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Exchange functionals used in density functional theory (DFT) are generally considered to simulate long-range electron correlation effects. It is shown that these effects can be traced back to the self-interaction error (SIE) of approximate exchange functionals. An analysis of the SIE with the help of the exchange hole reveals that both short-range (dynamic) and long-range (nondynamic) electron correlation effects are simulated by DFT exchange where the local density approximation (LDA) accounts for stronger effects than the generalized gradient expansion (GGA). This is a result of the fact that the GGA exchange hole describes the exact exchange hole close to the reference electron more accurately than the LDA hole does. The LDA hole is more diffuse, thus leading to an underestimation of exchange and stronger SIE effects, where the magnitude of the SIE energy is primarily due to the contribution of the core orbitals. The GGA exchange hole is more compact, which leads to an exaggeration of exchange in the bond and the nonbonding region and negative SIE contributions. Partitioning of the SIE into intra-/interelectronic and individual orbital contributions makes it possible to test the performance of a given exchange functional in different regions of the molecule. It is shown that Hartree–Fock exchange always covers some long-range effects via interelectronic exchange while self-interaction-corrected DFT is lacking these effects.

The multipath spin–spin coupling mechanism in cyclic compounds leads to NMR spin–spin coupling constants (SSCCs) strongly deviating from normal SSCCs. This is shown for nJ(CC), nJ(CH), and nJ(HH) coupling constants of cyclic and bicyclic compounds using the recently developed decomposition of of J into orbital contributions using orbital currents and partial spin polarization (J-OC-PSP). A typical multipath SSCC depends on a through-space part, two or more through-bond parts, and the path-path interaction part where the latter results from steric exchange repulsion between the bond paths. The sign and magnitude of the through-space contribution as well as the through-bond contributions can be predicted by analysis of the Fermi contact spin density distribution calculated from the localized molecular orbitals involved in the coupling mechanism. In this way, unusual SSCCs of cyclopropane and bicyclo[1.1.1]pentane are explained for the first time. Also, measured and calculated 2J(CC) coupling constants of cyclopentane and tetrahydrofuran are shown to be averages over the pseudorotational motion of these ring molecules where each individual SSCC of a conformation passed in the pseudorotation is the sum of different path contributions. The three-bond path contributions dominate the 2J(CC) coupling constants of the pseudorotating molecules and introduce its dependence on the pseudorotational phase angle.

The 2A″ state of ClOO and BrOO is investigated using single- and multi-reference DFT (density functional theory). Unrestricted DFT (UDFT) carried out with the BLYP functional exaggerates the ionic character of the X–OO bond (X=Cl, Br) and by this its bond dissociation energy, while UDFT with the B3LYP functional underestimates ionic character and bond dissociation energies. In previous investigations, this was overlooked and has led to a misleading interpretation of single determinant UDFT results for XOO(2A″). The correct description of the two radicals can only be achieved by an appropriate configurational state mixing between the doublet ground state (leading to ionic character) and the first excited state, a quartet state leading to covalent character of the X–OO bond. REKS (spin-restricted ensemble-referenced Kohn–Sham) theory provides a multireference description and is capable of describing bonding in XOO correctly provided it is carried out with the hybrid functional B3LYP rather than BLYP, which is the result of the self-interaction error of pure exchange functionals and the inclusion of non-specific non-dynamic electron correlation effects suppressing the specific ones introduced by REKS. The relevance of results for the DFT description of related compounds (HOOO radical, MOO with M =Cu, Ag or Au) or multi-reference problems in general is discussed.

A simple and variationally stable quasi-relativistic method based on a modified low-order (LO) approximation to the normalized elimination of the small component (NESC) method is presented. The modification of the original LO-NESC scheme implies the use of an energy-independent factor in the relativistic correction to the potential energy. This factor cuts off the potential energy at short distances from the nucleus and in this way restores the variational stability of LO-NESC. The new method, dubbed LO-NESC-effective potential (EP) was tested in calculations on one-, two- and many-electron atoms. The LO-NESC-EP can be easily implemented into the existing nonrelativistic quantum-chemical program codes because its Hamiltonian matrix can be expressed entirely in terms of the integrals appearing in a nonrelativistic calculation.

A 13C, 15N-labeled DNA hairpin molecule of the sequence d(GCGAAGC) = d(G1C2G3A4A5G6C7) is investigated by NMR spectroscopy to determine one-bond and two-bond NMR spin-spin coupling constants 1J(X, H) (X= C, N), 1J(C, X) (X= C, N), and 2J(X,H) (X=C,N). Measured J values for the Watson-Crick (WC) base-pairs G1C7, G6C2, the mismatched base-pair G3A5 and the unpaired base A4 were compared with calculated J values to verify sign and magnitude. For the J-calculations, coupled perturbed density functional theory in connection with the B3LYP hybrid functional and basis sets (9s5p1d/5s,1p)[6s,4p,1d/3s,1p] as well as (11s,7p,2d/6s,2p)[7s,6p,2d/4s,2p] was employed to determine diamagnetic spin-orbit, paramagnetic spin-orbit, Fermi contact, and spin-dipolar contributions to the total isotropic coupling constant J. Coupling constants 1J(C,H) and 2J(N,H) turn out to be very sensitive to the position of C and N in the pyrimidine or purine rings and, therefore, can be used for rapid structure determination. Coupling constant 1J(N1,C6) in G of GC clearly reflects the impact of H-bonding by an increase from -6.5 to -10.6 Hz. The direct investigation of H-bonding via the 2J(N,N') coupling constants reveals that these parameters depend on the distance R(N-N'), the bending angle N-H..N', and the degree of planarity at the H-donor group. Different types of H-bonding were identified. H-bonding is weaker in AG and therefore, leads to smaller changes in the J values of the bases A and G upon pairing than in the case of the WC base-pair GC.

For the first time, the Bergman reaction of a naturally occurring enediyne, namely dynemicin A, is fully investigated at the DFT level of theory using the B3LYP hybrid functional and VDZ basis sets. The calculated geometry of dynemicin A agrees well with the X-ray structure of deoxydynemicin A. The activation barrier is calculated to be 19.4 kcal/mol, while the reaction energy is exothermic by −2.1 kcal/mol, reflecting the destabilization of the enediyne unit by incorporation into a tricyclic ring system. The energetics of dynemicin A reveal that the enediyne is biologically active at body temperature.

The self-interaction error (SIE) of commonly used DFT functionals has been systematically investigated by comparing the electron density distribution ρ(r) generated by self-interaction corrected DFT (SIC-DFT) with a series of reference densities obtained by DFT or wavefunction theory (WFT) methods that cover typical electron correlation effects. Although the SIE of GGA functionals is considerably smaller than that of LDA functionals, it has significant consequences for the coverage of electron correlation effects at the DFT level of theory. The exchange SIE mimics long range (non-dynamic) pair correlation effects, and is responsible for the fact that the electron density of DFT exchange-only calculations resembles often that of MP4, MP2 or even CCSD(T) calculations. Changes in the electron density caused by SIC-DFT exchange are comparable with those that are associated with HF exchange. Correlation functionals contract the density towards the bond and the valence region, thus taking negative charge out of...

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.

Unrestricted density functional theory (UDFT) can be used for the description of open-shell singlet (OSS) biradicals provided a number of precautions are considered. Biradicals that require a two-determinantal wave function (e.g. OSS state of carbenes) cannot be described by UDFT for principal reasons. However, if the overlap between the open-shell orbitals is small (the single electrons are located at different atomic centers) errors become small and, then, the principal failure of UDFT in these cases is not apparent and may even be disguised by the fact that UDFT has the advantage of describing spin polarization better than any restricted open shell DFT method. In the case of OSS biradicals with two- or multiconfigurational character (but a onedeterminantal form of the leading configuration), reasonable results can be obtained by broken-symmetry (BS)-UDFT, however in each case this has to be checked. In no case is it reasonable to lower the symmetry of a molecule to get a suitable UDFT description. Hybrid functionals such as B3LYP perform better than pure DFT functionals in BS-UDFT calculations because the former reduce the self-interaction error of DFT exchange functionals, which mimics unspecified static electron correlation effects, so that the inclusion of specific static electron correlation effects via the form of the wavefunction becomes more effective.

The reaction modes of the three isomers, carbonyl oxide (A), dioxirane (B), and methylenebis(oxy) (C), with ethylene (E) were investigated by using CASPT2, CCSD(T), and B3LYP with a 6-311+G(2d,2p) basis set. Contrary to general expectations, A prefers to react with E via a [4+2] cycloaddition reaction (activation enthalpy ΔH#(298) = 1.0 kcal/mol) to yield 1,2-dioxolane (MA2) (reaction enthalpy, −65.0 kcal/mol) rather than via an epoxidation reaction (ΔH#(298) = 11.3 kcal/mol) leading to oxirane and formaldehyde. Epoxidation by B is slower in view of an activation enthalpy of 13.7 kcal/mol; however, it should proceed stereochemically similar as in the case of A. Biradicals C and E can undergo a pseudo-[4+2] cycloaddition reaction (ΔH#(298) = 1.8 kcal/mol), which leads to 1,3-dioxolane (MC2) in a strongly exothermic reaction (ΔHR(298) = −84.5 kcal/mol). The results obtained lead to a mechanistic reconsideration of epoxidation reactions observed in the course of the ozonolysis. They also provide a general ba...

A recently developed variationally stable quasi-relativistic method, which is based on the low-order approximation to the method of normalized elimination of the small component, was incorporated into density functional theory (DFT). The new method was tested for diatomic molecules involving Ag, Cd, Au, and Hg by calculating equilibrium bond lengths, vibrational frequencies, and dissociation energies. The method is easy to implement into standard quantum chemical programs and leads to accurate results for the benchmark systems studied.

A new Karplus equation for pseudorotating five-membered rings is derived by expanding calculated NMR spin-spin coupling constants (SSCCs) J as a function J(q,o) of the puckering amplitude q and the pseudorotational phase angle o. The approach was tested for cyclopentane but is equally applicable to ribose sugars and other biochemically interesting five-membered rings. It is based on the calculation of the conformational potential V(q,o), which in the case of cyclopentane was determined at the MBPT(2)/cc-pVTZ level of theory. Cyclopentane is a free pseudorotor (barriers ΔE and ΔH ≤ 0.01 kcal/mol) with a puckering amplitude q = 0.43 A and a barrier to inversion ΔH = 5.1 kcal/mol, in perfect agreement with experimental data. The SSCCs of cyclopentane were calculated at MBPT(2)/cc-pVTZ geometries by use of coupled perturbed density functional theory (CP-DFT) with the B3LYP functional and a (9s,5p,1d/5s,1p)-[6s,4p,1d/3s,1p] basis set. In addition, coupled-cluster singles and doubles (CCSD) calculations were carried out to verify the CP-DFT results. All geometrical parameters and the 10 SSCCs of cyclopentane are determined as functions of the phase angle o and averaged to give values that can be compared with experimental data. The following SSCCs (in hertz) were obtained at CP-DFT/B3LYP/[6s,4p,1d/3s,1p]: = 34.0; = 127.6, exp 128.2; = 2.3, exp (+)2.8; = -2.6, exp (-)3.0; = -12.4, exp (-)12.4; = 3.9; = 7.7, exp 7.7; = 5.6, exp 6.3; = 0.1; = -0.6. Magnitude and trends in calculated SSCCs are dominated by the Fermi contact term [with the exception of 1 J(CC)]. A new way of determining puckering amplitude and pseudorotational angle by a combination of measured and calculated SSCCs is presented.

Extensive quantum chemical calculations involving more than 20 different methods and including vibrational, temperature, entropic, and environmental corrections suggest that 11,11-dimethyl-1,6-methano[10]annulene (1) is characterized by a broad, asymmetric single well potential minimum in which the molecule can carry out a large-amplitude vibration. This result is obtained by using CASPT2(14,14) and CCSD(T) together with a VTZ basis set. The average R(C1C6) distance of 1 is close to 1.8 Å, in agreement with X-ray diffraction measurements. Lower level methods fail because a reliable account of the electronic structure of bridged annulenes requires a balanced description of nondynamical and dynamical electron correlation effects as well as a correct assessment of bridge-annulene interactions. An independent determination of the distance R using the mean deviation between the calculated and measured (13)C NMR chemical shifts of 1 leads to a value of 1.79 Å. By using electron density, energy density, and the local C1C6 stretching mode, it is demonstrated that the covalent bond ceases to exist at 1.695 Å and that for larger R values through-space homoaromatic interactions lead to some stabilization. The peculiar potential of 1 is shown to be a result of the interaction of the methyl groups with the perimeter CC bonds bisected by the symmetry plane of the molecule. CASPT2(14,14), CASPT2(10,10), CCSD(T), and BD(T) calculations were also used to provide for the first time reliable descriptions of the valence tautomeric potentials for the parent molecule, 1,6-methano[10]annulene (2), and the system 1,3,5-cycloheptatriene-norcardiene (3). In the latter case, calculations confirm a previous kinetic measurement of the free activation energy but correct NMR-based estimates. The methodology described can be applied to other annulenes and fullerenes.

Combination of the dithiol N,N'-bis(2-mercaptoethyl)isophthalamide, abbreviated as BDTH2 and as 1, with excess H2SeO3 in aqueous acidic (pH ≈ 1) conditions resulted in precipitation of BDT(S-Se-S) (6), with a (77)Se NMR chemical shift of δ = 675 ppm, and oxidized BDT. When the reaction is conducted under basic conditions Se(IV) is reduced to red Se(0) and oxidized 1. No reaction takes place between 1 and selenate (Se(VI)) under acidic or basic conditions. Compound 6 is stable in air but decomposes to red Se(0) and the disulfide BDT(S-S) (9) with heating and in basic solutions. Mechanisms and energetics of the reactions leading to 6 in aqueous solution were unraveled by extensive calculations at the ωB97X-D/aug-cc-pVTZ-PP level of theory. NMR chemical shift calculations with the gauge-independent atomic orbital (GIAO) method for dimethyl sulfoxide as solvent confirm the generation of 6 (calculated δ value = 677 ppm). These results define the conditions and limitations of using 1 for the removal of selenite from wastewaters. Compound 6 is a rare example of a bidentate selenium dithiolate and provides insight into biological selenium toxicity.

The electron correlation effects covered by density functional theory (DFT) can be assessed qualitatively by comparing DFT densities ρ(r) with suitable reference densities obtained with wavefunction theory (WFT) methods that cover typical electron correlation effects. The analysis of difference densities ρ(DFT)-ρ(WFT) reveals that LDA and GGA exchange (X) functionals mimic non-dynamic correlation effects in an unspecified way. It is shown that these long range correlation effects are caused by the self-interaction error (SIE) of standard X functionals. Self-interaction corrected (SIC) DFT exchange gives, similar to exact exchange, for the bonding region a delocalized exchange hole, and does not cover any correlation effects. Hence, the exchange SIE is responsible for the fact that DFT densities often resemble MP4 or MP2 densities. The correlation functional changes X-only DFT densities in a manner observed when higher order coupling effects between lower order N-electron correlation effects are included. ...

Density functional theory (DFT) predicts that bicyclo[3.1.0]hexatriene ( 2 ) is more stable than its isomer m -benzyne ( 1 ). Hess [Eur. J. Org. Chem. (2001) 2185] has argued that experimental findings suggesting 1 can equally or even better be associated with 2 . However, high level ab initio calculations (CCSD(T), CASPT2) show that 2 does not exist and that the previously measured infrared spectrum is correctly assigned to 1 . Bond stretch isomers are possible for p -benzynes but not for m -benzynes. The electrophilic character of m -benzynes is in line with 1 but not with 2 .

The van der Waals complexes benzene-argon (BAr), fluorobenzene-argon (FAr), p-difluorobenzene-argon (DAr) are investigated at the second-order Moller–Plesset (MP2) level of theory using the 6-31+G(d), cc-pVDZ, aug-cc-pVTZ, and [7s4p2d1f/4s3p1d/3s1p] basis sets. Geometries, binding energies, harmonic vibrational frequencies, and density distribution are calculated where basis set superposition errors are corrected with the counterpoise method. Binding energies turn out to be almost identical (MP2/[7s4p2d1f/4s3p1d/3s1p]: 408, 409, 408 cm−1) for BAr, FAr, and DAr. Vibrationally corrected binding energies (357, 351, 364 cm−1) agree well with experimental values (340, 344, and 339 cm−1). Symmetry adapted perturbation theory (SAPT) is used to decompose binding energies and to examine the influence of attractive and repulsive components. Fluorine substituents lead to a contraction of the π density of the benzene ring, thus reducing the destabilizing exchange-repulsion and exchange-induction effects. At the same ...

The equilibrium geometry, harmonic vibrational frequencies, and infrared transition intensities of p-benzyne were calculated at the MBPT(2), SDQ-MBPT(4), CCSD, and CCSD(T) levels of theory using different reference wave functions obtained from restricted and unrestricted Hartree-Fock (RHF and UHF), restricted Brueckner (RB) orbital, and Generalized Valence Bond (GVB) theory. RHF erroneously describes p-benzyne as a closed-shell singlet rather than a singlet biradical, which leads to orbital near-instabilities in connection with the mixing of orbital pairs b1u-ag (HOMO–LUMO), b2g-ag (HOMO-1-LUMO), and b1g-ag (HOMO-2-LUMO). Vibrational modes of the corresponding symmetries cause method-dependent anomalous increases (unreasonable force constants and infrared intensities) or decreases in the energy (breaking of the D2h symmetry of the molecular framework of p-benzyne). This basic failure of the RHF starting function is reduced by adding dynamic electron correlation. However RHF-MBPT(2), RHF-SDQ-MBPT(4), RHF-CCSD, RB-CCD, and RHF-CCSD(T) descriptions of p-benzyne are still unreliable as best documented by the properties of the b1u-, b2g-, and b1g-symmetrical vibrational modes. The first reliable spin-restricted description is provided when using Brueckner orbitals at the RB-CCD(T) level. GVB leads to exaggerated biradical character that is reduced at the GVB-MP2 level of theory. The best results are obtained with a UHF reference wave function, provided a sufficient account of dynamic electron correlation is included. At the UHF-CCSD level, the triplet contaminant is completely annihilated. UHF-CCSD(T) gives a reliable account of the infrared spectrum apart from a CCH bending vibrational mode, which is still in disagreement with experiment.

Unrestricted density functional theory (UDFT) is, in addition to its application to high spin multiplet systems, an efficient method for describing singlet biradical states. In this connection, spin contamination of the UDFT description as measured by the expectation values of Ŝ2 is of interest, but is difficult to assess since the calculation of (Ŝ2) as the expectation value of a twoparticle operator is not possible within the single-determinant approach of DFT. A new way of determining (Ŝ2) from the UDFT (UHF or any other) spin magnetization density (SMD) ms (r) = pα(r) −pβ(r) is described and applied to the stretched H2 molecule and the singlet state of the para-didehydrobenzene biradical for a number of different functionals. Although (Ŝ2) as calculated from the Kohn-Sham determinant is found to differ significantly from the corresponding value obtained with the help of the SMD in the case of singlet biradicals, the former result is a diagnostic value and can be used to assess spin contamination of th...

For seventeen molecules, complete basis set (CBS) geometries are obtained for Moller–Plesset perturbation methods at second (MP2), fourth (MP4), and sixth order (MP6) as well as for the Coupled Cluster methods CCD, CCSD, and CCSD( T ). The correlation consistent basis sets cc-pVDZ, cc-pVTZ, and cc-pVQZ were systematically applied and calculated geometries extrapolated to the limit of an infinitely large basis set. MP6 equilibrium geometries are more accurate than MP2 or MP4 geometries at the CBS limit and provide AH bond lengths with an accuracy of 0.001 A. However, AB bonds are always predicted too long because of the lack of sufficient coupling effects between p-electron correlation at MP6. CCSD( T ) provides reasonable AB bond lengths although these are in general too short by 0.003 A. Due to error cancellation very accurate geometries are obtained at the CCSD( T )/cc-pVTZ and CCSD( T )/cc-pVQZ level of theory. With the help of the accurate equilibrium geometries obtained in this work, several experimentally based geometries could be corrected. The effects of HF-optimized basis sets, diffuse functions or the frozen core approximation on geometry optimizations are discussed. It is emphasized that the use of the cc-pVDZ or any other VDZ+P basis set should be avoided in correlation corrected ab initio calculations.

Single determinant Moller−Plesset perturbation (MP) theory at second order (MP2), third order (MP3), and fourth order (MP4) with standard basis sets ranging from cc-pVDZ to cc-pVQZ quality predicts the equilibrium geometry of FOOF qualitatively incorrect. Sixth-order MP (MP6), CCSD(T), and DFT lead to a qualitatively correct FOOF equilibrium geometry re, provided a sufficiently large basis set is used; however, even these methods do not succeed in reproducing an exact re geometry. The latter can be achieved only by artificially increasing anomeric delocalization of electron lone pairs at the O atoms into the σ*(OF) orbitals by selectively adding diffuse basis functions, adjusting exponents of polarization functions, or enforcing an increase of electron pair correlation effects via the choice of a rigid basis set. DFT geometries of FOOF can be improved in a similar way and, then, DFT presents the best cost-efficiency compromise currently available for describing FOOF and related molecules. DFT and CCSD(T) ...

Dimesitylketone O-oxide ( 1 ) rearranges in solution to yield the alcohol 2-methylhydroxy-pentamethylbenzophenone ( 5 ) and dimesitylketone ( 6 ). DFT-B3LYP/cc-pVTZ calculations reveal that H migration from an o -methyl group to the terminal O atom of the COO unit of 1 rather than the isomerization of 1 is energetically the most favorable process. Calculated activation enthalpies (gas phase: 12.8 kcal/mol; CH 3 CN solution: 12.4 kcal/mol) are in excellent agreement with measured activation enthalpies (CFCl 3 solution: 13.2±0.2 kcal/mol; CH 3 CN solution: 12.5±0.3 kcal/mol). The hydroperoxide formed by H migration decomposes to a OH and a benzyl radical. Recombination in the solvent cage leads to alcohol 5 while diffusion of OH out of the solvent cage yields 6 .

CCSDT-n methods (n=1, …, 4) are analyzed in terms of many-body perturbation theory and compared with CCSD, CCSD(T), and CCSDT. Correlation terms, which are introduced at each CCSDT-n level are identified and discussed with regard to their importance for the total energy. CCSDT-1a represents the strongest improvement of CCSD since it covers 75% of the T terms added at the CCSDT level. At CCSDT-2 and CCSDT-3, only partial energy terms are added where the positive ..TQ.. coupling terms at CCSDT-2 are more important than the slightly negative ..TTS terms at CCSDT-3. CCSDT-4 leads to new ..TT.. coupling effects, which lower the energy. Calculated CCSDT-n/correlation-consistent polarized-valence triple-zeta spectra reveal that the energy changes caused by CCSDT-2, CCSDT-3, CCSDT-4, and CCSDT largely cancel each other out; however, because of a dependence of these contributions on electron clustering the importance of these effects for the correct description of certain chemical reactions must be considered. It is shown that CCSDT-1 (as well as all other CCSDT-n) calculations lead to atomization energies as accurate as G2 values, where this result reflects the importance of including at least some of the T effects.

The 4-oxocyclohexa-2,5-dienylidenes are an interesting class of highly electrophilic carbenes. We investigated the reactivity of the 2,3,5,6-tetrafluorinated and -tetrachlorinated derivatives 1b and 1c with small molecules under conditions of matrix isolation. The reactions with molecular oxygen and with carbon monoxide produce the expected carbonyl O-oxides and ketenes, respectively. As a result of the extreme electrophilicity of 1b and c both carbenes insert with no or very small activation barriers into H2 or the CH bonds of hydrocarbons. Obviously, spin restrictions for these formally spin-forbidden reactions do not result in substantial thermal activation barriers.

Coupled-cluster (CC) theory including single (S) and double (D) excitations and carried out with a spin-unrestricted Hartree–Fock (UHF) reference wave function is free from S + 1 spin contamination as can be confirmed by an analysis of the expectation value of the spin operator, Ŝ2. Contamination by the S + 2 contaminant can be projected out by an approximate procedure (APCCSD) with a projection operator, P^, represented by the product of the spin annihilation operators Âs+1 and Âs+2. The computational cost of such a projection scales with O(M6) (M is the number of basis functions). The APCCSD energy obtained after annihilation of the S + 2 contaminant can be improved by adding triple (T) excitations in a perturbative way, thus leading to APCCSD(T) energies. For the 17 examples studied, the deviation of the UHF-CCSD(T) energies from the corresponding full configuaration interaction values is reduced from 4.0 to 2.3 mhartree on the average as a result of annihilating the S + 2 contaminant in an approximate way. In the case of single-bond cleavage, APCSSD leads to a significant improvement of the energy in the region where the bonding electrons recouple from a closed shell to an open shell singlet electron pair.

Fourth-order Moller–Plesset (MP4) correlation energies are computed for 28 atoms and simple molecules employing Dunning's correlation-consistent polarized-valence m-zeta basis sets for m=2, 3, 4, and 5. Extrapolation formulas are used to predict MP4 energies for infinitely large basis sets. It is shown that both total and partial MP4 correlation energies can be extrapolated to limit values and that the sum of extrapolated partial MP4 energies equals the extrapolated total MP4 correlation energy within calculational accuracy. Therefore, partial MP4 correlation energies can be presented in the form of an MP4 spectrum reflecting the relative importance of different correlation effects. Typical trends in calculated correlation effects for a given class of electron systems are independent of the basis set used. As first found by Cremer and He [(1996) J Phys Chem 100:6173], one can use MP4 spectra to distinguish between electron systems with well-separated electron pairs and systems for which electrons cluster in a confined region of atomic or molecular space. MP4 spectra for increasing size of the basis set reveal that smaller basis set calculations underestimate the importance of three-electron correlation effects for both classes by overestimating the importance of pair correlation effects. The minimum size of a basis set required for reliable MP4 calculations is given by a valence triple-zeta polarized basis, which even in the case of anions performs better than a valence double-zeta basis augmented by diffuse functions.

The rotational spectra of the 35Cl and 37Cl isotopes of the chlorobenzene–argon van der Waals dimer have been assigned using Fourier transform microwave spectroscopy techniques. Rotational constants and chlorine nuclear quadrupole coupling constants were determined which confirm that the complex has Cs symmetry. The argon is over the aromatic ring, shifted from a position above the geometrical ring center towards the substituted carbon atom, and at a distance of about 3.68 A from it. This distance is 0.1–0.2 A shorter than the similar distance in the benzene–argon and fluorobenzene–argon complexes. Experimental results are confirmed and explained with the help of second-order Mo/ller–Plesset perturbation calculations using a VDZP+diff basis set. The complex binding energy of the chlorobenzene–argon complex is 1.28 kcal/mol (fluorobenzene–argon, 1.17; benzene–argon, 1.12 kcal/mol) reflecting an increase in stability caused by larger dispersion interactions when replacing one benzene H atom by F or by Cl. T...

The electron density distribution ρ(r) generated by a DFT calculation was systematically studied by comparison with a series of reference densities obtained by wavefunction theory (WFT) methods that cover typical electron correlation effects. As a sensitive indicator for correlation effects the dipole moment of the CO molecule was used. The analysis reveals that typical LDA and GGA exchange functional already simulate effects that are actually reminiscent of pair and three-electron correlation effects covered by MP2, MP4, and CCSD(T) in WFT. Correlation functionals contract the density towards the bond and the valence region thus taking negative charge out of the van der Waals region. It is shown that these improvements are relevant for the description of van der Waals interactions. Similar to certain correlated single-determinant WFT methods, BLYP and other GGA functionals underestimate ionic terms needed for a correct description of polar bonds. This is compensated for in hybrid functionals by mixing in...

For 30 molecules and two atoms, MPn correlation energies up to n = 6 are computed and used to analyse higher order correlation effects and the initial convergence behaviour of the MPn series. Particularly useful is the analysis of correlation contributions EXY (n) ...(n = 4,5,6; X, Y,... = S, D, T, Q denoting single, double, triple, and quadruple excitations) in the form of correlation energy spectra. Two classes of system are distinguished, namely class A systems possessing well separated electron pairs and class B systems which are characterized by electron clustering in certain regions of atomic and molecular space. For class A systems, electron pair correlation effects as described by D, Q, DD, DQ, QQ, DDD, etc., contributions are most important, which are stepwise included at MPn with n = 2,...,6. Class A systems are reasonably described by MPn theory, which is reflected by the fact that convergence of the MPn series is monotonic (but relatively slow) for class A systems. The description of class B s...

Seven criteria are developed and discussed that lead to the design of a new enediyne anticancer drug, which should have low toxicity but high biological selectivity and activity when attacking the DNA of tumor cells. These criteria concern (among others) the thermodynamic and kinetic stability of the species involved in the reaction of an enediyne, the biradical character and H-abstraction ability of the intermediate biradical generated in a Bergman reaction of the enediyne, and the basicity of the enediyne and its associated biradical. Thirteen different heteroenediynes were investigated with the help of B3LYP/6-31G(d,p) calculations to find a suitable candidate for a new enediyne anticancer drug, which fulfills the seven criteria. These calculations included the determination of reaction profiles for Bergman and retro-Bergman reactions, the calculation of singlet−triplet splittings of biradicals formed from enediynes, and the prediction of pKa values. Results were tested by using a larger basis set (6-3...

Sixth order Moller−Plesset perturbation theory (MP6) in connection with correlation consistent basis sets cc-pVDZ, cc-pVTZ, and cc-pVQZ was used to calculate accurate equilibrium geometries for 14 ...

(N,N-Dimethylaminoxy)trifluorosilane, F3SiONMe2 (1), was prepared by the reaction of LiONMe2 with SiF4 in Me2O at -96 degrees C as a colorless, air-sensitive liquid, which was identified by gas-phase IR spectroscopy and NMR spectroscopy of the nuclei H-1, C-13, N-15, O-17,F-19, and Si-29. The gas-phase geometry of 1, as determined by electron diffraction analysis refined in C-s symmetry, is influenced by weak attractive interactions between Si and N: Si ... N 2.273(17) Angstrom, Si-O-N 94.3(9)degrees, [Si-O 1.619(8) Angstrom, N-O 1.479(7) Angstrom, O-Si-Fin-plane 104.1(10)degrees, O-Si-Fout-of-plane 111.8(10)degrees]. X-ray diffraction analysis of 1 reveals that intramolecular Si N interactions are much stronger in the solid state than in the gas phase: Si ... N 1.963(1) Angstrom, Si-O-N 77.1(1)degrees [Si-O 1.639(1) Angstrom, N-O 1.508(1) Angstrom, O-Si-Fin-plane 102.5(1)degrees, O-Si-Fout-of-plane 118.0(1)degrees and 120. 1(1)degrees]. Using measured NMR chemical shifts in C6D6 solution, the geometry of 1 in solution was determined with the NMR/ab initio/DFT-IGLO method to fall between that of the gas-phase geometry and the geometry in the solid state. MP2 and DFT calculations reveal that electrostatic interactions between 1 and the surrounding medium increase with the dielectric constant epsilon since mutual charge polarization enhances the molecular dipole moment from 4 to more than 6 D, which implies a compression of the Si-O-N angle and the Si N distance. Since electrostatic attraction between N and Si supports these changes, the increase in molecular energy upon reduction of the Si ... N distance is small and compensated by the gain of stabilizing intermolecular interactions. The analysis of the calculated electron density distribution shows that the main aspects of bonding in 1 are not changed in the solid state and that the Si ... N attraction is not of covalent nature, but rather due to strong electrostatic and dipole interactions.

The bond energy (BE) of a polyatomic molecule cannot be measured and, therefore, deter- mination of BEs can only be done within a model using a set of assumptions. The bond strength is reflected by the intrinsic BE (IBE), which is related to the intrinsic atomization energy (IAE) and which represents the energy of dissociation under the provision that the degree of hybridization is maintained for all atoms of the molecule. IBE and BE differ in the case of CC and CH bonds by the promotion, the hybridization, and the charge reorganization energy of carbon. Since the latter terms differ from molecule to molecule, IBE and BE are not necessarily parallel and the use of BEs from thermochemical models can be misleading. The stretching force constant is a dynamical quantity and, therefore, it is related to the bond dissociation energy (BDE). Calculation and interpretation of stretch- ing force constants for local internal coordinate modes are discussed and it is demonstrated that the best relationship between BDEs and stretching force constants is obtained within the model of adiabatic internal modes. The valence stretching force constants are less suitable since they are related to an artificial bond dissociation process with geometrical relaxation effects suppressed, which leads to an intrinsic BDE (IBDE). In the case of AX n molecules, symmetric coordinates can be used to get an appropriate stretching force constant that is related to the BE. However, in general stretching force constants determined for symmetry coordinates do not reflect the strength of a particular bond since the related dissociation processes are strongly influenced by the stability of the products formed. Keywords Bond energy (BE), Intrinsic bond energy (IBE), Bond dissociation energy (BDE), Force constants, Adiabatic internal mode

The photochemistry of butatriene (2), matrix-isolated in argon at 10 K, was investigated. UV irradiation (248 nm) produces vinylacetylene (1) and the dimer of acetylene and in addition methylenecyclopropene (3) as a major product. The photochemical 2 → 3 rearrangement is reversible, and on visible light irradiation (λ > 420 nm) 3 is transformed back to 2. The formation of 3 from 2 requires a [1,2]-H migration to allenylcarbene (8). According to MP2 and DFT calculations, 8 is a minimum on both the triplet (T) and the singlet (S) potential energy surface (PES). The comparison of measured and calculated infrared spectra suggests that two forms of 8 (either syn and anti form of S-8 or a mixture of S-8 and T-8) can be trapped at low temperatures in the matrix. The rearrangement 2 → 3 proceeds in a stepwise manner with S-8 as intermediate on the S−PES (calculated heat of formation at 298 K, ΔH°f(298) = 131.7 kcal/mol) and T-8 on the T-PES (ΔH°f(298) = 129.0 kcal/mol).

Size-extensive Quadratic CI with single (S), double (D), triple (T), and quadruple (Q) excitations (QCISDTQ) and its non-iterative extension to a method correct at sixth-order perturbation theory, QCISDTQ(6), are developed and applied to electronic systems, for which full CI (FCI) results are available. It is shown that QCISDTQ results are more accurate than either QCISDT or CCSDT. In particular, QCISDTQ(6) correlation energies differ from FCI correlation energies on the average by just 0.04 mhartree. The improvement is caused preferentially by the balanced addition of connected and disconnected four-electron correlation effects, which confirms observations that four-electron correlation effects are important for a balanced description of electron correlation.

A long-standing controversy regarding the re structure of cyclopropane is resolved by performing high-level quantum chemical calculations and analyzing the experimental rotational constants for C3H6 and C3H4D2 augmented by calculated vibrational corrections. For the latter, a least-squares fit yields the following set of parameters: re (CC) = 1.5030(10) A, re(CH) = 1.0786(10) A, and αe(HCH) = 114.97(10)°, which compare favorably with both the pure computational result obtained at the CCSD(T)/cc-pVQZ level as well as an earlier estimate of the re structure of cyclopropane based on analysis of gas-phase electron diffraction data. Our results are in rather poor agreement with a structure based on a previous analysis of the rotational constants that used empirically estimated vibrational corrections.

CAS-DFT is presented as a method that allows an economical simultaneous treatment of static and dynamic correlation effects in molecules with multi-reference character. Central problems of CAS-DFT concern the double counting of dynamic correlation effects and the choice of the proper input quantities for the DFT functional. Also, the question of treating both active and inactive orbitals in a consistent way is discussed. Test calculations with CAS-DFT for the ring opening of dioxirane and the excitation energies of methylene prove that the method works reasonably.

The convergence behavior of the Moller–Plesset (MP) perturbation series is investigated utilizing MP correlation energies up to order 65 calculated at the full CI (FCI) level. Fast or slow convergence, initial oscillations, or divergence of the MPn series depend on the electronic system investigated and the basis set used for the FCI calculation. Initial oscillations in the MPn series are observed for systems with electron clustering due to the fact that MP theory exaggerates electron-correlation effects at even orders and corrects this at odd orders. In such cases, it is important that the s, p basis is first saturated before diffuse functions are added. With a VDZ+diff basis, too much weight is given to high-order correlation effects described by pentuple and higher excitations, which leads to the formation of artificial intruder states and to the divergence of the MPn series. This can be corrected by extending to VQZ or VPZ basis sets before one adds diffuse functions. Alternatively, one can use m-order Feenberg scaling to exclude backdoor intruder states from the convergence region of the MPn series. For all cases considered, divergence of the MPn series caused by unbalanced basis sets including diffuse functions can be suppressed by Feenberg scaling. Also, initial oscillations of the MPn series can be dampened and convergence acceleration of the MPn series achieved if the appropriate order of Feenberg scaling is determined for the problem in question. The relationship between electronic structure, basis set, and convergence of the MPn series is discussed. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 306–330, 2000

Vibrational spectra contain explicit information on the electronic structure and the bonding situation of a molecule, which can be obtained by transforming the vibrational normal modes of a molecule into appropriate internal coordinate modes, which are localized in a fragment of the molecule and which are associated to that internal coordinate that describes the molecular fragment in question. It is shown that the adiabatic internal modes derived recently (Int. J. Quant. Chem., 67 (1998) 1) are the theoretical counterparts of McKean's isolated CH stretching modes (Chem. Soc. Rev., 7 (1978) 399). Adiabatic CH stretching frequencies obtained from experimental vibrational spectra can be used to determine CH bond lengths with high accuracy. Contrary to the concept of isolated stretching frequencies a generalization to any bond of a molecule is possible as is demonstrated for the CC stretching frequencies. While normal mode frequencies do not provide a basis to determine CC bond lengths and CC bond strengths, this is possible with the help of the adiabatic CC stretching frequencies. Measured vibrational spectra are used to describe different types of CC bonds in a quantitative way. For CH bonds, it is also shown that adiabatic stretching frequency leads to the definition of an ideal dissociation energy, which contrary to the experimentally determined dissociation energy is a direct measure of the bond strength. The difference between measured and ideal dissociation energies gives information on stabilization or destabilization of the radicals formed in a dissociation process.

The reaction of dimethyl ether (1) with atomic oxygen generated by photolysis of ozone or N2O was examined in low-temperature matrices. The major reaction products are two conformers of methoxymethanol (5). IR absorptions of the products were assigned by isotopic labeling (18O and D) and DFT calculations at the B3LYP/6-311++G(d,p) level of theory. The mechanism of the formation of 5, in particular H abstraction from 1 by atomic oxygen (O3P and O1D), was investigated using UMP, UCCSD(T), and UDFT. In both the H abstraction and the O(1D) insertion reaction, the out-of-plane C−H bonds of 1 are preferentially attacked since the in-plane C−H bonds are about 10 kcal/mol stronger. In the case of a reaction with O(3P), an Arrhenius activation energy of 3.5 kcal/mol is calculated at 298 K, which compares well with an experimental value of 2.85 kcal/mol. In the exit channel of the reaction, a radical−radical complex between CH3CH2• and •OH (−2.7 kcal/mol relative to separated products) is found. The latter is the s...

UV photolysis of 2,6-dimethylcyclohexa-2,5-dien-1-on-4-ylidene (4), matrix isolated in argon at 10 K, results in the formation of a labile species which is characterized as α,3-didehydro-5-methyl-6-hydroxybenzene (5) by comparison of the experimental IR spectrum with calculations at the ROSS-BLYP/6-31G(d,p) level of theory. This assignment is confirmed by isotopic labeling and by investigating the subsequent photochemistry of 5, which leads to 3-hydroxy-4-methylhepta-1,2,4-trien-6-yne (6). The ring opening of diradical 5 to eneyne−allene 6 corresponds to the reversion of a Myers cyclization.

Formation and decomposition of dioxirane ( 2a ), methyldioxirane ( 2b ) and dimethyldioxirane ( 2c ) in the gas phase were investigated by carrying out CCSD(T), MR-AQCC and B3LYP calculations with the 6-31G(d, p), 6-311+G(3df, 3pd) and cc-VTZ2P+f, d basis sets. The inclusion of f functions in the basis set was essential to determine the heat of formation Δ H f o (298) of carbonyl oxide ( 1a ) and 2a to be 27.0 and −0.3 kcal/mol, respectively. With the latter value, we calculate the same ring strain energy for cyclopropane, oxirane and 2a . Molecule 2a decomposes at 298 K with an activation enthalpy of 18 kcal/mol to methylenebis(oxy) ( 3a ), which is calculated to be 1.2 kcal/mol less stable than 2a , in contrast to previous investigations. Two methyl substituents increase the ring opening barrier to 23 kcal/mol and, thereby guarantee the kinetic stability of 2c . The biradicals 3 decompose with barriers smaller than 4 kcal/mol to esters and therefore will be difficult to intercept in dioxirane decomposition reactions.

The description of open-shell singlet OSS s-p biradicals by density functional theory DFT requires at least a . two-configurational TC or, in general, a MC-DFT approach, which bears many unsolved problems. These can be avoided . by reformulating the TC description in the spirit of restricted open shell theory for singlets ROSS and developing an exchange-correlation functional for ROSS-DFT. ROSS-DFT turns out to lead to reliable descriptions of geometry and . vibrational frequencies for OSS biradicals. The relative energies of the OSS states obtained at the ROSS-B3LYPr6-311G d,p level are often better than the corresponding ROSS-MP2 results. However, in those cases where spin polarization in a conjugated p systems plays a role, DFT predicts the triplet state related to the OSS state 2-4 kcalrmol too stable. q 1998 Elsevier Science B.V. All rights reserved.

A new way of analyzing measured or calculated vibrational spectra in terms of internal vibrational modes associated with the internal parameters used to describe geometry and conformation of a molecule is described. The internal modes are determined by solving the Euler–Lagrange equations for molecular fragments ϕn described by internal parameters ζn. An internal mode is localized in a molecular fragment by describing the rest of the molecule as a collection of massless points that just define molecular geometry. Alternatively, one can consider the new fragment motions as motions that are obtained after relaxing all parts of the vibrating molecule but the fragment under consideration. Because of this property, the internal modes are called adiabatic internal modes, and the associated force constants ka, adiabatic force constants. Minimization of the kinetic energy of the vibrating fragment ϕn yields the adiabatic mass ma (corresponding to 1/Gnn of Wilson's G matrix) and, by this, adiabatic frequencies ωa. Adiabatic modes are perfectly suited to analyze and understand the vibrational spectra of a molecule in terms of internal parameter modes in the same way as one understands molecular geometry in terms of internal coordinates. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 1–9, 1998

Adiabatic internal frequencies are compared with c-vector frequencies and intrinsic frequencies. It is shown that c-vector modes are not suitable to characterize molecular fragments f since they are not localized in f and their definition leads to nn unreasonable frequency values. Intrinsic frequencies suffer from a strong dependence on the set of internal parameters chosen to describe the geometry of the molecule. Apart from this, they represent averaged frequencies, for which mass effects and electronic effects are not properly separated. Adiabatic frequencies are based on a dynamic principle, separate properly mass effects and electronic effects and do not depend in any

The concept of characterizing normal vibrational modes l in terms of m internal vibrational modes v typical of molecular fragments or structural subunits is n developed. Essential for this concept is the amplitude A that provides the basis for a nm quantitative comparison of modes l and v and, by this, facilitates the extraction of m n chemical information out of vibrational spectra. Twelve possibilities of defining amplitude . .

The CNM characterization of normal modes method for extracting chemical information out of vibrational spectra is tested for vibrational spectra of molecules with relatively strong or relatively weak coupling between internal vibrational modes. Symmetry, parameter set stability, and frequency uncertainty tests are applied to check whether internal vibrational modes, internal mode frequencies, and amplitudes A comply with symmetry, are independent of the set of internal parameters O used to nU n describe molecular geometry or fulfill a Lorentzian correlation between amplitudes AnU and frequency differences a a â a a a . In all cases considered, amplitudes A nU n U n U based on adiabatic internal modes and mass or force constant matrices as metric O are superior to any other definition of amplitude. They represent the basic elements of the new CNM method that leads to chemically reasonable results and presents a new way of extracting chemical information out of vibrational spectra. A number of deficiencies of e. the potential energy distribution PED analysis is discussed. a 1998 John Wiley & Sons, Inc. Int J Quant Chem 67 :4 1 a55, 1998

The formic acid dimer in its C2h-symmetrical cyclic form is stabilized by two equivalent H-bonds. The currently accepted interaction energy is 18.75 kcal/mol whereas the experimental binding energy D0 value is only 14.22 ±0.12 kcal/mol [F. Kollipost, R. W. Larsen, A. V. Domanskaya, M. Norenberg, and M. A. Suhm, J. Chem. Phys. 136, 151101 (2012)]. Calculation of the binding energies De and D0 at the CCSD(T) (Coupled Cluster with Single and Double excitations and perturbative Triple excitations)/CBS (Complete Basis Set) level of theory, utilizing CCSD(T)/CBS geometries and the frequencies of the dimer and monomer, reveals that there is a 3.2 kcal/mol difference between interaction energy and binding energy De, which results from (i) not relaxing the geometry of the monomers upon dissociation of the dimer and (ii) approximating CCSD(T) correlation effects with MP2. The most accurate CCSD(T)/CBS values obtained in this work are De = 15.55 and D0 = 14.32 kcal/mol where the latter binding energy differs from the experimental value by 0.1 kcal/mol. The necessity of employing augmented VQZ and VPZ calculations and relaxing monomer geometries of H-bonded complexes upon dissociation to obtain reliable binding energies is emphasized.