Some thoughts about the stability and reliability of commonly used exchange–correlation functionals – coverage of dynamic and nondynamic correlation effects

 The self-interaction error (SIE) of commonly used density functional theory (DFT) exchange functionals mimics long-range (nondynamic) pair correlation effects in an unspecified way. Slater exchange suffers from a larger SIE and, therefore, covers more nondynamic correlation effects than Becke exchange, which is the reason why exchange–correlation (XC) functionals based on Slater exchange lead to stabler restricted DFT solutions than those based on Becke exchange. However, the stability of an XC functional does not guarantee higher accuracy. On the contrary, if system-specific nondynamic correlation effects have to be introduced via the form of the wave function, these will be suppressed by nondynamic correlation effects already covered by the exchange functional. Hybrid functionals suffer less from the SIE and, therefore, cover a smaller number of nondynamic electron correlation effects. Accordingly, they are better suited when nondynamic electron correlation has to be introduced by the form of the wave function. It is shown that, for example, broken-symmetry unrestricted DFT calculations are more accurate when carried out with B3LYP than BLYP contrary to claims made in the literature. Received: 8 November 2001 / Accepted: 30 January 2002 / Published online: 8 April 2002     

芳香性氨基酸的二次谐波非线性光学性质

采用密度泛函理论(DFT)-B3LYP方法在6-31G^*基组水平上,对芳香性氨基酸分子体系(Phe, [Phe―H]^-,PheH^*, Tyr, [Tyr―H]^-, TyrH⁺, Trp, [Trp―H]^-和TrpH⁺)进行结构优化. 在优化所得构型的基础上, 利用含时密度泛函理论(TDDFT)-B3LYP在6-31G^*基组上计算了它们的激发态性质,并结合态求和方法研究了它们在二次谐波过程中的二阶极化率值. 同时讨论了二次谐波非线性光学响应的起源及其产生变化的原因. 计算结果表明,相对于中性的氨基酸分子, 去质子化和质子化后的氨基酸分子的二阶极化率值都有明显的增加, 且符合规律Phe < PheH⁺ < [Phe―H]^-和Tyr < TyrH⁺ < [Tyr―H]^-. 通过对它们电极化起源的分析, 我们得到对于中性氨基酸分子, 侧链芳香环上的π→π^*跃迁对二阶极化率起主要贡献; 对去质子化和质子化后的氨基酸分子, 吲哚环上的π→π^*电荷跃迁和α碳原子相连的氨基和羧基基团内电荷跃迁对二阶极化率起到同样重要的贡献.     

Rotational and vibrational temperatures of naphthalene in a naphthalene-argon supersonic jet

In the $\text{A}$¹B_2u-$\text{X}$¹A_g system of naphthalene in a supersonic jet, rotational contour calculations show rotational temperatures of 2–60 K for argon carrier gas pressures of 1520-120 Torr. The b_1u vibration v₂₄ shows a high vibrational temperature which corresponds to the seeding temperature for pressures <400 Torr.     

Density functional theory and molecular clusters

Density functional theory (DFT) methods, including nonlocal density gradient terms in the exchange and correlation energy functionals, were applied to various types of molecular clusters: H-bonded, ionic, electrostatic, and London. Reliable results on the structure and stabilization energy were obtained for the first two types of cluster as long as Becke3LYP and Becke3P86 functionals and basis sets of at least DZ + P quality were used. DFT methods with currently available functionals failed completely, however, for London-type clusters, for which no minimum was found on the potential energy surfaces. DFT interaction energy exhibits the same basis set extension dependence as the Hartree-Fock (HF) interaction energy. Therefore, the Boys-Bernardi function counterpoise procedure should be employed for elimination of the DFT basis set superposition error. © 1995 John Wiley & Sons, Inc.     

Theoretical Study on Resonance Raman Spectra of Tetraoxaporphyrin Dication by TDDFT Calculation

The B state excited resonance Raman scattering of tetraoxaporphyrin dication (TOP²⁺) was theoretically studied with DFT/TDDFT calculations and the sum-over-states approach of polarizability including both the A and B terms contributions. The resonance Raman spectra calculated with PBE1PBE, B3LYP, Cam-B3LYP, and B3LYP-D3 functionals are similar to each other in general, with PBE1PBE and B3LYP being better in reproducing resonance Raman intensities in comparison with the experiment. The calculated relative intensities of the totally symmetric modes are excellently consistent with the experiment. The TDDFT calculations manifested a considerable deformation of the B state along theυ2,υ6, υ7, and υ8 modes, which is responsible for the strong resonance Raman intensities of these modes. The resonance Raman intensities of non-totally symmetric modes were calculated to be weaker than the totally symmetric modes by one or two order of magnitude, whichqualitatively agrees with the experiment. However, the resonance Raman intensity of the υ10 mode (C_βC_β stretch, B_1g symmetry) predicted by TDDFT calculations is unexpectedly small whereas that of the υ11 mode (symmetric C_αC_m stretch, B_1g symmetry) is too large, which is assumed to be caused by the Jahn-Teller instability for the B state of TOP²⁺.     

Plectranthoic acid A & B, two new triterpenoids from Plectranthus rugosus

Two new triterpenoid acids, designated as plectranthoic acid A and plectranthoic acid B, have been isolated from P. rugosus and are characterised as (20-S)-3α-hydroxy-18α,19α-$\text{H}\text{-}$-urs-12-en-30β-oic acid and (14-S)-3α-hydroxy-18α, 19α $\text{H}\text{-}$-urs-12-en-27α-oic acid.     

Theory of titration curves: Locations of points of maximum slope on potentiometric heterovalent (“asymmetrical”) precipitation titration curves

By a wholly rigorous general treatment of the potentiometric titration curve representing the titration of B^m+ with A^n- to give the precipitate B_nA_m, where n ≠ m, it is shown on taking into account the effect of dilution that: (1) If $\text{n}\text{m}$ > 1, the inflection point must precede the equivalence point, but there is no inflection point if the initial concentration of the ion titrated is smaller than a certain value, which is determined by the values of m, n, and the solubility product of the precipitate. (2) If $\text{n}\text{m}$ < 1, the inflection point may follow the equivalence point — though not by more than a certain definite amount — or may precede it or coincide with it. In every such case there is a concentration of A^n- that will cause the equivalence point to coincide with an inflection point; this concentration depends on the values of m, n, and the solubility product of the precipitate. (3) Unless the difference between the equivalence and inflection points is negligibly small, the traditional treatment in which dilution is neglected gives seriously erroneous estimates of the location of the inflection point.     

DFT investigation for 1:2 complexes of bis(hexafluoroacetylacetonato)copper(II) coordinated with 4-(N-tert-butyl-N-oxyamino)pyridine

With the aim to explore the nature of interaction between organic radicals and paramagnetic ion, unrestricted density functional theory (UDFT) and restricted open shell DFT (RO-DFT) calculations using 6-31G(d) and LANL2DZ basis sets have been performed on the 1:2 complexes of bis(hexafluoroacetylacetonato)copper coordinated with 4-(N-tert-butyl-N-oxyamino)pyridine, complex 1. Structural data revealed by X-ray crystal analysis are used. It is found that the calculated results depend on the selected functionals, model orientation, basis set form and symmetry constraint. The proper chemical models for investigated system are RO-B3LYP, RO-BLYP, RO-PBE, and RO-PBE0.     

B24N24 nanocages: a GIAO density functional theory study of 14N and 11B nuclear magnetic shielding and electric field gradient tensors

Abstract  

Density functional theory (DFT) calculations were performed to determine boron-11 and nitrogen-14 nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) spectroscopy parameters in the three most stable B₂₄N₂₄ fullerenes for the first time. The considered samples were first allowed to relax entirely, and then the NMR and NQR calculations were performed on the geometrically optimized models. The calculations of the ¹¹B and ¹⁴N nuclear magnetic shielding tensors and electric field gradient tensors employed the Gaussian 98 software implementation of the gauge-including atomic orbital (GIAO) method using the Becke3, Lee-Yang-Parr (B3LYP) DFT level and 6-311G** and 6-311++G** standard basis sets in each of the three optimized forms, and converted the results to experimentally measurable NMR parameters.The calculated NMR chemical shieldings of the three cages show significant differences, providing a way to identify these clusters. The evaluated NQR parameters of the ¹¹B and ¹⁴N nuclei in the clusters are also reported and discussed.     

Stereochemistry of copper- and nickel-catalyzed insertion of carbon dioxide into epoxides. A microwave study

Reaction of trans-1,2-dideuterioethene oxide ($\text{1}$) with carbon dioxide, using copper and nickel catalysts, and subsequent analysis of the product ethene carbonate-d₂ ($\text{2}$) by microwave spectroscopy, shows that the copper-catalyzed reaction is stereo-specific (retention) whereas the nickel-catalyzed reaction is non-stereospecific.     

One-step protection of the nucleoside base in thymidine and uridine

Unprotected thymidine and uridine react with 4-nitrophenylsulfonyl ethene ($\text{3}$) in a base catalyzed Michael type addition to give O⁴-(4-nitrophenylsulfonylethyl)thymidine-($\text{6}$) and -uridine ($\text{7}$), respectively. The 4-nitrophenylsulfonylethyl group is cleaved within 2.5 hours at 50–55°C by concentrated aqueous ammonia, via β-elimination.     

Chemical synthesis of the 5-́half molecule of E.coli tRNA2GLY

A tritriacontanucleotide which has the sequence of the 5$\text{-}\text{?}$half molecule of E.coli glycine tRNA₂, was synthesized by the phosphotriester method involving p-anisidate protection for the 3$\text{-}\text{?}$phosphate ends. Di- and trinucleotide units were prepared from 5$\text{-}\text{?}$dimethoxytrityl-2$\text{-}\text{?}$O-tetrahydrofuranyl-3?-O-(o-chlorophenyl)phosphoryl derivatives of uridine, N-benzoylcytidine, N-benzolyadenosine and N-iso-butyrylguanosine by condensation with 3$\text{,}\text{?}$5$\text{-}\text{?}$unprotected nucleosides followed by phosphorylation to give 3$\text{-}\text{?}$phosphodiester blocks. The 3$\text{-}\text{?}$terminal dimers and trimers were synthesized by using 3$\text{-}\text{?}$(o- chlorophenyl)phosphoro-p-anisidates instead of 3?,5?-unprotected nucleosides. The 3?-phosphodiesters of oligonucleotides with a chain length of larger than 5 were obtained by removal of the 3?-phosphoro-p-anisidate with isoamyl nitrite. The 5$\text{-}\text{?}$dimethoxytrityl group was removed by treatment with zinc bromide under anhydrous conditions. Fragments were designed to use common dimer blocks and to reduce the step for 5$\text{-}\text{?}$deblocking of larger fragments. Finally a 3$\text{-}\text{?}$phosphodiester block with a chain length of 20 was condensed with a 5$\text{-}\text{?}$OH component (tridecanucleotide). The fully protected 33 mer was deblocked and purified by chromatography. The structural integrity of the product was confirmed by mobility shift analysis and complete digestion with RNase T2.     

B<Subscript>24</Subscript>N<Subscript>24</Subscript> nanocages: a GIAO density functional theory study of <Superscript>14</Superscript>N and <Superscript>11</Superscript>B nuclear magnetic shielding and electric field gradient tensors

Abstract  Density functional theory (DFT) calculations were performed to determine boron-11 and nitrogen-14 nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) spectroscopy parameters in the three most stable B₂₄N₂₄ fullerenes for the first time. The considered samples were first allowed to relax entirely, and then the NMR and NQR calculations were performed on the geometrically optimized models. The calculations of the ¹¹B and ¹⁴N nuclear magnetic shielding tensors and electric field gradient tensors employed the Gaussian 98 software implementation of the gauge-including atomic orbital (GIAO) method using the Becke3, Lee-Yang-Parr (B3LYP) DFT level and 6-311G** and 6-311++G** standard basis sets in each of the three optimized forms, and converted the results to experimentally measurable NMR parameters.The calculated NMR chemical shieldings of the three cages show significant differences, providing a way to identify these clusters. The evaluated NQR parameters of the ¹¹B and ¹⁴N nuclei in the clusters are also reported and discussed. Graphical abstract        

Assessing the performance of density functional theory for the dynamic polarizabilities of amino acids: Treatment of correlation and role of exact exchange

The theoretical determination of electric response properties of the biological systems is a field where the application of density functional theory (DFT) appears to be quite promising. In this work, the performance of 41 density functional methods is evaluated in predicting dynamic polarizabilities of an experimental benchmark set of 20 proteinogenic amino acids. The behavior of a large number of density functionals, including various types of the local spin density approximation (LSDA), generalized gradient approximation (GGA), meta‐GGA (m‐GGA), hybrid‐GGA (h‐GGA), hybrid meta‐GGA (hm‐GGA), and range‐separated hybrid‐GGA (rsh‐GGA), has been assessed for the purpose. Analyzing the results of our DFT benchmarking, we found that these computationally economical methods show very diverse predictive capability and a careful selection of DFT functionals is very important in the polarizability calculations. Considering the role of exchange, correlation, dispersion and long‐range corrections, it turned out that in the LSDA class, SVWN3 gives better results than SPL and SVWN5 toward the reference values. Of the GGA methods, OPBE outperforms all other functionals. The M06‐L is the best method of m‐GGA class. The B3LYP and TPSSh are the best functionals of h‐GGA and hm‐GGA lineages, respectively. Finally, CAM‐B3LYP is the best method of rsh‐GGA functionals that predicts the most accurate polarizability for amino acids by a large margin with respect to others. Overall, the best performing functionals turn out to be hm‐GGAs TPSSh, TPSS1KCIS, M05, tau‐HCTHhyb, and h‐GGA B3LYP. Hopefully, the results of this investigation might provide the useful guidance to propose a new exchange‐correlation functional for calculating the optical properties of biomolecular materials. © 2013 Wiley Periodicals, Inc.     

A synthetic approach to crown ether analogs by the remote photocyclization with a pai system of phthalimide and methylthio groups

Upon irradiation a homologous series of certain phthalimides ($\text{2a}$-$\text{c}$) possessing a terminal sulfide function in their N-poly-ether side chain undergo regioselective remote photocyclization affording seven to fifteen-membered crown ether analogs ($\text{3a}$-$\text{c}$) in moderate yields.