Theoretical prediction of nuclear magnetic shieldings and indirect spin-spin coupling constants in 1,1-, cis-, and trans-1,2-difluoroethylenes.

Theoretical prediction of nuclear magnetic shieldings and indirect spin-spin coupling constants in 1,1-, cis-, and trans-1,2-difluoroethylenes Farhod Nozirov, Teobald Kupka, and Michał Stachów Citation: The Journal of Chemical Physics 140, 144303 (2014); doi: 10.1063/1.4870396 View online: http://dx.doi.org/10.1063/1.4870396 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/14?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Quantitative prediction of gas-phase N 15 and P 31 nuclear magnetic shielding constants J. Chem. Phys. 132, 064109 (2010); 10.1063/1.3310282 Quantitative prediction of gas-phase O 17 nuclear magnetic shielding constants J. Chem. Phys. 131, 024116 (2009); 10.1063/1.3167766 Theoretical predictions of nuclear magnetic resonance parameters in a novel organo-xenon species: Chemical shifts and nuclear quadrupole couplings in HXeCCH J. Chem. Phys. 127, 234314 (2007); 10.1063/1.2805389 Quantitative prediction of gas-phase 13 C nuclear magnetic shielding constants J. Chem. Phys. 118, 10407 (2003); 10.1063/1.1574314 Solvent effects on nuclear shieldings and spin–spin couplings of hydrogen selenide J. Chem. Phys. 108, 2528 (1998); 10.1063/1.475656

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THE JOURNAL OF CHEMICAL PHYSICS 140, 144303 (2014)

Theoretical prediction of nuclear magnetic shieldings and indirect spin-spin coupling constants in 1,1-, cis-, and trans-1,2-difluoroethylenes Farhod Nozirov,1,a) Teobald Kupka,a) and Michał Stachów2,b) 1 2

Department of Physics, 4513 Manhattan College Parkway Riverdale, New York 10471, USA Faculty of Chemistry, Opole University, 48, Oleska Street, 45-052 Opole, Poland

(Received 7 January 2014; accepted 24 March 2014; published online 9 April 2014) A theoretical prediction of nuclear magnetic shieldings and indirect spin-spin coupling constants in 1,1-, cis- and trans-1,2-difluoroethylenes is reported. The results obtained using density functional theory (DFT) combined with large basis sets and gauge-independent atomic orbital calculations were critically compared with experiment and conventional, higher level correlated electronic structure methods. Accurate structural, vibrational, and NMR parameters of difluoroethylenes were obtained using several density functionals combined with dedicated basis sets. B3LYP/6-311++G(3df,2pd) optimized structures of difluoroethylenes closely reproduced experimental geometries and earlier reported benchmark coupled cluster results, while BLYP/6-311++G(3df,2pd) produced accurate harmonic vibrational frequencies. The most accurate vibrations were obtained using B3LYP/6-311++G(3df,2pd) with correction for anharmonicity. Becke half and half (BHandH) density functional predicted more accurate 19 F isotropic shieldings and van Voorhis and Scuseria’s τ -dependent gradient-corrected correlation functional yielded better carbon shieldings than B3LYP. A surprisingly good performance of Hartree-Fock (HF) method in predicting nuclear shieldings in these molecules was observed. Inclusion of zero-point vibrational correction markedly improved agreement with experiment for nuclear shieldings calculated by HF, MP2, CCSD, and CCSD(T) methods but worsened the DFT results. The threefold improvement in accuracy when predicting 2 J(FF) in 1,1-difluoroethylene for BHandH density functional compared to B3LYP was observed (the deviations from experiment were −46 vs. −115 Hz). © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4870396] I. INTRODUCTION

Perfluorinated polymers are significantly more stable and durable at elevated temperatures and in the corrosive environment than conventional materials containing hydrogen atoms. For example, in many demanding fields of application teflon is superior to polyethylene. Among small size molecules containing fluorine,1 the difluoroethylenes2–6 are simple models, suitable to study cis/trans isomers, as well as the presence of one or two halogen atoms at single carbon atom.7–10 In addition, as the lightest and most electronegative halogen, fluorine is computationally attractive. The 19 F isotope is also a very sensitive magnetic nuclei11 in nuclear magnetic spectroscopy (NMR). Its sensitivity is close to 1 H but its signals are spread over significantly larger chemical shift range (about 400 ppm vs 10 ppm in typical proton spectra). This makes fluorine an ideal NMR probe for studies of the structure and properties of both small and large molecular size systems. The use of small molecules as a spectroscopic probe, sensitive to environment and confinement12 is of great importance in nanotechnology, for example, in experimental estimation of pore size distribution in the solid matrix.13, 14 The impact of surface causes modification of structure, electron density redistribution within the probe resulting in changes a) Authors to whom correspondence should be addressed. Electronic ad-

dresses: [email protected] and [email protected].

b) Electronic mail: [email protected].

0021-9606/2014/140(14)/144303/18/$30.00

of vibrational and NMR parameters of “bound” or interacting molecules vs. free ethane12 or SF6 .15 Obviously, a single atom could be used as a probe.16, 17 For example, hyperpolarized xenon has been used in material science and for lung disease diagnostics.17 In the past we used 1 H NMR to study water imbibition (soaking) into hardened cement matrix.18 Recently, studies of cis- and trans-1,2-difluoroethylenes interaction with inner walls of single walled carbon nanotubes were reported.19 In this report the stability of confined difluoroethylenes, as compared with free molecules20 were influenced by interactions with the carbon nanotube walls.19 On the other hand, experimentally it is much easier to follow changes of spectroscopic parameters of the free and confined probe molecule than directly characterize the porous matrix. Among the most suitable techniques for such studies are the vibrational (IR/Raman) and NMR spectroscopies. Surprisingly, there are few recent multinuclear NMR characterization studies of difluoroethylenes.21–26 The old NMR studies at low magnetic field performed about 50 years ago provided inaccurate and incomplete results.21 From an experimental point of view, the problem associated with obtaining, handling, and measuring such gaseous compounds is not trivial. Unfortunately, detailed density functional theory (DFT27 ) studies of nuclear shieldings and spin-spin coupling constants of difluoroethylenes using families of basis sets providing systematic convergence toward the complete basis set (CBS) limit are lacking in the literature. The only high level

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Nozirov, Kupka, and Stachów

predictions of 19 F nuclear shieldings have been reported for small molecules.28 The aim of this study is to use DFT27 to predict structure, vibrational frequencies and multinuclear magnetic shieldings and indirect spin-spin coupling constants of 1,1-, cis-, and trans-1,2-difluoroethylenes. DFT is currently the best compromise between the accuracy and size of the system (the coupled cluster methodology, used with very large basis sets, is impractical in the case of material science studies dealing with hundreds and thousands of atoms). We will explore the advantages and limitations of the selected density functionals for accurate prediction of structure, vibrational and NMR parameters of three model fluorine compounds. The obtained results would hopefully give us some guidelines for future studies on larger size fluorine containing molecules. The accurate structure of difluoroethylenes was recently calculated by Feller and co-workers29 at the coupled cluster30–32 level of theory, with inclusion of core-valence and relativistic contributions combined with very large basis sets. Their benchmark calculations agreed very well with experimental2, 33–35 and recent semi-experimental5 data. In addition, another high level coupled cluster30–32 study of a similar system, difluoroethyne (structure and indirect spin-spin coupling constants, additionally augmented with zero-point vibration corrections) was reported by Faber and Sauer.36 Obviously, structural studies on difluoroethylenes were often based on their infrared spectra.2, 3 Moreover, vibrational analysis of their experimental data3 was supported by theoretical predictions including anharmonic effects.4–10 Among a large number of currently used density functionals37 for practical reasons we selected B3LYP38–40 and BLYP39–41 for structural and vibrational calculations. The first one, in combination with medium and large size basis sets including polarization and diffuse functions, is very efficient (and widely used) in predicting various parameters in all kinds of small and medium size molecules.42 A good performance of these two density functionals in predicting structural and vibrational parameters of a large set of molecules was analyzed using small (3-31G*) and large (6-311++G(3df,2p)) Pople’s type, as well as Dunning’s augcc-pVQZ basis sets.43–47 For example, the authors42 using 631++G* and aug-cc-pVTZ basis sets, noticed a significantly better agreement of BLYP predicted harmonic frequencies with experiment in comparison to widely used B3LYP. Obviously, the predictive power of a particular density functional in case of selected structural and spectroscopic parameters could be related to their ability of fortuitous error cancellation. Thus, in our study, as suggested by one of the reviewers, “BLYP method is judged to be more reliable than B3LYP since better agreement of harmonic computed frequencies with their anharmonic experimental counterparts only shows that there is a fortuitous error compensation between underestimation of harmonic contributions and neglect of anharmonic corrections.” This could be a simple explanation of a closer agreement between BLYP harmonic frequencies and experiment in comparison to B3LYP.42 On the other hand, B3LYP overestimates the harmonic frequencies by 3%–5% and the predicted values are often scaled before comparison with experiment.48, 49 To avoid this

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empirical approach we will use the BLYP density functional which provides significantly lower harmonic frequencies42 (see also our earlier studies50, 51 ). Besides, we will use the second order vibrational perturbation theory52–54 (VPT2) to obtain B3LYP anharmonic frequencies. VPT2 was chosen as a suitable theoretical way leading to a correct way of accounting for anharmonic effects. A significant progress on theoretical treatment of anharmonic effect in molecules of different size has been reported by Barone and co-workers.54–59 Besides, Martin and co-workers60 reported on accurate anharmonic computations on ethylene and a detailed and careful analysis of hybrid methods for the anharmonic analysis of halogen-substituted hydrocabons was recently published from Barone group61 and references therein. Apart from vibrational frequencies, the IR and Raman activities are of great importance. However, their accurate theoretical prediction and analysis is more difficult and will not be considered in the current study. The prediction of 19 F NMR parameters is not an easy task using low level theory.28, 62 Thus, the Becke half and half (BHandH) density functional63, 64 was selected for calculations of fluorine NMR parameters. This functional, combined with large basis sets, was shown62 fairly accurate in calculations of NMR parameters in case of H2 O, F2 , and F2 O. On the other hand, in comparison to B3LYP, the van Voorhis and Scuseria’s τ -dependent gradient-corrected correlation (VSXC) density functional65 was more accurate in predicting carbon shieldings in our earlier studies.66, 67 The systematic pc-n, pcS-n, and pcJ-n series of basis sets (n = 0, 1, 2, 3, and 4), and the corresponding diffuse function augmented (aug-), developed by Jensen43–45 will be used in all NMR calculations. Apparently, the values of three bond FCCF coupling constants should be a sensitive parameter for characterization of cis/trans systems.68–70 However, earlier studies by Sauer and co-workers36 pointed out the serious discrepancy between theory and experiment for the spin-spin coupling constants (SSCC) involving fluorine nuclei in difluoroethyne. In detailed studies involving coupling constants in molecules containing fluorine attached to C=C double bond, Del Bene, Alkorta and Elguero71 observed similar performance of two methods – second-order polarization propagator approximation72, 73 (SOPPA) and equation-ofmotion coupled cluster singles and doubles74 (EOM CCSD). Contreras and co-workers75 noticed an inferiority of the B3LYP density functional in comparison to SOPPA in predicting J(FF) in 1,1-, cis-, and trans-difluoroethylenes. It is worth to note that in these calculations, aug-cc-pVTZ-J basis set, constructed for reliable prediction of indirect spin-spin coupling constants was used46, 72, 75, 76 In particular, the 2 J(FF) value in 1,1-difluoroethylene was underestimated by about 115 Hz by B3LYP while the SOPPA(CCSD) result underestimated experimental coupling only by 18 Hz. It was also noticed that the accuracy of DFT calculated NMR parameters (nuclear shieldings and coupling constants) critically depends on the chosen density functional type and basis set quality (and construction) for a particular molecule or atoms involved in the coupling.66, 77 It is hoped that a well-chosen density functional and basis set combination could significantly improve the predicting power of DFT


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applied to calculations of multinuclear shieldings and indirect spin-spin coupling constants in difluoroethylenes. In this study we will show the possibility of using DFT to predict accurate NMR parameters in three difluoroethylenes using as input their B3LYP/6-311++G(3df,2pd) optimized structures. Obviously, DFT calculations with significantly larger basis set, for example, B3LYP/aug-ccpVTZ are feasible61 but our goal is to use a reasonable level of calculations, applicable to larger molecules containing fluorine. The DFT (BHandH and VSXC) calculated nuclear shieldings and shielding anisotropies of the title compounds in the current study will be estimated toward the CBS limit using a two-parameter formula.78 The final isotropic nuclear magnetic shieldings, shielding anisotropies and indirect spin-spin coupling constants corrected for zero-point vibrational (ZPV) effects79, 80 will be critically compared with available experimental data, as well as theoretical results from the literature and calculated at Hartree-Fock (HF), MP2, CCSD, and CCSD(T) levels of theory. II. METHODS

Most calculations were performed using Gaussian 09 program package.64 CFOUR81 program was used for calculating NMR properties at CCSD and CCSD(T) levels of theory. Pople type basis set 6-311++G(3df,2pd) from Gaussian internal library was used for geometry optimization. Jensen’s type pc-n, pcS-n, and pcJ-n, where n = 0, 1, 2, 3, and 4, basis sets and augmented with diffuse functions (marked with prefix aug-) were downloaded from EMSL Basis Set Exchange.82, 83 Ethylene, 1,1-difluoroethylene, cis-1,2difluoroethylene, and trans-1,2-difluoroethylene were used to assess the accuracy of the used methodology. Their structures and atom numbering are shown in Scheme 1. These model molecules were fully optimized at the B3LYP/ 6-311++G(3df,2pd) and BLYP/6-311++G(3df,2pd) levels of theory. The subsequent vibrational analysis verified the presence of minimum energy structures48, 84 (lack of imaginary frequencies). Anharmonic corrections to B3LYP and BLYP vibrational frequencies were calculated in Gaussian 09 using the default deperturbed VPT2 (DVPT2).54 Gauge-independent atomic orbital (GIAO) NMR nuclear isotropic shieldings and shielding anisotropies were calculated at B3LYP/6-311++G(3df,2pd) structures. Initially, BHandH/aug-pcJ-2 shieldings and shielding anisotropies were calculated for molecules I–IV. The ZPV corrections to nuclear shieldings in 1,1-difluoroethylene were calculated in CFOUR81 program using Hartree-Fock method combined

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with dzp, tz2p, qz2p, and pz3d2f basis sets. The empirical values28, 66, 77, 79, 80, 85, 86 of shieldings and couplings (Xemp ) were obtained by augmenting experimental values (Xexp ) with calculated ZPV (subtracting from experiment) or adding ZPV to theoretical values (Xcalc ): Xemp = Xcalc +ZPV

(1)

Xemp = Xexp − ZPV.

(2)

or

The nonrelativistic nuclear shieldings87 (σ ) were calculated as the sum of diamagnetic (σ dia ) and paramagnetic terms (σ para ): σ = σdia + σpara .

All nonrelativistic Ramsay components88 of indirect spin-spin coupling constant between two spins (A and B), separated by n bonds, e.g., Fermi contact (FC), spin-dipol (SD), diamagnetic spin-orbit (DSO) and paramagnetic spin-orbit (PSO) were calculated: n

J (AB) = FC + SD + DSO + PSO.

(4)

We did not calculate ZPV corrections to SSCCs since the HF calculated indirect spin-spin coupling constants are unreliable. The BHandH calculated SSCCs were directly compared to CCSD/pcJ-2 results treated as benchmark and to experiment. NMR parameters calculated using CCSD are close to CCSD(T) results89 and pcJ-2 basis set is large enough to provide accurate coupling constants.44 Initially, the B3LYP/6-311++G(3df,2pd) structures were used as input for GIAO90, 91 NMR calculations and estimation of SSCC values using BHandH density functional and aug-pcJ-2 basis set. Next, detailed GIAO NMR calculations were performed at the level of CCSD and CCSD(T) using two families of basis sets: pc-n and aug-pcS-n (for n = 0, 1, 2, 3, and 4) in the parallel version of the CFOUR program.81, 92 All calculations of SSCC parameters at CCSD/(aug-) pcJ-n level of theory were also performed in CFOUR. This program also allowed calculating ZPV correction to nuclear shieldings at Hartree-Fock level using several Karlsruhe type basis sets (dzp, tz2p, qz2p, pz3d2f, and 13s9p4d3f93–95 ). Finally, the GIAO NMR calculations of the difluoroethylenes nuclear shielding tensor at Hartree-Fock, MP2, BHandH, and VSXC levels of theory were performed in Gaussian 09.64 The nuclear shieldings and coupling constant values (and their components), calculated with two largest basis sets (e.g., for n and n − 1, where n indicates the size of Jensen’s basis sets pc-n, pcJ-n, aug-pcS-n, aug-pcJ-n, and ACBS and B are the fitting parameters), were used for estimation of ACBS parameters using a simple two-parameter formula:78 Y (n) = ACBS +B/n3 .

SCHEME 1. Structures and atom numbering in (I) ethylene, (II) 1,1-difluoroethylene, (III) cis-1,2-difluoroethylene, and (IV) trans-1,2difluoroethylene.

(3)

(5)

This formula, originally derived for accurate thermochemical calculations, was used in our previous studies on accurate estimation of NMR parameters, including nuclear shieldings, shielding anisotropy, and indirect spin-spin coupling constants in the model systems.66, 67, 77 Recently, Gauss and co-workers applied a similar fitting to obtain accurate NMR properties in the CBS limit.96


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TABLE I. Theoreticala and experimental structuresb of ethylene and its selected difluoro-derivatives. Parameter Method

B3LYP BLYP Best composite theoryc Best composite theoryd Semi-experimental re e

r(CC)

r(CH) Ethylene 1.0823 1.0887 1.0809 1.0803 1.0805(10)

1.3246 1.3341 1.3307 1.3308 1.3305(10)

Deviation from semiexperimental re B3LYP − 0.0059 BLYP 0.0036 0.0002 Best composite theoryc Best composite theoryd 0.0003 B3LYP BLYP Best composite theoryf Semi-experimental re f

1.3209 1.3318 1.3246 1.323(1)

0.0011 0.0073 − 0.0004 cis 1,2-difluoroethylene 1.079 1.0856 1.0772 1.075(1)

Deviation from semi-experimental re B3LYP − 0.0021 BLYP 0.0088 0.0016 Best composite theoryf B3LYP BLYP Best composite theoryf Semi-experimental re f

1.3196 1.3304 1.3239 1.324(1)

0.0040 0.0106 0.0022

RMSg (deviation from semi-experimental re ) B3LYP 0.0040 BLYP 0.0069 0.0009 Best composite theoryc,f 0.0009 Best composite theoryd,f

1.3207 1.3389 1.3157 1.3157(2)

119.82 119.90 119.38 119.40(1)

125.24 125.25 125.14 125.16(2)

0.0050 0.0232 0.0000

0.42 0.50 − 0.01

0.08 0.09 − 0.02

1.3376 1.355 1.3336 1.334(1)

122.75 122.99 122.76 122.5(1)

122.70 122.72 122.19 122.3(1)

0.0036 0.0210 − 0.0004

trans 1,2-difluoroethylene 1.0796 1.0859 1.0777 1.078

Deviation from semi-experimental re B3LYP − 0.0044 BLYP 0.0064 − 0.0001 Best composite theoryf

CCF

0.29 0.34 − 0.01 − 0.05

1,1-Difluoroethylene 1.0765 1.0827 1.0750 1.0754(1)

1.3151 1.3253 1.3181 1.3175(4)

CCH

121.74 121.79 121.44 121.4 121.45(10)

0.0018 0.0082 0.0004 − 0.0002

Deviation from semi-experimental re B3LYP − 0.0024 BLYP 0.0078 0.0006 Best composite theoryf B3LYP BLYP Best composite theoryf Semi-experimental re f

r(CF)

1.3435 1.3616 1.3396 1.339(1)

0.25 0.49 0.26

0.40 0.42 − 0.11

125.4 125.83 125.34 125.1(1)

120.23 120.07 119.72 119.8

0.0016 0.0079 − 0.0003

0.0045 0.0226 0.0006

0.30 0.73 0.24

0.43 0.27 − 0.08

0.0024 0.0086 0.0011 0.0011

0.0044 0.0223 0.0004 0.0004

0.32 0.53 0.18 0.18

0.34 0.29 0.08 0.07

a

Calculated in this study with 6-311++G(3df,2pd) basis set. Bond lengths in Å and bond angles in degrees. Available experimental uncertainties in parentheses. c From Ref. 99. d From Ref. 100. e From Ref. 101. f From Ref. 29. g RMS is calculated as root mean square deviation of calculated values from experiment (semi-experimental value): RMS √ = [(x1 (calc) − x(expt))2 + . . . . + ((xn (calc) − x(expt))2 /n]. b

III. RESULTS AND DISCUSSION

Since NMR calculations are performed on experimental or optimized structure we first selected a level of theory suitable for producing fairly accurate geometry of larger molecules containing fluorine atoms. Thus, instead of

performing high level CCSD(T) geometry optimization we selected, somehow pragmatically (e.g., as a trade-off between accuracy and computational cost), the traditional hybrid density functional B3LYP and the Pople type basis set 6-311++G(3df,2pd). The BLYP was selected to check its feasibility of predicting harmonic frequencies involving C-F


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TABLE II. Differences in DFT predicteda bond lengths (in Å) in difluoroethylene isomers. cis–trans Method B3LYP BLYP Best composite theory Semi-experimental re a

cis–geminal

geminal–trans

CC

CH

CF

CC

CH

CF

CC

CH

CF

0.001 0.001 0.001 − 0.001

− 0.001 0.000 − 0.001 − 0.003

− 0.006 − 0.007 − 0.006 − 0.005

0.006 0.007 0.006 0.006

0.002 0.003 0.002 0.000

0.017 0.016 0.018 0.018

− 0.005 − 0.005 − 0.006 − 0.007

− 0.003 − 0.003 − 0.003 − 0.003

− 0.023 − 0.023 − 0.024 − 0.023

Using 6-311++G(3df,2pd) basis set. Literature values from Ref. 29 are given for comparison.

vibrations closer to experiment than other density functionals.50, 51 Selection of such large and flexible basis set, additionally augmented with diffuse functions, should produce results similar to obtained with Dunning’s type aug-cc-pVDZ, and sometimes aug-cc-pVTZ basis sets.43–47 On the other hand, this basis set is significantly smaller than aug-cc-pVTZ or pc-3. Obviously, the results of calculations with 6-311++G(3df,2pd) basis set are still far from the complete basis set limit (CBS97, 98 ). However, this level of theory warrants obtaining structural and vibrational parameters for relatively large molecules without significant cutting on accuracy.42

A. DFT structure of difluoroethylenes

In the first step of our study we performed fully unconstrained geometry optimization with B3LYP and BLYP density functionals, combined with 6-311++G(3df,2pd) basis set, and followed by a vibration analysis for ethylene (as the starting molecule), 1,1-difluoroethylene, cis- and trans-1,2difluoroethylenes (see Scheme 1). The B3LYP and BLYP bond lengths and bond angles, calculated with 6-311++G(3df,2pd) basis set and compared with semi-experimental values and high level theoretical parameters from the literature are gathered in Table I. Calculated structural parameters of the title difluoroethylenes were compared with semi-experimental and best composite theory results reported by Feller and co-workers.29 It is worth noting that the overall root mean square (RMS) deviations with respect to semi-experimental data are small (0.002 Å for C–H, 0.004 Å for C=C and C–F bonds, and 0.3◦ for angles calculated with B3LYP) and the applied density functionals approach the performance of the best composite theory29, 99, 100 (RMS for CH, CC and CF bonds are about 0.0004–0.001 Å and for angles from 0.07 to 0.2◦ ). The BLYP predicted parameters (RMS of CF distances and angles are 0.02 Å and 0.5◦ ) are somehow worse than the B3LYP ones. The quality of DFT predicted structural parameters was reflected in the method’s ability to reproduce the so-called “cis-effect.10, 102 ” The cis-effect in dihalogenoethylenes is manifested by an observation that the C-halogen bond in cis isomer is markedly shorter than in the trans one (Table II). It is also apparent from Table II that the C–F bond in 1,1difluoroethylene calculated with B3LYP and BLYP density functionals is significantly shorter than in cis- or trans isomers. These DFT calculated differences in C–F bonds be-

tween the isomers are consistent and identical (within 0.001– 0.002 Å) to semi-experimental and benchmark values.29 Besides, for brevity, in the supplementary material we compared graphically the deviations of structural parameters calculated using DFT and Hartree-Fock methods with several basis sets from the best available semi-empirical ones (see Figures S1(a) and S1(b) in the supplementary material.119 ) The HF method was used for obtaining ZPV corrections at reasonable computational time.81 The results in Figures S1A and S1B indicate about five time smaller deviations of bond lengths from experiment in 1,1-difluoroethylene calculated using B3LYP density functional in comparison to HartreeFock (HF). It is also important to note, that the improvement of basis set quality slightly worsens deviations of HF calculated structural parameters from experiment. B. DFT calculated harmonic and anharmonic vibrations of difluoroethylenes

The theoretically predicted harmonic B3LYP, BLYP, and anharmonic B3LYP wavenumbers are gathered in Table III. Experimental IR103, 104 and semi-experimental101 structural data for ethylene were compared to our parameters and the best reported theoretical results.99, 100 The observed harmonic (calculated benchmark data for cis- and trans- species) and fundamental wavenumbers for 1,1-difluoroethylene,4, 5 cis-1,2-difluoroethylene,3, 29 and trans-1,2-difluoroethylene3, 8 were used for comparison with calculated frequencies. Interestingly, in case of ethylene103, 104 the deviation between theoretical harmonic wavenumbers calculated with B3LYP density functional and the observed fundamental values is nearly three times higher than for BLYP (RMS of about 77 vs. 27cm−1 ) and the significantly more expensive VPT2 calculations using B3LYP functional produces the best agreement (RMS = 17.4 cm−1 ). In case of 1,1-, cis, and trans-difluoroethylenes3, 8, 29 the same order of RMS values is observed (B3LYP > BLYP > B3LYP(anharm)). However, in case of 1,1-difluoroethylene4, 5 larger values of RMS are obtained for harmonic and anharmonic wavenumbers calculated with B3LYP (RMS of about 53 and 18 cm−1 ) while BLYP is less efficient (RMS = 36 cm−1 ). This shows the difficulties in calculating BLYP vibrational frequencies in the case of two fluorine atoms attached to the same carbon atom. On the other hand, the results from Table III point out at BLYP density functional combined with a fairly flexible basis set (6-311++G(3df,2pd)) as a pragmatic choice for calculating reliable fundamental frequencies


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of cis- and transdifluoroethylenes (VPT2 combined with B3LYP density functional and 6-311++G(3df,2pd) basis set for larger molecules is significantly more computationally demanding than BLYP/6-311++G(3df,2pd) calculations better reproducing experimental frequencies). C. DFT predicted nuclear magnetic shielding constants in difluoroethylenes

First we compared the performance of BHandH density functional combined with the aug-pcJ-2 basis set in predicting nuclear shieldings in molecules I–IV. This basis set is

fairly large and primarily designed for predicting coupling constants.44 However, it is also very efficient in predicting shielding parameters.66 Thus, the selection of this basis set should allow prediction of fairly accurate shieldings and couplings in a single calculation. In addition, this level of theory could be applicable to larger molecular systems including carbon and fluorine atoms. Theoretical BHandH/aug-cc-pcJ-2//B3LYP/6-311++G (3df,2pd) calculated isotropic shieldings and few available experimental results for ethylene and its difluoro derivatives are compared in Table IV with a few limited theoretical values28, 66, 96 and experiment.24, 25, 107

TABLE III. Comparison of harmonic B3LYP, BLYP and anharmonic B3LYP frequencies calculated with 6-311++G(3df,2pd) basis set with observed (or benchmark) harmonic and fundamental wavenumbers (in cm−1 ) for 1,1-, cis-, and trans-1,2-difluoroethylenes. DFT calculated modes and symmetries are given according to decreasing wavenumbers. Observed vibration Mode (symmetry)

9 (B2u ) 5 (B3g ) 1 (Ag ) 11 (B1u ) 2 (Ag ) 12 (B1u ) 3 (Ag ) 6 (B3g ) 4 (Au ) 7 (B3u ) 8 (B2g ) 10 (B2u )

Harmonic

Fundamental

B3LYP

BLYP

B3LYP (anharm)

Assignment

3239.1 3206.9 3156.4 3129.8 1656.4 1471.8 1372.3 1248.5 1044.6 968.3 960.3 844.1

3104.89 3083.36 3022.03 2988.64 1625.40 1442.47 1343.54 1222.00 1025.59 948.77 939.86 825.93

Ethylenea 3224.5 3196.8 3139.7 3125.9 1689.2 1479.4 1381.3 1246.5 1063.5 985.5 979.5 836.7

3146.6 3118.0 3063.6 3051.9 1635.5 1445.7 1347.1 1216.2 1034.5 946.1 942.0 818.9

3081.2 3056.0 3006.9 2975.5 1646.8 1444.9 1356.8 1223.8 1040.6 968.8 964.0 835.4

CH2 as stretch CH2 as stretch CH2 s stretch CH2 s stretch CC stretch CH2 scissor CH2 scissor CH2 rock CH2 twist CH2 wag CH2 wag CH2 rock

27.3

17.4

3175.6 3075.2 1735.0 1375.8 1305.0 953.8 925.8 802.1 708.2 609.5 549.6 436.9

77.4 1,1-Difluoroethyleneb 3294.1 3194.9 1768.4 1415.0 1296.9 963.1 938.4 836.3 722.6 632.7 550.0 442.9

3217.4 3121.8 1696.0 1378.5 1220.3 926.7 891.4 790.0 695.0 597.9 525.6 429.5

3153.4 3048.2 1732.2 1359.2 1264.3 945.1 923.6 819.2 706.5 624.0 545.8 442.8

36.1

17.8

3136.0 3122.0 1716.0 1374.0 1263.0 1130.0 1015.0 839.0 769.0 756.0 495.0 237.0

52.7 cis 1,2-difluoroethylenec 3236.3 3214.2 1758.7 1394.8 1287.8 1137.2 1020.4 880.8 779.4 779.2 517.4 239.6

3154.6 3132.9 1680.0 1346.0 1244.7 1081.3 970.6 823.0 749.3 741.3 493.3 232.2

3103.3 3127.0 1725.5 1363.9 1265.2 1112.7 995.6 853.7 764.6 769.6 507.9 238.8

RMS (fundamentals) 9 (B2 ) 1 (A1 ) 2 (A1 ) 3 (A1 ) 10 (B2 ) 11 (B2 ) 4 (A1 ) 7 (B1 ) 6 (A2 ) 8 (B1 ) 5 (A1 ) 12 (B2 )

3313.9 3204.0 1775.9 1418.5 1337.5 973.4 940.8 828.3 721.8 619.5 554.5 437.8

RMS (fundamentals) 8 (A1 ) 1 (B2 ) 2 (A1 ) 9 (B2 ) 3 (A1 ) 10 (B2 ) 4 (A1 ) 6 (A2 ) 11 (B2 ) 12 (B2 ) 7 (A2 ) 5 (A1 ) RMS (fundamentals)

3252.2 3226.6 1751.3 1394.6 1278.9 1147.6 1018.3 829.8 770.6 769.2 498.1 232.8

45.1

26

CH2 as stretch CH2 s stretch C=C stretch CH2 scissor CF2 as stretch CH2 rock CF2 s stretch CH2 wag C=C twist CF2 wag CF2 scissor CF2 rock

CH as stretch CH s stretch C=C stretch FCH scissor FCH scissor CF s stretch CF as stretch CH scissor CCF def CH2 scissor FC=CF torsion CCF def

14.6


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TABLE III. (Continued.) Observed vibration Mode (symmetry)

1 (Ag ) 9 (Bu ) 2 (Ag ) 3 (Ag ) 10 (Bu ) 11 (Bu ) 4 (Ag ) 8 (Au ) 6 (Bg ) 5 (Ag ) 7 (Au ) 12 (Bu )

Harmonic

Fundamental

3241.9 3232.5 1735.2 1303.3 1290.9 1178.7 1150.6 894.3 780.9 552.0 332.8 311.8

3109.0 3101.0 1702.0 1286.0 1274.0 1159.0 1123.0 874.0 788.0 552.0 335.0 324.0

B3LYP trans 1,2-difluoroethylened 3222.9 3216.1 1746.1 1312.4 1298.5 1164.6 1148 910.5 833.7 557.5 338.1 320.9

RMS (fundamentals) a

103

52.9

BLYP

B3LYP (anharm)

Assignment

3144.7 3138.6 1666.9 1274.1 1256.3 1101.4 1090.5 868.1 778.6 534.9 321.5 310.1

3086.0 3100.4 1706.3 1290.3 1272.9 1143.3 1128.4 887.8 815.7 551.0 336.6 321.3

CH s stretch CH as stretch C=C stretch HCF sciss HCF sciss CF as stretch CF s stretch CHF wag CHF wag CCF def CHF twist CHF rock

28.2

12.3

104

Observed harmonic and fundamental wavenumbers. Mode assignment from Refs. 105 and 106. Harmonic and fundamental vibrations taken from Refs. 4 and 5. Assignment from Refs. 9 and 106. c Harmonic CCSD(T)(FC)/aug-cc-pVTZ calculated29 and experimental fundamental vibrations taken from Ref. 3. Assignment from Refs. 6 and 106. d Harmonic CCSD(T)(FC)/aug-cc-pVTZ calculated29 and experimental fundamental vibrations taken from Refs. 3 and 8. Assignment from Refs. 6 and 106. b

Calculated NMR shieldings of ethylene were compared with available empirical66, 108 and literature values.94 It is apparent that in the case of ethylene, BHandH correctly predicts proton isotropic shieldings108 (they deviate from empirical value66 by about −0.5 ppm) but significantly (by about −21 ppm) underestimates absolute carbon shieldings.66, 94, 96 This is a typical drawback of DFT methods which tends to overestimate the paramagnetic component of total shielding96, 109 (the dominating term in case of carbon and oxygen nuclei). Obviously, the use of a reference molecule significantly would improve the agreement of theoretical chemical shift with experiment. Moreover, taking into account a very large range of 19 F NMR chemical shift (about 400 ppm), the RMS of fluorine isotropic shieldings (8.0 ppm) is acceptable. However, it is surprising to notice a very poor agreement between calculated and experimental proton shieldings (RMS = 2.3 ppm). This is a significantly worse performance of BHandH density functional, combined with a fairly large basis set, than observed before for a set of over 40 density functionals.66 Obviously, the inclusion of ZPV corrections would produce even worse proton shieldings (increasing them by about 0.5 ppm, see Refs. 66 and 96). In the next step we analyzed the sensitivity of both isotropic nuclear shieldings and shielding anisotropy of all nuclei in the investigated difluoroethylenes to the basis set quality using two density functionals, BHandH and VSXC in comparison to the results of HF, MP2, CCSD, and CCSD(T) calculations. In these calculations we selected a general purpose pc-n basis set and aug-pcS-n. The latter polarizationconsistent basis set is dedicated for nuclear shieldings prediction but is significantly larger than the former one. We also expected to see a systematic convergence of DFT and HF predicted nuclear shieldings and shielding anisotropy toward the CBS limit for n > 1. The patterns of multinuclear isotropic

shieldings in cis-difluoroethylene (Figures 1(a)–1(c)) and the corresponding shielding anisotropies (Figures 2(a)–2(c)) are shown as representative examples, illustrating the behavior of the calculated NMR shielding parameters upon improving the basis set size and quality. For brevity, the remaining figures are included in the supplementary material119 (Figures S2 and S3). In all cases the results obtained with n = 0 are very far from the converged numbers (for n = 3 and 4). So, it is important to stress here that the CCSD(T)/aug-pcS-0 calculated carbon shielding in cis isomer is about 30 ppm higher than the corresponding value obtained for n = 2. Thus, it is much better to predict nuclear shieldings in these systems using HF or DFT methods with larger basis sets (n = 2 or higher). In fact, for n = 2 to 4 all the changes of NMR parameters are very small. Besides, the NMR parameters obtained for pc-0 and aug-pcS-0 differ significantly and for n = 2 the results obtained with basis sets without, or with inclusion of diffuse functions, are very similar. The decreasing (or increasing) of NMR parameter values along with increase of n from 0 to 2 is common for all methods (from DFT to HF and coupled clusters). Unfortunately, due to computer resources problems, the largest calculations with correlated methods were unsuccessful. On the other hand, there were problems with HF convergence in cases (VSXC/aug-pcS-4), and some calculations failed. The results shown in Figure 1 indicate some important features of methods used for nuclear shielding calculation in cis-1,1-difluoroethylene. First, the carbon shieldings predicted with HF, MP2, and coupled cluster methods are higher by about 10 and 15 ppm than the VSXC and BHandH results (for n = 2–4). In case of fluorine shieldings these differences are more significant (35 and 20 ppm) and HF overestimates the correlated results by about 10 ppm. In case of proton shieldings (Figure 1(c)), both density functionals


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TABLE IV. Theoreticala and experimental isotropic shieldings for selected ethylene derivatives compared with benchmark literature values and experiment. Isotropic shielding Method BHandH/aug-pcJ-2 Lit. Empirical

C1

C2 Ethylene

F

48.4151 69.71b 69.4c

25.4077 26.05b 25.93c

Deviation from empirical value BHandH/aug-pcJ-2 − 20.9849 BHandH/aug-pcJ-2 Expt. Lit. Empirical

8.8544

− 0.5223 1,1-Difluoroethylene 116.9854 265.9004 278.6d 287.6f 277.4g

Deviation from empirical (or experimental) value BHandH/aug-pcJ-2 BHandH/pcJ-2 Expt. Lit.c Empirical(theory)

35.4071

− 11.500 cis 1,2-difluoroethylene 354.7943

27.212 29.801e

− 2.589 24.7834 27.370h

370.7f 361.4i

Deviation from empirical (or experimental) value BHandH/aug-pcJ-2 BHandH/aug-pcJ-2 Expt. Lit.c Empirical (theory)

H

25.0246

Deviation from empirical (or experimental) value BHandH/aug-pcJ-2 RMS BHandH/aug-pcJ-2

− 6.606 trans 1,2-difluoroethylene 385.3029

− 2.587 23.5767 26.421h

397.7f 389.3j − 3.997

− 2.844

7.997

2.332

a

GIAO BHandH/aug-pcJ-2 calculations on B3LYP/6-311++G(3df,2pd) optimized structure. CBS extrapolated result, CCSD(T)/aug-cc-pCV[TQ] from Ref. 96, and based on Refs. 78, 79, 86, and 87. c CBS extrapolated result, CCSD(T)/CBS(pcS-n) from Ref. 66. d Experimental value taken from Ref. 28. e 60 MHz 1 H NMR in cyclohexane,24, 25, 107 shielding calculated using σ (TMSliq ) = 33.485 ppm from Refs. 96, 110, and 111. f CCSD(T)/13s9p4d3f//CCSD(T)/cc-pVTZ result from Ref. 28. g CCSD(T)/13s9p4d3f//CCSD(T)/cc-pVTZ result augmented with MP2/qz2p/MP2/cc-pVTZ calculated ZPV (−7.79 ppm) and temperature correction (−0.43), from Ref. 28. h 60 MHz 1 H NMR in cyclohexane,24, 25, 107 shielding calculated using σ (TMSliq ) = 33.485 ppm from Refs. 96, 110 and 111. i CCSD(T)/13s9p4d3f// CCSD(T)/cc-pVTZ result augmented with MP2/qz2p/MP2/cc-pVTZ calculated ZPV (−8.63 ppm) and temperature correction (−0.63), from Ref. 28. j CCSD(T)/13s9p4d3f// CCSD(T)/cc-pVTZ result augmented with MP2/qz2p/MP2/cc-pVTZ calculated ZPV (−7.83 ppm) and temperature correction (−0.62), from Ref. 28. b

underestimate the coupled cluster and MP2 result by about 0.6 ppm and HF produces only slightly overestimated results (by about 0.1 ppm). The behavior of the calculated NMR shielding anisotropies with BHandH and VSXC density functionals in cis-1,2-difluoroethylene upon improving the basis set size and quality is shown in Figures 2(a)–2(c). In this case the calculated parameters are roughly constant for n = 2–4. Interestingly, the carbon shielding calculated with HF and BHandH is about 15 ppm higher than the VSXC and CCSD result. On the contrary, the DFT calculated fluorine shielding anisotropy is about 30 ppm higher than the CC result (HF underestimates the CCSD result by less than 10 ppm). The difference between VSXC and HF calculated

proton shielding anisotropy is about 0.6 ppm only. In this case the HF result is also able to closely reproduce the CCSD result. Accurate prediction of NMR parameters requires inclusion of zero-pint vibrational corrections (ZPV) and temperature corrections (TC). The latter term is typically an order of magnitude smaller than ZPV correction and is often omitted. It is important to notice that due to very expensive calculations, the ZPV are often obtained at significantly lower level of theory (HF or DFT) than coupled cluster. Besides, the ZPV correction values for 19 F shieldings in a large set of small molecules, recently obtained by Gauss and co-workers28 using HF and MP2 methods, were fairly similar (within 10%–15%). Thus, in Table V we compared isotropic nuclear


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FIG. 1. Convergence of (a) carbon, (b) fluorine, and (c) proton nuclear isotropic shieldings in cis-1,2-difluoroethylene calculated with BHandH and VSXC density functionals combined with pc-n and aug-pcS-n basis set (for n = 0–4). For comparison results of HF, MP2, CCSD, and CCSD(T) calculations are shown.

shieldings and shielding anisotropies for 1,1-difluoroethylene obtained at HF level of theory before and after inclusion of ZPV. The ZPV corrections were calculated using HF method combined with several basis sets, ranging from dzp to 13s9p4d3f, and with available literature values.28 These results indicate a relatively small impact of geometry calculation (basis set quality) on the ZPV corrections. In short, for C1, C2, F and H shieldings in 1,1difluoroethylene the predicted ZPV correction values are roughly −3, −2, −7, and −0.5 ppm. The earlier reported ZPV correction values28 for 19 F nuclear shieldings in cis-, trans-, and 1,1-difluoroethylenes calculated using HF (−7.65, −6.68, and −6.89 ppm) and MP2 methods (−8.63, −7.83, and −7.79 ppm) are within 10%–20%. Therefore, we could assume that the calculated in our study ZPV corrections could be used as “transferable” values between different molecules (e.g., we could assume roughly similar values of multinuclear ZPVs for 1,1-, cis-, and trans-isomers). We also gathered the DFT calculated, and subsequently CBS estimated (using two-parameter formula) nuclear shieldings and shielding anisotropies of the difluoroethylenes using pc-n and aug-pcS-n basis sets (Table VI). For comparison the CBS values obtained at the HF level of theory, as well as the MP2, CCSD, and CCSD(T) results calculated with the largest possible basis sets are also included. The VSXC functional predicts significantly better carbon shielding parameters than

BHandH. However, in case of 19 F shieldings the quality of results is reversed. Finally, both the studied density functionals underestimate proton shielding in difluoroethylenes (see Figure 1 and Table VI). In case of shielding anisotropy the performance of these density functionals is similar (see also Figures S4 and S5 in the supplementary material.119 ) The data from Table VI (and Figure 1) suggest using pc-n instead of significantly larger aug-pcS-n basis set for estimating CBS values at DFT or HF level of theory. Besides, the DFT calculated shieldings and shielding anisotropies are significantly worse than those, obtained at the correlated levels of theory. Again, the simplest method without electron correlation (c) performs significantly better than DFT. In order to illustrate the differences in performance of different methods in predicting 19 F isotropic nuclear shielding (notoriously known as very difficult to predict theoretically) we calculated the deviation of our results for 1,1difluoroethylene from experimental value in Table VII. To make a direct comparison we included the ZPV corrections and TC values obtained at HF (−6.89, −0.28 ppm) and MP2 (−7.79 and −0.43 ppm) levels of theory reported by Gauss and co-workers.28 The results in Table VII are very surprising. First, they indicate that fluorine shielding is very sensitive to ZPV and temperature corrections. Thus, raw data (without correction) predict fluorine shielding significantly underestimated


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FIG. 2. Convergence of (a) carbon, (b) fluorine, and (c) proton shielding anisotropies in cis-1,2-difluoroethylene calculated with BHandH and VSXC density functionals combined with pc-n and aug-pcS-n basis set (for n = 0–4). For comparison results of HF, MP2, CCSD, and CCSD(T) calculations are shown.

by VSXC and BHandH (−21 and −13 ppm) and overestimated by HF by about 23 ppm). Besides, the MP2 method predicts its value better than coupled cluster theory (7 vs. 10 and 9 ppm). However, in this case one could suspect that the MP2 results were obtained with significantly better quality basis set than the CCSD or CCSD(T) shieldings. The inclusion of ZPV and TC corrections calculated at MP2 level of theory28 significantly improves shieldings calculated with HF, MP2, CCSD, and CCSD(T) methods (the deviations decrease to 15, −1, 7, and 2 ppm). The use of these corrections calculated at HF level increases the deviations by only about 1 ppm. However, the DFT shieldings augmented with ZPV corrections are significantly worse (deviations of −20 to −29 ppm). These results point out the difficulties of DFT in predicting 19 F nuclear shieldings and a surprisingly good result obtained with HF method. In other words, no ZPV correction should be applied to DFT predicted nuclear shieldings. Obviously, the exceptional good performance of HF could originate from a fortuitous error cancellation. This observation is in agreement with earlier studies.28 D. DFT predicted indirect spin-spin coupling constants in difluoroethylenes

In analogy to nuclear shieldings, we started with BHandH/aug-pcJ-2 calculations of indirect spin-spin coupling constants in ethylene as the parent molecule and its three difluoro derivatives. BHandH density functional was success-

ful in predicting water coupling constants,112 for example, it fairly well reproduced the experimental value of 1 JOH and also showed the dominating role of Fermi contact term (FC). In Table VIII are gathered all Ramsay terms of spin-spin couplings, the total theoretical value predicted at BHandH/aug-pcJ-2 level of theory and the available calculated70, 71, 75, 77, 79, 113 and experimental22–25, 107, 114–117 value for the studied molecules. In case of ethylene79, 86, 114 this level of theory predicts fairly accurate coupling constants (RMS deviation of 3.3 Hz, no correction for ZPV included). It is apparent from Table VIII that the calculated spin couplings between geminal, cis and trans protons in ethylene differ significantly (2 J(HH)gem , 3 J(HH)cis and 3 J(HH)trans are 0.9, 13.9, and 20.2 Hz). Besides, all couplings in ethylene are dominated by Fermi contact (FC) term and only in case of 2 J(HH) the PSO term dominates (4.2 Hz). However, the PSO term is nearly completely cancelled by DSO (−3.8 Hz) and the total SSCC value is very small (0.9 Hz). In fact, all the SSCC values in ethylene are fairly correctly calculated at this level of DFT theory. Obviously, it is relatively easy to calculate SSCC parameters in ethylene fairly accurately using DFT while determining them experimentally is not so trivial since the molecular symmetry has to be lowered by selective labeling with 13 C atom. Different Ramsay terms dominate one, two and threebond couplings between various nuclei in difluoroethylenes (Table VIII). The PSO term dominates coupling constants involving the two fluorine atoms in geminal, cis, or trans


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TABLE V. HF calculated isotropic shieldings and shielding anisotropies (in ppm) in 1,1-difluoroethylene before and after inclusion of ZPV correction. Basis set Parameter

dzp

tz2p

qz2p

pz3d2f

Isotropic shielding ZPV correction Isotropic shielding + ZPV Shielding anisotropy Shielding anisotropy + ZPV

45.732 − 2.002 43.73 99.42 100.326

C1 30.692 − 1.879 28.813 108.099 108.927

28.676 − 1.971 26.705 110.817 111.731

28.15 − 2.008 26.141 109.825 110.756


139.933 − 3.109 136.824 70.531 71.12

C2 130.678 − 2.955 127.723 74.672 75.04

128.32 − 3.04 125.28 74.716 75.128

128.972 − 3.077 125.895 74.427 74.845


318.948 − 6.746 312.202 69.504 77.189

F 306.499 − 6.894 299.605 80.207 87.827

309.245 − 7.026 302.22 73.418 81.118

308.426 − 6.929 301.498 71.289 79.002


28.277 − 0.474 27.803 5.956 5.716

H 28.475 − 0.481 27.994 5.394 5.164

28.466 − 0.477 27.989 5.236 5.007

28.336 − 0.473 27.863 5.173 4.929

Lit.

302.7a ; 291.7b − 6.89c ; −7.79d

a

HF /qz2p//CCSD(T)/cc-pVTZ from Ref. 28. CCSD(T)/qz2p//CCSD(T)/cc-pVTZ from Ref. 28. c HF /tz2p from Ref. 28. d MP2/qz2p from Ref. 28. b

positions. On the contrary, the FC term is prevailing for the remaining couplings. As mentioned before, DFT significantly underestimates the 2 J(FF). Comparing the SOPPA results, Barone and co-workers75 noticed that this coupling, calculated with B3LYP in 1,1-difluoroethylene, was underestimated by about 115 Hz! Our value, obtained with BHandH density functional, is about two to three times more accurate and deviates from the literature value by about −46 Hz. Interestingly, in case of 3 J(FF), the BHandH functional performs markedly better for both cis and trans isomers and deviates from experiment only by 12.5 and 12.2 Hz. In addition, BHandH is also unable to correctly predict 1 J(CF) in 1,1difluoroethylene (−322 calculated vs. −287 Hz observed). Overall, the total RMS deviation of BHandH/aug-pcJ-2 calculated couplings in difluoroethylenes from available experimental values is fairly high (16.7 Hz). In the next step we compared the performance of BHandH/aug-pcJ-2 in predicting n J(FF) indirect spin-spin coupling constants in difluoroethylenes with results produced by CCSD (chosen as a significantly more advanced method). Thus, in Figure 3 are shown changes of individual Ramsay terms in n J(FF) calculated with BHandH/aug-pcJ2 and CCSD methods using a few smaller (affordable for this level of calculation) basis sets dedicated for predicting coupling constants in 1,1-, cis-, and transdifluoroethylenes. The lower accuracy of BHandH in predicting fluorine-fluorine

TABLE VI. CBS estimated nuclear shieldings and shielding anisotropy (in ppm, results for n = 3 and 4 fitted with two-parameter function) in difluoroethylenes (B3LYP/6-311++G(3df,2pd) geometry) using BHandH and VSXC density functionals. For comparison are shown the corresponding RHF, MP2 as well as CCSD and CCSD(T) results obtained with the largest feasible basis sets. Isotropic shielding Method

pc-n

aug-pcS-n

HF VSXC BHandH MP2(full) CCSD CCSD(T)

22.660 13.975 8.480 20.231b 24.201b 24.233d


123.168 126.641 116.856 132.449b 128.333b 131.511d

1,1-difluoroethylene C1 22.342 14.662a 8.384 20.888a 29.492c 29.246c C2 122.912 127.043a 116.739 132.658a 131.261c 132.918c

HF VSXC

301.367 257.484

F 301.300 257.354a

Shielding anisotropy pc-n

aug-pcS-n

109.652 97.3354 111.219 100.243b 101.337b 96.930d

109.814 97.240a 111.268 99.942a 100.128c 97.667c

79.858 63.483 83.098 66.571b 71.468b 68.787d

80.006 63.513a 83.148 66.353a 68.329c 65.395c

89.587 97.242

89.586 97.165a


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TABLE VI. (Continued.) Isotropic shielding Method

pc-n

BHandH MP2(full) CCSD CCSD(T)

265.758 285.578b 293.450b 288.650d


27.820 27.642 27.195 27.700b 27.738b 27.940d

Shielding anisotropy

aug-pcS-n

pc-n

aug-pcS-n

265.783 285.805a 296.879c 291.839c H 27.820 27.647a 27.194 27.665a 27.909c 27.912c

94.230 83.515b 85.176b 88.033d

94.187 84.019a 83.055c 83.555c

5.044 4.452 4.701 5.114b 5.031b 5.124d

5.045 4.448a 4.701 5.114a 5.145c 5.108c

80.961 63.374 80.622 65.668b 67.361b 64.846d

81.086 63.456 80.625 65.345a 65.006c 62.600c

147.073 194.593 188.775 169.957b 155.196d 162.553d

147.218 194.792 188.860 169.296a 152.626c 157.363c

4.152 4.718 4.522 4.350b 4.082b 3.779d

4.149 4.714 4.520 4.367a 3.917c 4.023c

cis-1,2-difluoroethylene HF VSXC BHandH MP2(full) CCSD CCSD(T)

48.809 42.357 35.171 50.003b 52.717b 54.592d


383.557 339.436 354.732 373.302b 375.962b 370.603b


25.573 24.722 24.751 25.146b 25.411a 25.582d

HF VSXC BHandH MP2(full) CCSD CCSD(T) HF VSXC BHandH MP2(full) CCSD CCSD(T) HF VSXC BHandH MP2(full) CCSD CCSD(T) a

aug-pcS-3 result. pc-3 result. c aug-pcS-1 result. d pc-2 result. b

C 48.484 42.325 35.045 50.420a 57.794c 58.173c F 383.546 339.308 354.764 373.014a 379.138c 374.926c H 25.572 24.723 24.751 25.109a 25.603c 25.529c

trans-1,2-difluoroethylene C 38.259 37.926 92.57113 33.310 33.893a 73.49056 24.757 24.635 91.7657 41.221a 75.404b 40.808b 45.053d 49.02a 76.835d d c 45.820 49.639 74.013d F 412.622 412.627 75.632 368.729 368.703a 111.329 385.283 385.324 105.656 401.533b 401.381a 91.972b d c 400.657 405.311 83.776d d c 396.051 401.226 87.867d H 24.30327 24.303 5.03217 4.41331 23.5938 23.598a 23.5437 23.543 5.01801 23.943a 4.447b 23.982b 24.527d 24.421c 4.246d 24.455d 24.359c 4.183d

92.702 73.420a 91.773 75.064a 74.067c 71.448c 75.708 111.556a 105.720 91.320a 79.510c 82.774c 5.033 4.414a 5.019 4.448a 4.095c 4.058c

TABLE VII. Deviationa of 19 F nuclear isotropic shielding in 1,1difluoroethylene, calculated with pc-n basis set (CBS values are used in case of DFT and HF), from experimental value. Deviation Method HF VSXC BHandH MP2(full) CCSD CCSD(T) Lit.b

No correction

HF correction

MP2 correction

22.767 − 21.116 − 12.842 6.978 14.85 10.05 9.000

15.597 − 28.286 − 20.012 − 0.192 7.68 2.88 1.83

14.547 − 29.336 − 21.062 − 1.242 6.63 1.83 0.78

The ZPV correction and TC values calculated at HF (−6.89, −0.28 ppm) and MP2 levels of theory (−7.79 and −0.43 ppm) and experimental nuclear shielding (278.6 ppm) were taken from earlier work.28 b CCSD(T)/13s9p4d3f//CCSD(T)/cc-pVTZ result from Ref. 28.

a

coupling constants is obvious from Figure 3 since three terms, FC, SD, and PSO are predicted completely differently than by the CCSD method. On the other hand, the PSO and DSO components calculated with CCSD method are not very sensitive to the basis set. The deviation of BHandH and CCSD in predicting fluorine-fluorine coupling constants in these three isomers is clearly seen from Figure 4. Thus, both BHandH and CCSD predict significantly more accurately n J(FF) in cis- and transdifluoroethylenes than in 1,1-’difluoroethylene. Besides, the quality of results produced by BHandH is about three times lower than in case of CCSD. In order to see the basis set effect in details, the BHandH/aug-pcJ-2 predicted couplings, discussed in Table VIII, were supported by additional calculations using all basis sets, e.g., for n = 0–4, in the two selected families. Thus, in Table IX we compared the CBS estimated results of systematic BHandH calculations using pcJ-n and aug-pcJ-n basis sets series with benchmark CCSD/pcJ-2 results and available experimental data. For completeness, both the DFT/CBS estimated individual coupling components and their total values for all indirect spin-spin coupling constants in 1,1-difluoroethylene, cis- and trans 1,2-difluoroethylenes are shown. Obviously, the CCSD/pcJ-2 calculated total coupling constants are significantly closer to available experimental values (smaller deviations and RMS values in Table IX). The remaining CCSD results, obtained with pcJ-1 and aug-pcJ-1 basis sets are included in the supplementary material119 (Table SI and SII). The BHandH values (Table IX) were estimated in the complete basis set limit from a series of calculations using both pcJ-n and aug-pcJ-n basis set families. As expected, both basis sets produced identical CBS values. However, the difference between the results obtained with pcJ-0 and aug-pcJ0 basis sets was fairly large and about one order of magnitude smaller for n = 1. Besides, for n = 2, 3, and 4 both kinds of basis sets produced nearly identical results (and very close to CBS). Good examples of total SSCC sensitivity to the basis set size and quality could be seen from convergence patterns of 1 J(CH), 1 J(CF), and 2 J(CF) in trans-, cis-, and 1,1-difluoroethylenes (Figure 5). In the first case


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TABLE VIII. BHandH calculateda and experimental indirect spin-spin coupling constants for ethylene and its difluoro derivatives compared with literature valuesb–d and experiment. The dominating Ramsay terms are marked in bold. J coupling

FC

Lit.

Expt.

Deve

2.9f 13.5f 20.7f 74.7f 153.2h ; 165.3f −1.3f

2.39g 11.66g 19.02g 67.46g 156.30g −2.40g

−1.47 2.28 1.2 7.18 1.36 −1.05 3.25

SD

PSO

DSO

TOTAL

0.16 14.30 20.29 80.46 156.67 −1.72

0.41 −0.07 0.34 4.53 0.16 0.14

4.19 0.81 3.17 −10.41 0.40 −1.17

−3.84 −1.10 −3.58 0.07 0.42 −0.70

0.92 13.94 20.22 74.64 157.66 −3.45

−7.12 67.85 34.62 3.07 127.06 166.95 −0.75 −286.45 39.85

0.18 19.85 0.73 −1.02 5.37 0.15 −0.02 −5.73 12.17

4.20 −96.26 −1.45 −2.43 −7.80 0.72 −1.29 −31.18 −19.24

−3.79 −1.15 −2.56 −0.52 0.28 0.66 −0.24 0.93 −0.38

1,1-Difluoroethylene −6.52 −9.72 13.9b ; 18.1c ; 31.9d ; 24.1k ; 45.3l 31.33 −0.89 124.92 123.7c,l ; 119.7l 168.48 −2.29 −322.44 −319.0k ; −290.2l 32.39 14.1k ; 8.4l

76.08 4.07 20.26 7.53 108.27 203.86 24.91 −289.59 22.61

−2.84 −0.21 1.29 35.57 5.83 0.24 0.08 −1.36 15.06

8.35 0.66 −3.51 −48.88 −8.98 −0.52 −0.68 −4.16 −24.96

−2.02 −0.70 −2.52 −0.42 0.27 0.99 −0.39 0.64 −0.27

cis 1,2−difluoroethylene 79.56 3.83 15.52 −6.21 −13.7b ; −13.6c ; −19.2d ; −8.4k ; −15.1l 105.38 109.7k ; 105.0l 204.57 23.92 −294.47 −283.1k ; −259.4l 12.44

79.27 −7.97 10.98 0.50 125.39 201.35 5.27 −282.83 51.84

−2.78 33.40 0.44 −0.02 6.33 0.25 0.07 −0.55 17.85

9.36 −168.60 2.99 1.28 −10.22 −0.63 −1.06 2.77 −9.28

−1.99 −1.77 −3.43 −0.50 0.27 1.02 −0.47 0.61 −0.20

trans 1,2-difluoroethylene 83.86 −144.94 −133.6b ; −129.2c; −137.6d,l; −150.2k 10.98 1.26 121.76 123.1k ; 117.2l 202.00 3.80 −280.00 −271.6k ; −246.5l 60.20 54.8k ; 48.0l

Ethylene 2 J(HH)

gem

3 J(HH)

cis

3 J(HH)

trans

1 J(CC) 1 J(CH) 2 J(CH)

RMS 2 J(HH) 2 J(FF)

gem

gem

3 J(HF)

trans

3 J(HF)

cis 1 J(CC) 1 J(CH) 2 J(CH) 1 J(CF) 2 J(CF)

2 J(HF)

gem

3 J(HH) 3 J(HF) 3 J(FF)

cis

trans

cis

1 J(CC) 1 J(CH) 2 J(CH) 1 J(CF) 2 J(CF)

2 J(HF) 3 J(FF)

gem

trans

3 J(HH) 3 J(HF)


trans

cis

RMS

−4.62i ;−4.60j 30.72i ; 32.7m ; 36.40n ; 33.85i ;33.90n,j 0.60i ; 0.70n ; 0.64j

30.93j ;

−1.9 −46.12 −2.57 −1.59

−287o

−35.44

71.84j ; 72.7n,p 2.07j ; 2.0p 19.77j ; 20.4p 19.04j ; −18.7n,p

6.86 1.83 −4.88 12.49

5.9q 75.10j ; 74.3p 133.46j ; −124.8p ;−132.70p,m 9.53j ; 9.5p 2.80j ; 4.4p

9.56 −12.24 1.48 −1.54

16.72

a

Individual terms and total value of BHandH/aug-pcJ-2 calculated SSCCs using B3LYP/6-311++G(3df,2pd) optimized structure. SOPPA result from Ref. 75. c SOPPA(CCSD) result from Ref. 75. d EOM CCSD result from Ref. 70. e Deviation = Total (calculated) – (experimental). f B3LYP result from Ref. 79. g from Ref. 114. h SOPPA result from Ref. 113. i In cyclohexane from Ref. 107. j In cyclohexane, from Ref. 24. k SOPPA result from Ref. 117. l EOM CCSD result from Ref. 117. m Cited from Refs. 115 and 117. n From Ref. 22. o◦ Cited in Refs 116, 117. p Gas phase, from Ref. 23. q Cited from Refs. 115 and 117, p. 277. b

(Figure 5(a)), there is a significant jump of one bond carbonproton coupling from n = 0 to 1 (about 15 Hz). However, the improvement of basis set quality by adding diffuse functions is only about 5 Hz for n = 0 and very small for n = 2. There-

fore, it is sufficient to use pcJ-2 or pcJ-3 basis sets instead of larger ones with augmented diffuse functions (aug-pcJ-2 or aug-pcJ-3). Besides, there is a very small gain when performing calculations with n = 2, 3, or 4. Obviously, the two last


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J. Chem. Phys. 140, 144303 (2014)

FIG. 3. Individual Ramsay terms in n J(FF) calculated with BHandH/aug-pcJ-2 and CCSD methods combined with a few smaller basis sets (dedicated for predicting coupling constants) in (a) 1,1-difluoroethylene, (b) cis-1,2-difluoroethylene, and (c) trans-1,2-difluoroethylene.

basis sets would involve significant (and unnecessary) computational time for larger molecules.44, 77, 118 It is worth mentioning here that, to our best knowledge, the first example of using CBS fitting of ethylene SSCC values, based on purely

FIG. 4. Deviation of the total n J(FF) in the three difluoroethylene isomers calculated with BHandH and CCSD methods and the selected basis sets.

empirical exponential convergence, was reported in 2002 by San Fabian and co-workers.86 In case of one bond carbon-fluorine coupling constant there is about 100 Hz difference for results obtained with pcJ0 and aug-pcJ-0 basis sets (Figure 5(b)). This difference is still significant (about 10 Hz) for n = 1 and gets negligible for n = 2 and more. In case of two bond carbon-fluorine coupling the inclusion of diffuse functions for n = 0 changes the calculated parameter by 5–15 Hz (Figure 5(c)). The overall BHandH/CBS estimated coupling constants in difluoroethylenes are of lower accuracy than CCSD/pcJ-2 results (RMS of 17.2 vs 3.0 Hz with regard to sparse experimental data, see Table IX). The most striking differences are for n J(FF) coupling. This coupling is relatively well predicted by DFT in case of cis- and trans- isomers. However, the experimental and CCSD values are significantly underestimated by DFT in case of 1,1-difluoroethylene. Obviously, the dominating FC term is still not reproduced well by BHandH (leading to underestimation of the total coupling by −46 Hz). This deviation is still unacceptable though a large improvement is observed when using BHandH instead of B3LYP (deviation of about 115 Hz.75 )


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J. Chem. Phys. 140, 144303 (2014)

TABLE IX. Comparison of DFT/CBS estimateda indirect spin-spin coupling terms and their total values (in Hz) with CCSD/pcJ-2 results and available experimental data. FC Coupling

2 J(HH) 2 J(FF)

gem

gem

3 J(HF)

trans

3 J(HF)

cis 1 J(CC) 1 J(CH) 2 J(CH) 1 J(CF) 2 J(CF)

2 J(HF)

gem

3 J(HH) 3 J(HF) 3 J(FF)

cis

trans

cis

l 1J(CC) 1 J(CH) 2 J(CH) 1 J(CF) 2 J(CF)

2 J(HF) 3 J(FF)

gem

trans

3 J(HH) 3 J(HF)


trans

cis

SD

PSO

DSO

Expt.

DFT − Expt.

CC − Expt.

DFT-CC

1,1-Difluoroethylene −3.8 −3.8 −6.5 −1.2 −1.1 −9.5 −2.6 −2.6 31.2 −0.5 −0.5 −0.8 0.3 0.3 121.2 0.7 0.7 169.7 −0.2 −0.2 −2.3 0.9 0.9 −325.8 −0.4 −0.4 32.7

−6.0 36.2 29.7 −0.9 119.2 164.4 −0.9 −285.0 27.1

−4.62b 36.40c 33.90c 0.7c

− 1.88 − 45.9 − 2.7 − 1.5

− 1.38 − 0.2 − 4.2 − 1.6

−287d

− 38.8

2

− 0.5 − 45.7 1.5 0.1 2 5.3 − 1.4 − 40.8 5.6

8.4 0.7 −3.5 −48.9 −9.0 −0.5 −0.7 −4.2 −25.0

cis 1,2-difluoroethylene 8.6 −2.0 −2.0 80.2 0.6 −0.7 0.7 3.9 −2.6 −2.52 −2.52 15.75 −37.4 −0.4 −0.4 −6.6 −8.0 0.3 0.3 106.3 −0.5 1.0 1.0 206.1 −0.6 −0.4 −0.4 24.2 2.7 0.6 0.6 −297.9 −21.1 −0.3 −0.3 12.4

71.6 4.5 15.94 −15.2 101.5 196.2 24.0 −253.4 7.3

72.7c,e 2.0e 20.4e −18.7e

9.4 −168.6 3.0 1.28 −10.2 −0.6 −1.1 2.8 −9.3

trans 1,2-difluoroethylene 9.5 −2.0 −2.0 84.6 −139.2 −1.8 −1.8 −145.2 3.0 −3.4 3.4 11.1 1.31 −0.50 −0.50 1.27 −9.0 0.3 0.3 122.9 −0.6 1.0 1.0 203.5 −0.9 −0.5 −0.5 3.9 8.4 −0.6 0.6 −283.4 −8.4 −0.2 −0.2 60.5

75.2 −130.3 16.3 1.08 116.3 194.6 5.8 −239.6 48.3

74.3e −132.7e 9.5e 2.80e

CC

DFT

CC

DFT

CC

−7.1 68.6 34.9 3.1 128.3 168.2 −0.7 −289.8 40.3

−6.5 80.7 32.7 2.4 122.4 162.8 0.5 −262.0 36.4

0.2 19.7 0.8 −1.0 5.3 0.1 −1.8 −5.7 12.1

0.2 27.6 0.6 −1.0 3.5 0.2 −0.1 −0.6 7.7

4.2 −96.6 −1.4 −2.4 −7.8 0.8 −1.3 −31.2 −19.3

4.2 −70.9 −1.1 −1.8 −7.0 0.8 −1.2 −23.3 −16.6

76.7 4.1 20.4 7.5 109.3 205.4 25.2 −293.0 22.8

67.5 3.0 20.1 1.2 105.5 195.4 25.0 −260.8 19.4

−2.8 −0.2 1.3 35.4 5.8 0.2 0.1 −1.4 14.9

−2.6 0.2 0.96 21.5 3.7 0.2 0.0 4.1 9.2

70.2 −8.3 9.6 0.52 121.1 193.9 7.2 −253.8 45.9

−2.8 33.2 0.4 0.01 6.3 0.2 0.1 −0.6 17.7

−2.5 19.0 0.3 −0.25 3.9 0.3 0.0 5.2 10.9

Dev. CC

DFT

79.9 −8.1 11.0 0.48 126.5 202.9 5.4 −286.2 52.4

Tot.

DFT

RMS

CC

DFT

5.9f

7.5 1.9 − 4.65 12.1

− 1.1 2.5 − 4.46 3.5

6.5

1.4

10.3 − 12.5 1.6 − 1.53

0.9 2.4 6.8 − 1.72

17.2

3.0

8.6 − 0.6 − 0.19 8.6 4.8 9.9 0.2 − 44.5 5.1 9.4 − 14.9 − 5.2 0.19 6.6 8.9 − 1.9 − 43.8 12.2 17.9

a

BHandH result calculated with pcJ-n (and aug-pcJ-n) basis sets and CBS estimated using two-parameter fit. Dominating terms are marked in bold. In cyclohexane from Ref. 107. c From Ref. 22. d Cited in Refs. 116 and 117. e Gas phase, from Ref. 23. f Cited from Refs. 115 and 117, p. 277. b

Because of lack of all experimental couplings in the studied molecules, we also compared in Table IX the deviations of BHandH/CBS values from CCSD/pcJ-2 results, assumed here as benchmark reference. This comparison gives a more general picture of BHandH/CBS performance. Apparently, there are two couplings in 1,1-difluoroethylene which are extremely difficult to calculate by DFT(BHandH): 2 J(FF) and 1 J(CF) with huge deviations of −45.7 and −40.8 Hz (deviations below 6 Hz are observed for the remaining couplings). In case of cis- and trans-isomers the 1 J(CF) is significantly underestimated by DFT (−44.5 and −43.8 Hz lower than the CCSD values). Besides, the 3 J(FF) coupling in these two molecules differs less (8.8 and −14.9 Hz) from the CCSD predicted values than 2 J(FF) in case of 1,1-difluoroethylene (−45.7 Hz). The RMS for BHandH/CBS results calculated for 1,1-, cis-1,2, and trans-1,2-difluoroethylenes with respect

to CCSD/pcJ-2 predicted couplings are 20.61, 15.90, and 16.77 Hz. The total RMS calculated with respect to CCSD results and experiment is very similar (17.9 and 17.2 Hz) and about six times higher than for CCSD (RMS of 3.0 Hz). The results presented in Figure 5 could be used to distinguish between the three isomers of difluoroethylenes. Thus, the 1 J(CH) converges toward CBS value at about 160 Hz for 1,1-difluoroethylene and about 190–200 Hz for both cis- and trans-1,2-difluoroethylenes (Figure 5(a)). In case of 1 J(CF), the corresponding CBS values are better separated (CBS values of about −300, −320 and −350 Hz, see Figure 5(b)). The final diagnostics for the presence of these isomers is supported by the CBS values of 2 J(CF). In this case the corresponding coupling constant for trans-, cis-, and 1,1-isomers are very well separated (CBS values of about 60, 10, and 30 Hz, see Figure 5(c)).


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J. Chem. Phys. 140, 144303 (2014)

FIG. 5. Basis set dependence of 1 J(CH), 1 J(CF), and 2 J(CH) in 1,1-, cis-, and trans-1,2-difluoroethylenes calculated using BHandH combined with pcJ-n and aug-pcJ-n.

IV. CONCLUSIONS

We have examined in detail the performance of several density functionals for obtaining accurate structural, vibrational and NMR parameters of three difluoroethylenes. The obtained results were compared with available experimental data and earlier reported benchmark CCSD(T) calculations. The purpose of our study was to find an affordable level of calculations (here DFT) for future characterization of larger atomic systems containing one or two fluorine atoms connected to carbon. These systems are also good models of cis and trans isomers. We also estimated selected NMR parameters in the complete basis set limit and compared the DFT results with those, obtained at HF, MP2, CCSD, and CCSD(T) levels of theory. Geometries of 1,1-, cis-, and trans-1,2-dufluoroethylenes were accurately optimized using B3LYP and BLYP density functionals combined with 6-311++G(3df,2pd) basis set. The structural parameters of these molecules closely reproduced advanced calculations using composite methods and coupled cluster approach. However, in comparison to the best literature reports and experiment, the B3LYP harmonic wavenumbers were few times worse than the anharmonic

B3LYP, calculated using the VPT2 approach, or harmonic BLYP results. The VSXC density functional predicted carbon isotropic shieldings in difluoroethylenes better than BHandH. The reverse situation was observed for fluorine shieldings. A surprisingly good performance of traditional Hartree-Fock method in predicting fluorine and carbon nuclear shieldings was noticed. BHandH, CCSD and CCSD(T) methods predicted absolute 19 F nuclear isotropic shielding in 1,1difluoroethylene with similar accuracy (deviations from experiment were −12.8, 14.9, and 10.0 ppm). However, the inclusion of ZPV correction markedly improved the CCSD and CCSD(T) results but seriously spoiled the DFT value (deviations of 1.8, 0.8, and −21.0 ppm were observed). BHandH density functional predicted the majority of indirect spin-spin coupling constants in difluoroethylenes fairly well (RMS deviation from CCSD/pcJ-2 results without the four largest ones was about 6.5 Hz). However, it completely failed to predict 2 J(FF) and 1 J(CF) and underestimated the experimental and CCSD/pcJ-2 values by about 41–46 Hz. Moreover, the 3 J(FF) in cis and trans-1,2-difluoroethylene were also poorly calculated and deviated from experiment by about 12 and −12 Hz, respectively. The RMS deviation for


144303-17


BHandH/CBS estimated coupling constants in the three difluoroethylenes from experiment and CCSD/pcJ-2 were 17.2 and 17.9 Hz (the RMS for CCSD deviation from available experimental data was only about 3.0 Hz). The current performance of BHandH in predicting 2 J(FF) in 1,1-difluoroethylene was about three times better than the earlier reported B3LYP result (deviation of −46 vs −115 Hz). It was possible to distinguish 1,1-, cis-, and trans-1,2-difluoroethylenes by checking their 2 J(FF), 3 J(FF), and 1 J(CF) coupling constants calculated at BHandH/aug-pcJ-2 level of theory (or the significantly more computationally demanding BHandH/CBS estimates). The current studies also point out the need for future experimental NMR studies on the difluoroethylenes and for a very challenging task of designing a novel density functional(s), capable to correctly calculate coupling constants involving fluorine-fluorine and fluorine-carbon atoms. ACKNOWLEDGMENTS

F.N. is grateful for the VA Montgomery GI bill, VA education benefit from the U.S. Department of Veteran Affairs. This work was also partially supported by the Faculty of Chemistry, University of Opole (Grant 8/WCH/2012-S). Michał Stachów is a recipient of a Ph.D. fellowship from a project funded by the European Social Fund, Uniwersytecki Program Stypendialny 2013–2014. The calculation facilities and software in the Supercomputing and Networking Center ACK CYFRONET AGH in Krakow within a calculation grant MNiSW/SGI3700/UOpolski/061/2012 and calculation facilities and software at the Supercomputing and Networking Center in Wrocław are also acknowledged. Ibon Alkorta is thanked for discussing experimental and theoretical coupling constants. We are also very grateful to both of our anonymous reviewers for their constructive critics leading to a significant improvement of the original text. 1 B.

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Phosphorus-31 Fourier transform nuclear magnetic resonance study of mononucleotides and dinucleotides. 2. Coupling constants.

Accurate measurements of coupling constants from two-dimensional nuclear magnetic resonance spectra of proteins and determination of phi-angles.

Calculating nuclear magnetic resonance shieldings using systematic molecular fragmentation by annihilation.

Computational study of interactions and nuclear magnetic shielding constants in linear chains of formamide clusters.

13C-nuclear magnetic resonance study of [85% 13C-enriched proline]thyrotropin releasing factor: 13C-13C vicinal coupling constants and conformation of the proline residue.

Calculation of nuclear spin-spin coupling constants using frozen density embedding.

17O and 33S nuclear magnetic shielding of sulfur trioxides from the experimental measurements and theoretical calculations.

Distal and proximal ligand interactions in heme proteins: correlations between C-O and Fe-C vibrational frequencies, oxygen-17 and carbon-13 nuclear magnetic resonance chemical shifts, and oxygen-17 nuclear quadrupole coupling constants in C17O- and 13CO-labeled species.

QSPR prediction of the stability constants of gadolinium(III) complexes for magnetic resonance imaging.

"Ask Ernö": a self-learning tool for assignment and prediction of nuclear magnetic resonance spectra.

13C nuclear magnetic resonance spectra of 1,2-dioctadec-cis-enoyl-sn-glycero-3-phosphorylcholines.

pH-dependence of 13C chemical shifts and 13C,H coupling constants in imidazole and L-histidine.

Triarylmethyl Radicals: EPR Study of 13C Hyperfine Coupling Constants.

Triple-bridged ferromagnetic nickel(II) complexes: a combined experimental and theoretical DFT study on stabilization and magnetic coupling.

Universal J-coupling prediction.

Hyperfine coupling constants of the cyclohexadienyl radical in benzene and dilute aqueous solution.

Proton, muon and ¹³C hyperfine coupling constants of C₆₀X and C₇₀X (X = H, Mu).

Combined use of homo- and heteronuclear coupling constants as restraints in molecular dynamics simulations.

An ab initio reinvestigation of PC and PH coupling constants in phosphates.

Cis-trans isomerization of an angiotensin I-converting enzyme inhibitor. An enzyme kinetic and nuclear magnetic resonance study.

Theoretical study of spectroscopic constants and anharmonic force field of SiF2.

Theoretical prediction of structural, vibrational and NMR parameters of plastic optical fiber (POF) material precursors. Cis and trans perhydro- and perfluoro-2-methylene-4,5-dimethyl-1,3-dioxolanes.

Production of cis-11-eicosenoic acid by Mortierella fungi.

Accurate Prediction of Hyperfine Coupling Constants in Muoniated and Hydrogenated Ethyl Radicals: Ab Initio Path Integral Simulation Study with Density Functional Theory Method.