 3.1 7.8

10.0 5.3 10.0 6.8 13.9 12.0 6.3 9.2 2.4 2.5 12.6 3.0 9.9 21.7 16.7 10.7 22.3 5.9 6.7 17.7 3.0 9.0 14.3 16.2 4.3 6.8 8.3 15.0 6.6 10.9 36.4 27.1 4.6 8.9 12.0 20.9 19.9 2.6 19.0


5.7 6.1 4.9 7.3 13.0 7.1 6.7 8.1 1.6 3.4 11.4 1.4 10.8 19.5 11.4 11.3 20.3 1.9 7.5 15.7 1.8 10.0 8.3 18.0 0.6 7.5 7.3 12.9 1.4 11.9 32.3 23.9 0.3 10.1 7.4 18.3 20.5 6.8 16.5

10.7 5.8 10.7 7.4 14.8 12.7 6.8 9.6 2.4 2.8 13.3 3.1 10.7 22.9 17.9 11.6 23.7 6.2 7.2 18.7 3.1 9.7 14.8 17.5 4.6 7.4 8.7 15.7 6.9 11.8 38.7 28.7 4.9 9.6 12.4 22.2 21.2 2.9 20.0

6.3 6.6 5.5 7.9 13.9 7.8 7.2 8.6 1.6 3.7 12.1 1.2 11.7 20.7 12.5 12.2 21.6 2.1 8.1 16.6 1.8 10.7 8.8 19.2 0.3 8.1 7.7 13.7 1.6 12.8 34.4 25.5 0.0 10.8 7.8 19.4 21.7 7.2 17.4


23

P N-3,4

2.0 14.0

5.4 12.0

8.7 29.8

Page 28 of 59

12.1 26.8

9.5 31.6

12.9 28.5

Generally, as stated in the pioneering milestone paper by Chesnut and Moore on the LDBS scheme, "the success of locally dense basis sets is clearly dependent upon the property being calculated. The chemical shift is sensitive to the electron distribution near the resonant nucleus, and therefore requires a good description of that distribution in the vicinity of the resonant nucleus and a lesser description further away".41 The development of these ideas was presented further in a number of related publications.42,43,44 As an example, the LDBS scheme was systematically and successfully employed for the calculation of 15N NMR chemical shifts in a number of nitrogen containing heterocycles.33,34,45,46,47 The same is done herewith in the calculations of 15N and 31P NMR chemical shifts of the extended series of azoles, phospholes and phosphazoles. Coming back to solvent effects, we see that basically solvent corrections to both 15N and 31P NMR shielding constants of nonpolar cyclohexane (accordingly, 2-3 and 5-6 ppm) are roughly half of those of polar acetone (4-7 and 12-13 ppm) and water (5-7 and 13-14 ppm). On the other hand, solvent corrections to

15

N

NMR shielding constants are about twice as those to 31P NMR shielding constants and follow the same trends.


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Figure 4. Averaged IEF PCM solvent corrections to 15N (yellow bars) and 31P (blue bars) NMR shielding constants of 1-23 calculated using OLYP and KT2 functionals.

In the case of strong solute-solvent interactions (which is not the case in the present study) there is another way to describe the environmental effects. This approach is referred to as Supermolecule Solvation Model (SSM).38 Within this approach, one or several molecules of solvent are placed into the calculation space of solute in an explicit way implying the coupling within the polarizable continuum formalism. The SSM approach is very demanding with respect to computational resources, although it may be of particular interest for heteroaromatic compounds, considered in this study, for which spectral data have been received in aromatic or in polar solvents. Herewith, we have used this approach by adding one, two or even three molecules of solvent (chloroform and acetone) into the computational space of several representative compounds of the studied series in an explicit way, as ACS Paragon Plus Environment


illustrated in Figure 5. Numerical data are presented in Table 2 which is given further on in the Section 3.6 (Benchmark calculations). It follows that generally SSM approach noticeably improves calculated values of chemical shifts as compared to experiment. As an example, adding one, two and three molecules of solvent (chloroform) into computational space of 1,2,4-oxazaphosphole (24) in an explicit way increases IEF-PCM value of 71.7 ppm to accordingly 76.9, 82.0 and 85.7 ppm as compared to experimental value of 84.0 ppm. Shown in Figure 6 is the evolution of the supermolecular solvation complex of 1,2,4-oxazaphosphole 24 with three molecules of chloroform during the minimization procedure involving the total of 51 minimization cycles. Unfortunately, SSM calculations are very demanding in the sense of computational resources and exceptionally time consuming.


Page 30 of 59

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Figure 5. Supermolecular solvation complexes of 1,2,4-oxazaphosphole with one, two and three molecules of chloroform (accordingly, 24a, 24b and 24c), phosphinine with one molecule of chloroform (25a), benzo[c][1,2,5]oxadiazole with one molecule of acetone (28a) and 9H-carbazole with one molecule of acetone (31a). Element colors: carbon - yellow, hydrogen - grey, nitrogen - blue, oxygen - red, phosphorous - brown and chlorine - green. All interatomic distances are given in Å.



Figure 6. Minimization process of the supermolecular solvation complex of 1,2,4oxazaphosphole with three molecules of chloroform 24c. Element colors: carbon yellow, hydrogen - grey, nitrogen - blue, oxygen - red, phosphorous - brown. E stands for the total inner energy while N denotes the number of optimization cycles. All interatomic distances are given in Å.

Generally speaking, in the SSM approach, solvent molecules are added directly into calculation space to form the solvation complexes in the IEF PCM medium. The classical IEF PCM model works quite well when no specific intermolecular solvate-solvent interactions are expected. However, it should be noted that supermolecular model is most effective when essential intermolecular ACS Paragon Plus Environment

Page 32 of 59

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solvate-solvent interactions are present (e.g. those enhanced by the intermolecular or hydrogen bonding). Very often solvent causes considerable changes in the predicted magnetic properties and the results of the performed calculations of chemical shifts depend significantly on the number of solvent molecules included in the computational space.48

3.4 Vibrational corrections In order to provide the best achievable agreement of the calculated

15

N and

31

P

NMR chemical shifts with those taken from the experimental data at the stage of benchmark calculations (vide supra), we have taken into account the influence of the molecular vibrational motion, which might play a significant role in the nitrogen and phosphorous magnetic properties. In this connection, we have calculated the zero-point vibrational corrections to nitrogen and phosphorous shielding constants (σ) within the formalism implemented in Dalton program package.49,50 This formalism makes use of the effective geometry used as an expansion point in a Taylor series of the electron potential energy surface on the deviations of the normal coordinates from the expansion point. The effective geometry is equivalent to a zero-point vibrationally averaged molecular geometry to a second-order in the order parameter (λ) of the perturbed vibrational wave function. Using the effective geometry as an expansion point instead of the equilibrium geometry results in the vanishing of the most important term in the first-order of the perturbation expansion in parameter λ of the expectation value of σ with respect to the vibrational wave function. In this case the anharmonicity of the potential is included indirectly through the use of the effective geometry as an expansion point instead of the equilibrium geometry, since the energy minimum criteria, which determines the effective geometry, involves the anharmonicity of the potential. Thus, the correction to a molecular property σ from the zero-point vibrational motion can be evaluated from a zero-order vibrational wave function alone. The vibrational correction to a property σ takes the form: ACS Paragon Plus Environment


Page 34 of 59

( 2)

0 < σ > 0, 0 = (σ eff − σ e0 ) +

1 N σ eff ,ii ∑ 4 i =1 ω i

(2)

Here σ eff0 and σ e0 stand for the shielding constant σ calculated accordingly at the effective and the equilibrium geometries; σ eff( 2),ii denotes the second derivative of σ with respect to the deviations of normal coordinates i from the expansion point (which is the effective geometry), and ωi are the harmonic frequencies. Calculated ranges of vibrational corrections to 15N and 31P NMR shielding constants in the studied series of azoles and phosphazoles are shown in Figure 7 while the numerical data are compiled in Table 4. It is seen that in the case of 15N NMR shielding constants vibrational corrections span from ca. -25 to +5 ppm being essentially negative in most cases. Thus the range of vibrational corrections totals to as much as 30 ppm which indeed is very impressive and claims for their mandatory accounting in the related calculations. The range of vibrational corrections to 15N NMR shielding constants is large for nitrogens in the moieties B, C, F and H as compared to K, L and M where they are almost constant. As an example, vibrational corrections fall into range of ca. -(10 - 25) ppm ranging for as much as 15 ppm in the moiety H while they are essentially constant (ca. -9 ppm) in K. In case of 31P NMR shielding constants, vibrational corrections are all negative falling into range of ca. -(12 - 19) ppm with a span of about 7 ppm. The largest variations are observed for moieties A and D while they are essentially constant for the rest of bonding situations involving phosphorous.


Page 35 of 59 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TABLE 4: Vibrational corrections (∆vibr, ppm) to chemical shieldings of 1-23 calculated at the GIAO-DFT-B3LYP/aug-pc-1 level Cmpd. 1 2 3 4

5

6

7

8

9

10

11 12

13

Atom N N-1 N-2 N-1 N-3 N-1 N-2 N-3 N-1 N-2 N-4 N-1 N-2 N-5 N-1 N-3 N-4 N-1 N-2 N-3 N-4 N-1 N-2 N-3 N-5 N-1 N-2,5 N-3,4 N-1 P N-1 N-2 P N-1 P N-5

∆vibr -6.1 -10.0 -5.3 -9.0 -6.8 -8.3 -10.6 -6.1 -9.0 -10.9 -6.9 -10.7 -11.2 -6.5 -7.5 -7.1 4.9 -7.8 -13.4 -15.5 -9.3 -8.5 -10.2 -10.5 -7.0 -9.3 -12.2 -13.5 -6.0 -18.6 -11.4 -5.0 -13.6 -8.9 -16.3 -1.5

Cmpd. 14

15

16

17

18

19

20

21

22

23

Atom N-1 P N-5 N-1 P N-3 N-1 P N-4 N-1 P N-4 N-1 P N-4 N-5 N-1 N-2 P N-4 N-1 P N-3 N-4 N1 P2 N3 N4 N5 P N-2 N-5 P N-3 N-4

∆vibr -9.4 -16.6 -6.7 -8.4 -15.7 -5.4 -8.7 -13.8 -5.8 -9.0 -15.1 0.2 -7.7 -14.2 -9.0 -6.0 -7.7 -10.5 -12.0 -6.2 -7.5 -15.8 -8.7 -5.1 -9.3 -14.1 -6.3 -8.3 -6.1 -11.7 -9.0 -8.7 -17.2 -9.3 -9.2

The general conclusion which can be reached at from these results is that vibrational corrections are an essential accuracy factor and are to be taken into ACS Paragon Plus Environment


account in the reliable calculations of

15

N and

31

P NMR shielding constants and

chemical shifts in a wider series of nitrogen and phosphorous containing heterocycles.


Page 36 of 59

Page 37 of 59 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Figure 7. Ranges of vibrational corrections to 15N (left) and 31P (right) NMR shielding constants.



Page 38 of 59

3.5 Relativistic effects The effects of relativity on phosphorus and nitrogen nuclear magnetic shielding constants have been given a minor attention in the present study. The reason was that azoles and phosphazoles considered herewith could safely be regarded as the “light” compounds, i.e. consisting of “light” elements only. Although the influence of relativistic effects on phosphorus (Z = 15), which is the heaviest element considered in this study, on its own shielding constant without any heavy surrounding could reach as much as about 19-20 ppm (as was found in a simplest molecule of PH3,51,52) the total relativistic corrections to phosphorous chemical shifts are at the most part reduced to the insignificant values of several parts per million. Nevertheless, at the stage of benchmark calculations where the prime goal was to compare calculated values with the experiment, we had to consider as much accuracy factors as possible. Thus, the influence of relativistic effects on phosphorus and nitrogen nuclear magnetic shieldings has been taken into account via the relativistic four-component DFT calculations. It was found that basically relativistic corrections to

15

N NMR chemical

shifts are vanishingly small (ca. 0.5 ppm) while those for 31P NMR shifts are a bit larger being of about 1-2 ppm, as follows from the data presented in Table 1. It thus appears that in the routine calculations of 15N and 31P NMR chemical shifts of azoles, phospholes, phosphazoles and related six-membered systems (pyridines, pyrimidines, pyrazines, triazines and their phosphorous analogues) together with a broad scope of condensed nitrogen and phosphorous containing heterocycles relativistic effects could safely be omitted.

3.6 Benchmark calculations To test the reliability of the proposed computational schemes, we performed benchmark calculations of 15N and

31

P NMR chemical shifts in a series of larger


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nitrogen and phosphorous containing heterocycles representing different bonding situations involving nitrogen and phosphorous 24-34 in comparison with experiment,16,53,54,55,56 (Table 5). Two most effective functionals, OLYP and KT2, were employed in combination with aug-pcS-3/aug-pcS-2 basis sets within the LDBS scheme with taking into account solvent effects with IEF-PCM. Generally, a good correlation was observed between calculated and experimental values, as shown in Figure 8 with OLYP functional demonstrating much better performance (MAE 5.6 ppm for the range of 500 ppm) as compared to KT2 (MAE 10.5 ppm for the range of 500 ppm). Based on these results, for the calculation of

15

N and

31

P NMR chemical

shifts in a wide series of nitrogen and phosphorous compounds at the DFT level we recommend OLYP functional in combination with aug-pcS-3/aug-pcS-2 locally dense basis set scheme. For more accurate results at much higher computational cost, the CCSD(T) level is of course recommended.



Page 40 of 59

TABLE 5: 15N and 31P NMR Chemical Shifts of 24-34 Calculated at the DFT Level Using OLYP and KT2 Functionals within the aug-pcS-3/aug-pcS-2 Locally Dense Basis Set Scheme with Taking into Account Solvent Effects

Cmpd. 24

25

Structure

a

NMR chemical shift (δ, ppm) b Solvent Chloroform

Chloroform

Nucleus P

P

OLYP

KT2

Exp.c

71.7

59.6

84.0

76.9d

61.0d

82.0e

65.0e

85.7f

68.4f

206.8

192.0

206.0d

187.1d

206.5

Chloroform

P

266.0

248.9

263.3

27

Chloroform

P

23.6

21.6

23.5

28

Diethyl ether

N

45.0

36.6

36.0

Acetone

N

41.6

33.6

36.3

39.8d

32.9d

N-2

32.3

18.4

44.9

N-3

52.6

39.4

60.9

N-1

-162.2

-166.6

-162.0

N-2

-7.3

-15.1

-4.0

N-3

-45.2

-54.0

-40.0

26

29

30

Acetone

Acetone


Page 41 of 59 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


31

Acetone

N

-266.8

-270.8

-264.1d

-267.3d

-268.1

32

Acetone

N

-268.9

-272.7

-275.4

33

Acetone

N

-57.6

-70.3

-54.0

34

Methanol

N

-72.7

-86.1

-86.5

a

All geometry optimizations are performed at the MP2/aug-cc-pVTZ level with solvent effects taken into account within the IEF-PCM scheme. b All calculated and experimental NMR chemical shifts are in ppm from neat nitromethane (for 15 N) and 85 % H3PO4 (for 31P). c Taken from different sources, see text for references. d Calculated with one molecule of solvent added to the computational space in an explicit way. e Calculated with two molecules of solvent added to the computational space in an explicit way. f Calculated with three molecules of solvent added to the computational space in an explicit way.



Page 42 of 59

Figure 8. Correlation plot of theoretical 15N (blue circles) and 31P (green diamonds) NMR chemical shifts of salient nitrogen and phosphorous containing heterocycles 24-34 calculated at the DFT level using OLYP (left) and KT2 (right) functionals and aug-pcS-3/augpcS-2 locally dense basis set scheme versus experiment.


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4. Conclusions In the present study, we have examined a number of computational schemes for the calculation of 15N and 31P NMR chemical shifts and shielding constants in a series of azoles, phospholes and phosphazoles bearing in mind the best performance at less computational costs. Thus for the five most representative compounds from this series, a very good correlation between calculated at the CCSD(T) level and experimental and

31

15

N

P NMR chemical shifts was observed. It was found that basically solvent,

vibrational and relativistic corrections are of the same order of magnitude and alternate in sign being rather significant in some cases. These results demonstrated the potential of CCSD(T) method with taking into account solvent, vibrational and relativistic corrections in calculation of

15

N and

31

P NMR chemical shifts.

However, CCSD(T) calculations are extremely computationally demanding, so that in the present study a performance of various DFT schemes was examined. In this line, the performance of nine exchange-correlation functionals including six conventional GGA functionals and three hybrid functionals was studied. The best results were demonstrated by OLYP and Keal-Tozer's family of functionals, KT1, KT2 and KT3. On the other hand, most popular B3LYP and PBE0 functionals showed most unreliable results. Based on these data, we highly recommend OLYP and KT2 functionals for the computation of 15N and 31P NMR chemical shifts in the diverse series of nitrogen and phosphorous containing heterocycles at the DFT level. Solvent effect is indeed a very salient accuracy factor. Basically, solvent corrections to both 15N and 31P NMR shielding constants of nonpolar cyclohexane (accordingly, 2-3 and 5-6 ppm) were shown to be roughly half of those of polar acetone (4-7 and 12-13 ppm) and water (5-7 and 13-14 ppm). It was thus demonstrated that solvent corrections to

15

N NMR shielding constants are about

twice as those to 31P NMR shielding constants. ACS Paragon Plus Environment


Page 44 of 59

For 15N NMR shielding constants, vibrational corrections were found to fall into range of ca. -25 to +5 ppm being negative in most cases. Thus the range of vibrational corrections totals to as much as 30 ppm which indeed is very impressive and claims for their mandatory accounting in the related calculations. In the case of 31P NMR shielding constants, vibrational corrections are all negative in sign falling into range of ca. -(12 - 19) ppm with a span of about 7 ppm. It thus follows that vibrational corrections are one of most essential accuracy factors and are to be taken into account in the reliable high-level calculations of 15N and 31P NMR shielding constants and chemical shifts in a wider series of nitrogen and phosphorous heterocycles. It was found that basically relativistic corrections to

15

N NMR chemical

shifts are not surprisingly very small (ca. 0.5 ppm) while those to 31P NMR shifts are a bit larger being of about 1-2 ppm. It thus appears that in the routine calculations of

15

N and

31

P NMR chemical shifts of azoles, phospholes,

phosphazoles and related six-membered systems together with a broad scope of condensed nitrogen and phosphorous containing heterocycles relativistic effects could be safely neglected. To test the reliability of the proposed computational schemes, the benchmark calculations of 15N and

31

P NMR chemical shifts in a series of larger

nitrogen and phosphorous containing heterocycles representing different bonding situations involving nitrogen and phosphorous were performed in comparison with experiment. Based on these results, for the calculation of

15

N and

31

P NMR

chemical shifts in a wide series of nitrogen and organophosphorus compounds at the DFT level the OLYP functional in combination with aug-pcS-3/aug-pcS-2 locally dense basis set scheme is highly recommended. For more accurate results at much higher computational cost, the CCSD(T) level is of course more preferable.

All calculations were performed at A.E. Favorsky Irkutsk Institute of Chemistry of the Siberian Branch of the Russian Academy of Sciences using computational facilities of Baikal Analytical Center. ACS Paragon Plus Environment

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5. Supporting information The following supporting information is available: S1 - Optimized gas phase geometries of 1-23; S2 - Optimized IEF-PCM geometries of 24-34; S3 - Optimized SSM geometries of 24, 25, 28 and 31;

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Figure 1. Correlation plot of theoretical 15N (blue circles) and 31P (green diamonds) NMR chemical shifts of five salient azoles, phospholes and phosphazoles calculated at the CCSD(T)/aug-pcS-4 level with taking into account solvent, vibrational and relativistic corrections versus experiment. 67x60mm (300 x 300 DPI)



Figure 2. Mean absolute errors of different functionals employed in the DFT calculations of 15N (yellow bars) and 31P (blue bars) NMR shielding constants and chemical shifts in the representative series of compounds 1-23. All values are given in ppm in respect to the CMA CCSD(T) results. 179x168mm (300 x 300 DPI)


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Figure 3. Normalized mean absolute errors of different functionals employed in the DFT calculations of 15N (yellow bars) and 31P (blue bars) NMR shielding constants and chemical shifts in the representative series of compounds 1-23. All normalized mean absolute errors represent a percentage of the CMA CCSD(T) values. 179x168mm (300 x 300 DPI)



Figure 4. Averaged IEF PCM solvent corrections to 15N (yellow bars) and 31P (blue bars) NMR shielding constants of 1-23 calculated using OLYP and KT2 functionals. 119x87mm (300 x 300 DPI)


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Figure 5. Supermolecular solvation complexes of 1,2,4-oxazaphosphole with one, two and three molecules of chloroform (accordingly, 24a, 24b and 24c), phosphinine with one molecule of chloroform (25a), benzo[c][1,2,5]oxadiazole with one molecule of acetone (28a) and 9H-carbazole with one molecule of acetone (31a). Element colors: carbon - yellow, hydrogen - grey, nitrogen - blue, oxygen - red, phosphorous - brown and chlorine - green. 66x62mm (300 x 300 DPI)



Figure 6. Minimization process of the supermolecular solvation complex of 1,2,4-oxazaphosphole with three molecules of chloroform 24c. Element colors: carbon - yellow, hydrogen - grey, nitrogen - blue, oxygen red, phosphorous - brown. E stands for the total inner energy while N denotes the number of optimization cycles. All interatomic distances are given in Å. 80x80mm (300 x 300 DPI)


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Figure 7. Ranges of vibrational corrections to 15N (left) and 31P (right) NMR shielding constants. 193x118mm (300 x 300 DPI)



Figure 8. Correlation plot of theoretical 15N (blue circles) and 31P (green diamonds) NMR chemical shifts of salient nitrogen and phosphorous containing heterocycles 24-34 calculated at the DFT level using OLYP (left) and KT2 (right) functionals and aug-pcS-3/aug-pcS-2 locally dense basis set scheme versus experiment. 68x31mm (300 x 300 DPI)


Page 58 of 59

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Graphical abstract 26x10mm (300 x 300 DPI)


Calculation of 15N and 31P NMR Chemical Shifts of Azoles

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