scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Performance of the DLPNO-CCSD and recent DFT methods in the calculation of isotropic and dipolar contributions to 14N hyperfine coupling constants of nitroxide radicals

11 Mar 2021-Journal of Molecular Modeling (Springer Berlin Heidelberg)-Vol. 27, Iss: 6, pp 194-194
TL;DR: In this paper, the performance of a set of density functionals, including BP86, PBE, OLYP, BEEF, PEF, BBEpow, TPSS, SCAN, PBEGXPBE, M06L, MN15L, CAM-B3LYP/N07D and PBE/n07D, were evaluated in the calculation of the 14N anisotropic hyperfine coupling (HFC) constants of 23 nitroxide radicals.
Abstract: In the present study, the performance of a set of density functionals: BP86, PBE, OLYP, BEEF, PBEpow, TPSS, SCAN, PBEGXPBE, M06L, MN15L, B3LYP, PBE0, mPW1PW, B97, BHandHLYP, mPW1PW, B98, TPSS0, PBE1KCIS, SCAN0, M06, M06-2X, MN15, CAM-B3LYP, ωB97x, B2PLYP, and the B3LYP/N07D and PBE/N07D schemes in the calculation of the 14N anisotropic hyperfine coupling (HFC) constants of a set of 23 nitroxide radicals is evaluated. The results are compared with those obtained with the DLPNO-CCSD method and experimental HFC values. Harmonic contribution to the 14N HFC vibrational correction was calculated at the revPBE0/def2-TZVPP level and included in the evaluation. With the vibrational correction, the DLPNO-CCSD method yielded HFC values in good agreement with the experiment (mean absolute deviation (MAD) = 0.3 G for the dipole-dipole contribution and MAD = 0.8 G for the contact coupling contribution). The best DFT results are obtained using the M06 functional with MAD = 0.2 G for the dipole-dipole contribution and MAD = 0.7 G for the contact coupling contribution. In general, vibrational correction significantly improved most DFT functionals’ performance but did not change its overall ranking.

Summary (1 min read)

Introduction

  • Density functional theory (DFT) is now the most used method in quantum chemical modeling as it affords the best balance of cost and accuracy for the time being.
  • While energy-based evaluation of DFT functionals' performance readily delivers natural metrics, electron density-based evaluation metrics are more ambiguous; see for discussion Marjewski et al. [3] and the references therein.
  • Besides, it is interesting to evaluate the DLPNO-CCSD method performance for "reallife" nitroxide radicals.
  • 14 N hyper ne couplings of nitroxide radicals were also calculated using the domain-based local pair-natural orbital coupled-cluster with singles and doubles (DLPNO-CCSD) method [17, 60, 61] with DLPNO-HFC1 set of the thresholds and quasi-restricted orbitals (QRO) from unrestricted B3LYP/COSMO calculation as a reference.
  • DLPNO-CCSD calculations were performed using uncontracted cc-pCVTZ basis set [54] augmented with four tight s-functions from aug-cc-pVTZ-J [55] basis set.

3.1 DLPNO-CCSD calculation and ZPVC

  • On the other hand, the performance of DFT methods in the spin dipole contribution to 14N HFCC calculation (here A dd z component is used) contradicts the trends in electron density and Fermi contact contribution to HFCC.
  • The best performers are the GGA and mGGA functionals (OLYP, PBE, PBEpow, PBEGXPBE, TPSS) and the M06-family functionals.
  • Though this is not necessarily always so, see, for example, Kossmann et al. [7] .
  • In a broader perspective, TPSS0 and B2PLYP functionals remain the most reliable choice for an HFC calculation in the DFT framework.
  • When the DLPNO-CCSD method's routine use in a preliminary experimental data interpretation by a brute force search of a suitable radical or calculation of large radicals' vibrational corrections and in other applications is too demanding.

Conclusions

  • In the present study, the authors have evaluated the performance of 26 different DFT functionals in conjunction with the harmonic contribution to the perturbative vibrational correction in the spin density calculating of a set of 23 nitroxide radicals and compared their results against the experiment and the results DLPNO-CCSD calculation.
  • The SCAN, SCAN0, and MN15 functionals were found to be the worst performers with relative errors in a iso up to 100% or even more.
  • Otherwise, the trends in the spin density description by DFT methods follow tendencies observed earlier in the electron density description.
  • The authors have found that the calculation of 14 N HFC in most DFT functionals signi cantly bene t from vibrational correction.

Did you find this useful? Give us your feedback

Figures (2)

Content maybe subject to copyright    Report

Page 1/17
Performance of the DLPNO-CCSD and Recent DFT Methods in the
Calculation of Isotropic and Dipolar Contributions to 14N
Hyperne Coupling Constants of Nitroxide Radicals
Oleg Gromov ( aalchm@gmail.com )
Moskovskij gosudarstvennyj universitet imeni M V Lomonosova Himiceskij fakul'tet https://orcid.org/0000-0002-4119-8602
Research Article
Keywords: EPR spectroscopy, nitroxide radical, DFT, hyperne coupling, DLPNO-CCSD
Posted Date: March 11th, 2021
DOI: https://doi.org/10.21203/rs.3.rs-279592/v1
License: This work is licensed under a Creative Commons Attribution 4.0 International License.  Read Full License

Page 2/17
Abstract
In the present study, the performance of a set of density functionals: BP86, PBE, OLYP, BEEF, PBEpow, TPSS, SCAN, PBEGXPBE, M06L,
MN15L, B3LYP, PBE0, mPW1PW, B97, BHandHLYP, mPW1PW, HSE06, B98, TPSS0, PBE1KCIS, SCAN0, M06, M06-2X, MN15, CAM-
B3LYP, ωB97x, B2PLYP, and the B3LYP/N07D and PBE/N07D schemes in the calculation of the
14
N anisotropic hyperne coupling
(HFC) constants of a set of 23 nitroxide radicals is evaluated. The results are compared with those obtained with the DLPNO-CCSD
method and experimental HFC values. Harmonic contribution to the
14
N HFC vibrational correction was calculated at the
revPBE0/def2-TZVPP level and included in the evaluation. With the vibrational correction, the DLPNO-CCSD method yielded HFC
values in good agreement with the experiment (MAD = 0.3 G for the dipole-dipole contribution and MAD = 0.8 G for the contact
coupling contribution). The best DFT results are obtained using the M06 functional with mean absolute deviation (MAD) = 0.2 G for
the dipole-dipole contribution and MAD = 0.7 G for the contact coupling contribution. In general, vibrational correction signicantly
improved most DFT functionals' performance but did not change its overall ranking.
Introduction
Density functional theory (DFT) is now the most used method in quantum chemical modeling as it affords the best balance of cost
and accuracy for the time being. Though DFT itself is an exact theory connecting the molecular system's many-electron density with
its energy via “exact” density functional, it relies on approximate functionals in practical applications. Hence many general-purpose
and particular property tailored functionals were developed for the last few decades [1]. New functionals are supposed to perform
better than the older ones. However, the common practice shows that one should not always prefer some newly developed techniques
over the previous ones thoughtlessly. Indeed as shown in the paper by Medvedev et al. [2], the common strategy of DFT functional
development tailoring molecular energetics and geometry might result in DFT functionals poorly describing electron density. While
energy-based evaluation of DFT functionals’ performance readily delivers natural metrics, electron density-based evaluation metrics
are more ambiguous; see for discussion Marjewski et al. [3] and the references therein. Though electron density also delivers some
natural and experimentally observable metrics such as (deviation in calculated) dipole moment (and higher moments) as used by Hait
and Head-Gordon [4]. Interestingly Hait and Head-Gordon found open-shell species to be the most dicult cases for DFT. Some open-
shell species, namely radicals (including some coordination compounds), deliver another electron density-based natural metric:
hyperne coupling (HFC) [5]. One can extract some information on spin density distribution in the radical from HFC directly measured
by Electron Paramagnetic Resonance (EPR) spectroscopy and use it in DFT functionals performance evaluation [5–7].
EPR spectroscopy is a widely used method in studying organic radicals and d-block metal complexes [8]. To interpret experimental
EPR spectra, one usually uses an effective spin Hamiltonian describing the interaction between an electron spin (
Ŝ
), magnetic nuclei
spins (
Î
), and an external magnetic eld (
B
):see formula 1 in the supplementary les.
The rst term is the Zeeman interaction between the electron spin and the external magnetic eld, with
g
being a 3x3 tensor. The
hyperne coupling tensors
A
i
describe the interaction of the unpaired electron and the magnetic moments of the nuclei
Î
i
. The hyperne
coupling tensor can be divided into the isotropic (
a
iso
) and the traceless spin-dipole contributions:see formula 2 in the supplementary
les.
where the isotropic Fermi contact termsee formula 3 in the supplementary les.
readily delivers the spin density at the nucleus N (ρ(R
N
) ), while
A
dip
tensor depends on the whole spin density distribution.
In the previous paper [6], we evaluated the well-established and widely used functionals. During the last decade, many new functionals
arrived. For example, the strongly constrained and appropriately normed semilocal density functional (SCAN) yields at the cost of a
non-hybrid mGGA functional [2] electron densities better than the B3LYP functional. While the B3LYP functional is well tested [5, 7, 9–
14], the SCAN functional performance data are insucient. It has been shown [5, 15] that SCAN, while being competitive to the
commonly used functionals in some cases, is not, in general, the best choice for HFC calculation. In some cases, SCAN and SCAN0
functionals even predicted qualitatively incorrect electronic structures of transition metal complexes [15]. For that reason, it is
interesting to expand this research on the SCAN performance on compounds of p-elements. The B98, PBE1KCIS, HSE06, and SCAN
functionals are listed in the paper by Medvedev et al. among the best functionals for electron density and are included in the present
research.

Page 3/17
The DFT calculations results can be compared either with the experimental values or with the values calculated using some accurate
ab initio
method. The former requires taking into account solvation and vibrational averaging effects and calculating accurate
geometry[16]. The latter way, which requires, for example, coupled-cluster calculation of the reference values, is therefore preferred,
especially if the test set consists of small species, easily treated using accurate
ab initio
methods. Both choices of the reference are
consistent. For example, the coupled cluster methods as shown by Barone and Puzzarini [16] for small X
2
NO Systems (X = F, Cl, Br, I),
bring HFC constants in excellent agreement with the experiment, given vibrational, media, and basis set effects are taken into account
in CCSD(T) calculation. A routine CCSD calculation of substantially large radical systems was recently made possible in the domain-
based local pair-natural orbital coupled-cluster with singles and doubles (DLPNO-CCSD) framework [17]. Hence it is possible to use
both references even for large radical systems. Besides, it is interesting to evaluate the DLPNO-CCSD method performance for "real-
life" nitroxide radicals.
Calculation Details
ORCA 4.2.0 program package [18] was used to perform all calculations. The nitroxide radicals' geometries were optimized at the
UKS/B2GP-PLYP/def2-TZVPP [19, 20] level with the COSMO solvation model [21]. The B2GP-PLYP functional was chosen for
geometry optimization according to a recent benchmark study [22].
14
N HFCC were calculated using some newer density functionals available in Libxc [23]. DFT functionals used are: strongly
constrained and appropriately normed semilocal density functional (SCAN) [24] (we didn't nd signicant differences between the
results of SCAN and revised SCAN functional [25] hence the results of the calculations using the latter are not presented), hybrid
SCAN0 [26] (also similar to the results of the revised version), bayesian error estimation functional (BEEF) [27], power series extension
of the PBE exchange functional [28] (PBEpow exchange functional combined with the PBE [29] correlation functional), PBE-GX
functional [30] (combined with the PBE correlation functional), MN15 and MN15-L functionals [31, 32], PBE1KCIS hybrid [33] (with
KCIS correlation functional [34]), screened Coulomb potential hybrid functional (HSE06) [35] and B98 hybrid [36]. We compared these
functionals with the functionals used in our previous paper [6]: GGA functionals BP86 [37, 38], PBE [29], OLYP [39]; the meta-GGA
functionals TPSS [40], M06L [41]; the hybrid GGA functionals B3LYP [42], PBE0 [43], mPW1PW [44], B97 [45], BHandHLYP [46]; the
hybrid meta-GGA functionals TPSS0 [40], M06 [47], M06-2X [47]; the range-separated functionals CAM-B3LYP [48], ωB97x [49], the
double-hybrid functional B2PLYP (with relaxed density) [50]. The B3LYP/N07D and PBE0/N07D functional/basis combinations [51, 52]
were also used. All DFT calculations were performed using unrestricted Kohn-Sham formalism.
Basis sets for coupled-cluster and DFT calculations were constructed similarly to the one used by Datta and Gauss [53]. DFT
calculations were performed using uncontracted cc-pCVQZ basis set [54] augmented with four tight even-tempered s-functions
(denoted cc-pCVQZ-Juc by analogy with an aug-cc-pVTZ-Juc basis set of Sauer et al. [55]). For further discussion on the basis sets for
HFC calculations, see Jakobsen and Jensen [56]. The RIJCOSX [57] approximation with auto-generated auxiliary basis sets [58] and
integration grid Grid7 (the tightest in ORCA) and Gridx9 were used throughout except for the calculation of the vibrational correction. In
the case of dubious results, calculations were performed without RI or RIJCOSX approximations (for example, calculations using the
MN15, SCAN, and SCAN0 functionals). The COSMO solvation model [21] with toluene as a solvent was used as non-polar solvents
implicit solvation models were shown to yield reasonable solvent shifts [16, 59].
14
N hyperne couplings of nitroxide radicals were also calculated using the domain-based local pair-natural orbital coupled-cluster
with singles and doubles (DLPNO-CCSD) method [17, 60, 61] with DLPNO-HFC1 set of the thresholds and quasi-restricted orbitals
(QRO) from unrestricted B3LYP/COSMO calculation as a reference. COSMO could not be used in DLPNO-CCSD calculation directly.
However, the introduction of solvation at the reference level yields results similar to those obtained using an additive scheme of
Barone [16]. T
1
diagnostic parameter values were always lower than 0.02. DLPNO-CCSD calculations were performed using
uncontracted cc-pCVTZ basis set [54] augmented with four tight s-functions from aug-cc-pVTZ-J [55] basis set.
Vibrational corrections to isotropic hyperne coupling constants were calculated using the perturbative approach [62–66]. Only
harmonic corrections, given by:see formula 4 in the supplementary les.
14
N hyperne coupling constants of 23 nitroxide radicals (Fig. 1) used as the reference were taken from Lebedev et al. [68]. The choice
of particular radicals was discussed in our previous paper [6].
14
N isotropic hyperne coupling constants (
a
iso
) were calculated from

Page 4/17
the hyperne coupling tensors at low temperatures. The labels used for nitroxide radicals by Lebedev et al. were adopted for use in the
present paper.
Results And Discussion
3.1 DLPNO-CCSD calculation and ZPVC
The experimental data by Lebedev et al. [68] were acquired at low temperatures, and vibrational averaging effects are reduced to some
extent. For example, Barone et al. [65] estimated ZPVC to
14
N
a
iso
of the 2,2,5,5-tetramethylpyrrolidin-1-yl)oxydanyl radical (Proxyl,
pyrrolidine series) to be 0.3 G at 0K (harmonic contribution is 0.2G and anharmonic contribution is 0.14G). We omitted vibrational
corrections in our previous [6] due to this relatively low value. On the other hand, Barone et al. [59] estimated vibrational correction to
14
N
a
iso
of the Proxyl radical at 298K to be up to 2.6G. Recently Auer et al. calculated ZPVC of 2,2,3,4,5,5-
hexamethylperhydroimidazol-1-oxyl radical (HMI, imidazolidine series) at the revPBE0 level (0.9G) and the DLPNO-CCSD level (1.3G).
In the present study,
14
N HFCCs were calculated at the DLPNO-CCSD level (table 1). The relative error of the DLPNO-CCSD calculation
to experiment varies from 7% up to 22%. Moreover, the correlation of calculated and experimental
14
N
a
iso
(Fig. 4, black) is not linear.
These observations, along with literature data, indicated the importance of vibrational correction. Indeed, the inclusion of perturbative
vibrational correction (revPBE0/def2-TZVPP) reduces relative errors of the DLPNO-CCSD calculation to 3-8%, and the correlation of the
calculated and the experimental
14
N
a
iso
(Fig. 4, red) readily becomes almost linear. The remaining errors of 0.3-1.3G (MAD = 0.8G)
originate from several small contributions. First, DFT calculation probably underestimates vibrational correction (see Auer et al. [67]).
On the other hand, the inclusion of only the harmonic contribution probably leads to the overestimation of vibrational correction,
especially in the
3-imidazoline-3-oxide-oxyl
series. Secondly, deviation of DLPNO-CCSD results from canonical CCSD results [5] and the
lack of triples correction [16] further draw calculated values away from the experiment. Finally, error from incompletion of the basis set
and approximate way of the solvent's inclusion in the calculation may also contribute to deviation from the experiment. Some of these
errors are covered in the papers by Barone et al. [16, 69–71]. The divergence between DLPNO-CCSD calculation and experimental spin-
dipole contribution to hyperne coupling tensor (
A
dd
z
), which is already relatively small (MAD = 0.5G), further benets from the
inclusion of the vibrational correction (MAD = 0.3G). In general DLPNO-CCSD method with the perturbative harmonic vibrational
correction (a
iso
MAD = 0.8G,
A
dd
z
MAD = 0.3G) outperforms most DFT methods (vide infra) and should be preferred even in routine
usage.
Table 1
14
N isotropic hyperne coupling constants of nitroxide radicals VI- LXXVIII (
a
iso
)
and the diagonal element of spin-dipole
contribution to hyperne coupling tensor (
A
dd
z
) calculated using the DLPNO-CCSD method and respective absolute errors (AE)
compared with the experiment. The vibrational correction (
Δa
iso
vib
and
ΔA
dd
z
vib
) is estimated at revPBE0/def2-TZVPP level

Page 5/17
Radical
Δa
iso
vib
(0K/140K)
a
iso
DLPNO-
CCSD
a
iso
DLPNO-
CCSD
corrected
a
iso
exp*
AE
iso
uncorrected
/corrected
ΔA
dd
z
vib
(0K/140K)
A
dd
z
DLPNO-
CCSD
A
dd
z
DLPNO-
CCSD
corrected
A
dd
z
Exp
AE
dd
uncorrected
/corrected
Piperidine series
VI 0.3/0.4 14.6 14.9 15.7 1.2/0.8 -0.1/-0.1 18.0 17.9 18.3 0.2/0.4
VII 0.3/0.3 14.6 14.9 15.8 1.3/1.0 -0.2/-0.2 18.5 18.3 18.4 0.1/0.1
VIII 0.4/0.5 14.4 14.9 16.1 1.7/1.3 -0.1/-0.1 18.3 18.2 18.7 0.4/0.5
X 0.3/0.3 14.5 14.9 15.9 1.4/1.0 -0.2/-0.2 18.3 18.2 18.1 0.2/0.1
XIII 0.3/0.3 14.5 14.8 15.8 1.4/1.0 -0.2/-0.2 18.4 18.2 18.5 0.1/0.3
XV 0.3/0.3 14.3 14.6 15.8 1.5/1.2 -0.2/-0.2 18.5 18.3 17.7 0.8/0.6
XIX 0.3/0.3 14.3 14.6 15.5 1.2/0.9 -0.1/-0.2 18.0 17.9 17.9 0.1/0.0
XX 0.3/0.3 14.4 14.7 15.7 1.3/1.0 -0.1/-0.2 18.0 17.8 18.1 0.1/0.3
Pyrroline series
XXXVII 1.3/1.6 12.0 13.6 14.7 2.8/1.1 -0.4/-0.4 19.7 19.3 19.3 0.4/0.0
Imidazoline series
XLIV 1.4/1.9 11.5 13.4 14.0 2.5/0.6 -0.4/-0.5 19.3 18.8 18.4 1.0/0.5
3-imidazoline-3-oxide-oxyl series
LII 2.3/2.9 11.0 13.9 14.1 3.2/0.3 -0.6/-0.7 19.2 18.4 18.1 1.1/0.4
LIII 1.1/1.6 11.5 13.1 13.9 2.4/0.8 -0.3/-0.4 19.1 18.7 18.6 0.5/0.1
LIX 1.9/2.5 11.0 13.5 14.0 3.0/0.5 -0.5/-0.6 19.2 18.5 18.2 0.9/0.3
LX 1.9/2.5 11.0 13.4 14.0 3.0/0.5 -0.5/-0.6 19.2 18.6 18.3 0.8/0.2
LXI 1.9/2.5 11.0 13.4 14.0 3.0/0.5 -0.5/-0.6 19.0 18.4 18.2 0.8/0.2
LXII 0.8/1.1 12.2 13.2 14.1 1.9/0.8 -0.2/-0.3 18.7 18.4 18.0 0.7/0.4
Pyrrolidine series
LXVII 0.9/1.4 12.1 13.5 14.0 1.9/0.5 -0.3/-0.4 19.5 19.1 19.0 0.5/0.1
LXVIII 1.1/1.6 11.5 13.1 14.0 2.5/0.9 -0.3/-0.4 19.3 18.9 19.3 0.0/0.4
Imidazolidine series
LXX 0.5/0.6 13.4 14.0 15.1 1.6/1.1 -0.2/-0.2 18.6 18.5 18.1 0.5/0.3
LXXI 0.5/0.6 13.5 14.0 14.7 1.2/0.7 -0.2/-0.2 18.4 18.2 18.1 0.4/0.2
LXXII 0.5/0.5 13.8 14.3 15.5 1.8/1.2 -0.2/-0.2 18.4 18.2 18.1 0.3/0.1
LXXIV 0.4/0.5 14.2 14.7 15.5 1.3/0.8 -0.2/-0.2 18.3 18.1 17.4 0.9/0.7
LXXVIII 0.8/0.9 12.5 13.4 13.9 1.4/0.5 -0.2/-0.3 19.1 18.8 18.7 0.4/0.1
* values calculated as an average of the diagonal elements (
A
n
) of the hyperne coupling tensors
3.2 DFT calculation
Our previous paper mentioned a slightly controversial trend: description of
14
N isotropic HFC in nitroxide radicals by DFT functionals
generally follows pattern noted by Medvedev et al. [2]. In contrast, the description of the dipole-dipole contribution to
14
N HFC is

Citations
More filters
Journal ArticleDOI
TL;DR: In this article, the authors proposed a more computationally tractable alternative, where the hyperfine coupling constant (HFCC) was computed with the coupled cluster theory exploiting locality of electron correlation.
Abstract: Electronic structure calculations are fundamentally important for the interpretation of nuclear magnetic resonance (NMR) spectra from paramagnetic systems that include organometallic and inorganic compounds, catalysts, or metal-binding sites in proteins. Prediction of induced paramagnetic NMR shifts requires knowledge of electron paramagnetic resonance (EPR) parameters: the electronic g tensor, zero-field splitting D tensor, and hyperfine A tensor. The isotropic part of A, called the hyperfine coupling constant (HFCC), is one of the most troublesome properties for quantum chemistry calculations. Yet, even relatively small errors in calculations of HFCC tend to propagate into large errors in the predicted NMR shifts. The poor quality of A tensors that are currently calculated using density functional theory (DFT) constitutes a bottleneck in improving the reliability of interpretation of the NMR spectra from paramagnetic systems. In this work, electron correlation effects in calculations of HFCCs with a hierarchy of ab initio methods were assessed, and the applicability of different levels of DFT approximations and the coupled cluster singles and doubles (CCSD) method was tested. These assessments were performed for the set of selected test systems comprising an organic radical, and complexes with transition metal and rare-earth ions, for which experimental data are available. Severe deficiencies of DFT were revealed but the CCSD method was able to deliver good agreement with experimental data for all systems considered, however, at substantial computational costs. We proposed a more computationally tractable alternative, where the A was computed with the coupled cluster theory exploiting locality of electron correlation. This alternative is based on the domain-based local pair natural orbital coupled cluster singles and doubles (DLPNO-CCSD) method. In this way the robustness and reliability of the coupled cluster theory were incorporated into the modern formalism for the prediction of induced paramagnetic NMR shifts, and became applicable to systems of chemical interest. This approach was verified for the bis(cyclopentadienyl)vanadium(II) complex (Cp2V; vanadocene), and the metal-binding site of the Zn2+ → Co2+ substituted superoxide dismutase (SOD) metalloprotein. Excellent agreement with experimental NMR shifts was achieved, which represented a substantial improvement over previous theoretical attempts. The effects of vibrational corrections to orbital shielding and hyperfine tensor were evaluated and discussed within the second-order vibrational perturbation theory (VPT2) framework.

1 citations

Journal ArticleDOI
TL;DR: In this paper , a detailed study of the magnetic and relaxation properties in solution of a series of oxovanadium(IV) complexes comprising the aqua ion [VO(H2O)5]2+ and [ VO(ox)2]2 (ox = oxalate), [VO (nta)]...
Abstract: We report a detailed study of the magnetic and relaxation properties in solution of a series of oxovanadium(IV) complexes comprising the aqua ion [VO(H2O)5]2+ and [VO(ox)2]2 (ox = oxalate), [VO(nta)]...
Journal ArticleDOI
TL;DR: In this article , the authors present a benchmark of isotropic electron-paramagnetic-resonance hyperfine coupling constants calculated for radical cation and anion complexes of molecules contained in the S22 test set using the frozen-density embedding quasi-diabatization approach.
Abstract: We present a systematic benchmark of isotropic electron-paramagnetic-resonance hyperfine coupling constants calculated for radical cation and anion complexes of molecules contained in the S22 test set using the frozen-density embedding quasi-diabatization (FDE-diab) approach. The results are compared to those from Kohn-Sham density-functional theory and frozen-density embedding, employing the domain-based local pair natural orbital coupled cluster singles and doubles method as a reference. We demonstrate that our new approach outperforms frozen-density embedding in all cases and provides reliable hyperfine couplings for radical cations using rather simple generalized-gradient approximation-type functionals. By contrast, more sophisticated and computationally less efficient exchange-correlation approximations are required for Kohn-Sham density-functional theory. For the radical anions, FDE-diab can at least provide an accuracy similar to that of Kohn-Sham density-functional theory. Finally, we demonstrate the computational advantages of FDE-diab for a π-stacked benzene octamer radical cation.
References
More filters
Journal ArticleDOI
TL;DR: A simple derivation of a simple GGA is presented, in which all parameters (other than those in LSD) are fundamental constants, and only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked.
Abstract: Generalized gradient approximations (GGA’s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. [S0031-9007(96)01479-2] PACS numbers: 71.15.Mb, 71.45.Gm Kohn-Sham density functional theory [1,2] is widely used for self-consistent-field electronic structure calculations of the ground-state properties of atoms, molecules, and solids. In this theory, only the exchange-correlation energy EXC › EX 1 EC as a functional of the electron spin densities n"srd and n#srd must be approximated. The most popular functionals have a form appropriate for slowly varying densities: the local spin density (LSD) approximation Z d 3 rn e unif

146,533 citations

Journal ArticleDOI
Axel D. Becke1
TL;DR: This work reports a gradient-corrected exchange-energy functional, containing only one parameter, that fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more.
Abstract: Current gradient-corrected density-functional approximations for the exchange energies of atomic and molecular systems fail to reproduce the correct 1/r asymptotic behavior of the exchange-energy density. Here we report a gradient-corrected exchange-energy functional with the proper asymptotic limit. Our functional, containing only one parameter, fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more.

45,683 citations

Journal ArticleDOI
TL;DR: The M06-2X meta-exchange correlation function is proposed in this paper, which is parametrized including both transition metals and nonmetals, and is a high-non-locality functional with double the amount of nonlocal exchange.
Abstract: We present two new hybrid meta exchange- correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amount of nonlocal exchange (2X), and it is parametrized only for nonmetals.The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree–Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree–Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochemistry, four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for molecular excitation energies. We also illustrate the performance of these 17 methods for three databases containing 40 bond lengths and for databases containing 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochemistry, kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chemistry and for noncovalent interactions.

22,326 citations

Journal ArticleDOI
TL;DR: A large set of more than 300 molecules representing all elements-except lanthanides-in their common oxidation states was used to assess the quality of the bases all across the periodic table, and recommendations are given which type of basis set is used best for a certain level of theory and a desired quality of results.
Abstract: Gaussian basis sets of quadruple zeta valence quality for Rb-Rn are presented, as well as bases of split valence and triple zeta valence quality for H-Rn. The latter were obtained by (partly) modifying bases developed previously. A large set of more than 300 molecules representing (nearly) all elements-except lanthanides-in their common oxidation states was used to assess the quality of the bases all across the periodic table. Quantities investigated were atomization energies, dipole moments and structure parameters for Hartree-Fock, density functional theory and correlated methods, for which we had chosen Moller-Plesset perturbation theory as an example. Finally recommendations are given which type of basis set is used best for a certain level of theory and a desired quality of results.

17,964 citations

Journal ArticleDOI
TL;DR: In this article, the unpolarized absorption and circular dichroism spectra of the fundamental vibrational transitions of the chiral molecule, 4-methyl-2-oxetanone, are calculated ab initio using DFT, MP2, and SCF methodologies and a 5S4P2D/3S2P (TZ2P) basis set.
Abstract: : The unpolarized absorption and circular dichroism spectra of the fundamental vibrational transitions of the chiral molecule, 4-methyl-2-oxetanone, are calculated ab initio. Harmonic force fields are obtained using Density Functional Theory (DFT), MP2, and SCF methodologies and a 5S4P2D/3S2P (TZ2P) basis set. DFT calculations use the Local Spin Density Approximation (LSDA), BLYP, and Becke3LYP (B3LYP) density functionals. Mid-IR spectra predicted using LSDA, BLYP, and B3LYP force fields are of significantly different quality, the B3LYP force field yielding spectra in clearly superior, and overall excellent, agreement with experiment. The MP2 force field yields spectra in slightly worse agreement with experiment than the B3LYP force field. The SCF force field yields spectra in poor agreement with experiment.The basis set dependence of B3LYP force fields is also explored: the 6-31G* and TZ2P basis sets give very similar results while the 3-21G basis set yields spectra in substantially worse agreements with experiment. jg

17,871 citations