The analog of Koopmans’ theorem for virtual Kohn-Sham orbital energies

Gritsenko, Oleg,Baerends, Evert Jan Canadian Science Publishing 2009 Canadian journal of chemistry Vol.87 No.10

<P> An analog of Koopmans’ theorem is formulated for the energies, εa, of virtual Kohn-Sham (KS) molecular orbitals (MOs) from the requirement that the KS theory provides, in principle, not only the exact electron density, but also its exact response. The starting point is the Kohn-Sham analog of Koopmans’ theorem, relating the vertical ionization energies, Ii, to the energies, εi, of the occupied MOs ( Chong, D.P.; Gritsenko, O.V.; Baerends, E.J. J. Chem. Phys. 2002, 116, 1760 ). Combining this with the coupled-perturbed equations of time-dependent density functional theory (TDDFT), exact relations between the energies, εa, of virtual KS MOs and the excitation energies, ωia, and vertical ionization energies (VIPs), Ii, are obtained. In the small matrix approximation for the coupling matrix K of TDDFT, two limiting cases of these relations are considered. In the limit of a negligible matrix element, Kia,ia, the energy, εa, can be interpreted as (minus) the energy of ionization from the ?i → ?a excited state, εa ≈ -Ia, where -Ia is defined from the relation Ii = ωia + Ia. This relation breaks down in special cases, such as charge-transfer transitions and the HOMO-LUMO (highest occupied molecular orbital - lowest unoccupied molecular orbital) transition of a dissociating electron-pair bond (also of charge-transfer character). The present results highlight the important difference between virtual orbital energies in the Kohn-Sham model (εa ≈ -Ia) and in the Hartree-Fock model (εa ≈ -Aa). Kohn-Sham differences εa - εi approximate the excitation energy, ωia, while Hartree-Fock differences [Formula: see text] do not approximate excitation energies but approximate the difference of an ionization energy and an electron affinity, Ii - Aa. </P>

A Frontier Orbital Study with ab Initio Molecular Dynamics of the Effects of Solvation on Chemical Reactivity: Solvent-Induced Orbital Control in FeO-Activated Hydroxylation Reactions

Bernasconi, Leonardo,Baerends, Evert Jan American Chemical Society 2013 JOURNAL OF THE AMERICAN CHEMICAL SOCIETY - Vol.135 No.24

<P>Solvation effects on chemical reactivity are often rationalized using electrostatic considerations: the reduced stabilization of the transition state results in higher reaction barriers and lower reactivity in solution. We demonstrate that the effect of solvation on the relative energies of the frontier orbitals is equally important and may even reverse the trend expected from purely electrostatic arguments. We consider the H abstraction reaction from methane by quintet [EDTAH<SUB><I>n</I></SUB>·FeO]<SUP>(<I>n</I>−2)+</SUP>, (<I>n</I> = 0–4) complexes in the gas phase and in aqueous solution, which we examine using ab initio thermodynamic integration. The variation of the charge of the complex with the protonation of the EDTA ligand reveals that the free energy barrier in gas phase increases with the negative charge, varying from 16 kJ mol<SUP>–1</SUP> for [EDTAH<SUB>4</SUB>·FeO]<SUP>2+</SUP> to 57 kJ mol<SUP>–1</SUP> for [EDTAH<SUB><I>n</I></SUB>·FeO]<SUP>2–</SUP>. In aqueous solution, the barrier for the +2 complex (38 kJ mol<SUP>–1</SUP>) is higher than in gas phase, as predicted by purely electrostatic arguments. For the negative complexes, however, the barrier is lower than in gas phase (e.g., 45 kJ mol<SUP>–1</SUP> for the −2 complex). We explain this increase in reactivity in terms of a stabilization of the virtual 3σ* orbital of FeO<SUP>2+</SUP>, which acts as the dominant electron acceptor in the H-atom transfer from CH<SUB>4</SUB>. This stabilization originates from the dielectric screening caused by the reorientation of the water dipoles in the first solvation shell of the charged solute, which stabilizes the acceptor orbital energy for the −2 complex sufficiently to outweigh the unfavorable electrostatic destabilization of the transition-state relative to the reactants in solution.</P><P><B>Graphic Abstract</B> <IMG SRC='http://pubs.acs.org/appl/literatum/publisher/achs/journals/content/jacsat/2013/jacsat.2013.135.issue-24/ja311144d/production/images/medium/ja-2012-11144d_0010.gif'></P><P><A href='http://pubs.acs.org/doi/suppl/10.1021/ja311144d'>ACS Electronic Supporting Info</A></P>

On the origin dependence of the angle made by the electric and magnetic vibrational transition dipole moment vectors

Nicu, Valentin Paul,Baerends, Evert Jan Royal Society of Chemistry 2011 Physical chemistry chemical physics Vol.13 No.36

<P>The concept of <I>robustness</I> of rotational strengths of vibrational modes in a VCD spectrum has been introduced as an aid in assignment of the absolute configuration with the help of the VCD spectrum. The criteria for robustness have been based on the distribution around 90° of the angles <I>ξ</I>(<I>i</I>) between electric and magnetic transition dipoles of all the modes <I>i</I> of a molecule. The angles <I>ξ</I>(<I>i</I>) (not, of course, the rotational strengths) are, however, dependent on the choice of origin. The derived criteria are for the center of mass chosen as the origin of the coordinate system. We stress in this note that application of the derived criteria assumes that excessive translation of the coordinate origin is not applied. Although the <I>ξ</I>(<I>i</I>) angles are not very sensitive to the position of the origin, very small displacements (a few Å) are not a problem, excessive translation of the origin does have considerable effect on the <I>ξ</I>(<I>i</I>) angles. In this note we quantify this effect and demonstrate how the distribution of <I>ξ</I>(<I>i</I>) angles is affected. Although it is possible to recalibrate the robustness criteria for the angles for a specific (large) displacement, we recommend that such displacement simply be avoided. It is to be noted that some modeling software does yield output with excessively displaced coordinate origin; this should be checked and corrected.</P> <P>Graphic Abstract</P><P>The origin dependence of the angle between the electric and magnetic dipole transition moment vectors of fundamental vibrational transitions is investigated using cinchona as example. <IMG SRC='http://pubs.rsc.org/services/images/RSCpubs.ePlatform.Service.FreeContent.ImageService.svc/ImageService/image/GA?id=c1cp21442j'> </P>

An abiotic analogue of the diiron(<small>IV</small>)oxo “diamond core” of soluble methane monooxygenase generated by direct activation of O₂ in aqueous Fe(<small>II</small>)/EDTA solutions: thermodynamics and electronic structure

Bernasconi, Leonardo,Belanzoni, Paola,Baerends, Evert Jan Royal Society of Chemistry 2011 Physical chemistry chemical physics Vol.13 No.33

<P>We study the generation of a dinuclear Fe(<SMALL>IV</SMALL>)oxo species, [EDTAH·FeO·OFe·EDTAH]<SUP>2−</SUP>, in aqueous solution at room temperature using Density Functional Theory (DFT) and <I>Ab Initio</I> Molecular Dynamics (AIMD). This species has been postulated as an intermediate in the multi-step mechanism of autoxidation of Fe(<SMALL>II</SMALL>) to Fe(<SMALL>III</SMALL>) in the presence of atmospheric O<SUB>2</SUB> and EDTA ligand in water. We examine the formation of [EDTAH·FeO·OFe·EDTAH]<SUP>2−</SUP> by direct cleavage of O<SUB>2</SUB>, and the effects of solvation on the spin state and O–O cleavage barrier. We also study the reactivity of the resulting dinuclear Fe(<SMALL>IV</SMALL>)oxo system in CH<SUB>4</SUB> hydroxylation, and its tendency to decompose to mononuclear Fe(<SMALL>IV</SMALL>)oxo species. The presence of the solvent is shown to play a crucial role, determining important changes in all these processes compared to the gas phase. We show that, in water solution, [EDTAH·FeO·OFe·EDTAH]<SUP>2−</SUP> (as well as its precursor [EDTAH·Fe·O<SUB>2</SUB>·Fe·EDTAH]<SUP>2−</SUP>) exists as stable species in a <I>S</I> = 4 ground spin state when hydrogen-bonded to a single water molecule. Its structure comprises two facing Fe(<SMALL>IV</SMALL>)oxo groups, in an arrangement similar to the one evinced for the active centre of intermediate <B>Q</B> of soluble Methane Monooxygenase (sMMO). The inclusion of the water molecule in the complex decreases the overall symmetry of the system, and brings about important changes in the energy and spatial distribution of orbitals of the Fe(<SMALL>IV</SMALL>)oxo groups relative to the gas phase. In particular, the virtual 3σ* orbital of one of the Fe(<SMALL>IV</SMALL>)oxo groups experiences much reduced repulsive orbital interactions from ligand orbitals, and its consequent stabilisation dramatically enhances the electrophilic character of the complex, compared to the symmetrical non-hydrated species, and its ability to act as an acceptor of a H atom from the CH<SUB>4</SUB> substrate. The computed free energy barrier for H abstraction is 28.2 kJ mol<SUP>−1</SUP> (at the BLYP level of DFT), considerably below the gas phase value for monomeric [FeO·EDTAH]<SUP>−</SUP>, and much below the solution value for the prototype hydrated ferryl ion [FeO(H<SUB>2</SUB>O)<SUB>5</SUB>]<SUP>2+</SUP>.</P> <P>Graphic Abstract</P><P>The CH<SUB>4</SUB> hydroxylation activity of Fe(<SMALL>IV</SMALL>)oxo/EDTA catalysts obtained from direct activation of atmospheric O<SUB>2</SUB> is strongly enhanced by water solvation. <IMG SRC='http://pubs.rsc.org/services/images/RSCpubs.ePlatform.Service.FreeContent.ImageService.svc/ImageService/image/GA?id=c1cp21244c'> </P>

Hydroxylation Catalysis by Mononuclear and Dinuclear Iron Oxo Catalysts: a Methane Monooxygenase Model System versus the Fenton Reagent Fe^IVO(H₂O)₅²⁺

Gopakumar, G.,Belanzoni, P.,Baerends, E.J. ACS AMERICAN CHEMICAL SOCIETY 2012 Inorganic Chemistry Vol.51 No.1

Double excitation effect in non-adiabatic time-dependent density functional theory with an analytic construction of the exchange–correlation kernel in the common energy denominator approximation

Gritsenko, Oleg V.,Jan Baerends, Evert Royal Society of Chemistry 2009 Physical chemistry chemical physics Vol.11 No.22

<P>Time-dependent density functional (response) theory (TDDF(R)T) is applied almost exclusively in its adiabatic approximation (ATDDFT), which is restricted to predominantly single electronic excitations and neglects additional roots of the TDDFT eigenvalue problem stemming from the interaction between single and double excitations. We incorporate the effect of the latter interaction into a non-adiabatic frequency-dependent and spatially non-local Hartree-exchange–correlation (Hxc) kernel <I>f</I> (<B>r</B><SUB>1</SUB>, <B>r</B><SUB>2</SUB>, <I>ω</I>), the explicit analytical expression of which is derived for interacting single and double excitations well separated from the other excitations, within the common energy denominator approximation (CEDA) for the Kohn–Sham (KS) and interacting density response functions, <I>χ</I><SUB>s</SUB> and <I>χ</I>, respectively. The kernel <I>f</I> (<B>r</B><SUB>1</SUB>, <B>r</B><SUB>2</SUB>, <I>ω</I>) obtained from the direct analytical inverse of <I>χ</I> and <I>χ</I><SUP>CEDA</SUP> is a sum of the delta-function and non-local orbital-dependent spatial terms with frequency-dependent factors, with which <I>f</I> acquires a modulated quadratic dependence on <I>ω</I>. The effective incorporation in <I>f</I> of the complete manifold of excited states (through the delta function term) represents an extension of the kernel reported by Maitra, Zhang, Cave, and Burke [<I>J. Chem. Phys.</I>, 2004, <B>120</B>, 5932]. In the TDDFT eigenvalue equations considered in the diagonal approximation, <I>f</I> generates two excitation energies <I>ω</I><SUB><I>q</I></SUB> and <I>ω</I><SUB><I>q</I>+1</SUB>, which both correspond to the same single KS excitation <I>ω</I>, thus producing the effect of the single–double excitation interaction.</P> <P>Graphic Abstract</P><P>Double excitations, not included in linear response TDDFT, can be captured with proper frequency dependence in the xc kernel. A common-energy-denominator based derivation of this frequency dependence is given. <IMG SRC='http://pubs.rsc.org/services/images/RSCpubs.ePlatform.Service.FreeContent.ImageService.svc/ImageService/image/GA?id=b903123e'> </P>

On the Equivalence of Conformational and EnantiomericChanges of Atomic Configuration for Vibrational Circular DichroismSigns

Heshmat, Mojgan,Nicu, ValentinPaul,Baerends, Evert Jan American Chemical Society 2012 The Journal of physical chemistry A Vol.116 No.13

<P>We study systematically the vibrational circular dichroism (VCD)spectra of the conformers of a simple chiral molecule, with one chiralcarbon and an “achiral” alkyl substituent of varyinglength. The vibrational modes can be divided into a group involvingthe chiral center and its direct neighbors and the modes of the achiralsubstituent. Conformational changes that consist of rotations aroundthe bond from the next-nearest neighbor to the following carbon, andbond rotations further in the chain, do not affect the modes aroundthe chiral center. However, conformational changes within the chiralfragment have dramatic effects, often reversing the sign of the rotationalstrength. The equivalence of the effect of enantiomeric change ofthe atomic configuration and conformational change on the VCD sign(rotational strength) is studied. It is explained as an effect ofatomic characteristics, such as the nuclear amplitudes in some vibrationalmodes as well as the atomic polar and axial tensors, being to a highdegree determined by the local topology of the atomic configuration.They reflect the local physics of the electron motions that generatethe chemical bonds rather than the overall shape of the molecule.</P><P><B>Graphic Abstract</B> <IMG SRC='http://pubs.acs.org/appl/literatum/publisher/achs/journals/content/jpcafh/2012/jpcafh.2012.116.issue-13/jp212545z/production/images/medium/jp-2011-12545z_0005.gif'></P><P><A href='http://pubs.acs.org/doi/suppl/10.1021/jp212545z'>ACS Electronic Supporting Info</A></P>

Understanding Solvent Effects in Vibrational Circular Dichroism Spectra: [1,1′-Binaphthalene]-2,2′-diol in Dichloromethane, Acetonitrile, and Dimethyl Sulfoxide Solvents

Nicu, Valentin Paul,Baerends, Evert Jan,Polavarapu, Prasad L. American Chemical Society 2012 The Journal of physical chemistry A Vol.116 No.32

<P>We present a combined experimental and computational investigation of the vibrational absorption (VA) and vibrational circular dichroism (VCD) spectra of [1,1′-binaphthalene]-2,2′-diol. First, the sensitive dependence of the experimental VA and VCD spectra on the solvent is demonstrated by comparing the experimental spectra measured in CH<SUB>2</SUB>Cl<SUB>2</SUB>, CD<SUB>3</SUB>CN, and DMSO-<I>d</I><SUB>6</SUB> solvents. Then, by comparing calculations performed for the isolated solute molecule to calculations performed for molecular complexes formed between solute and solvent molecules, we identify three main types of perturbations that affect the shape of the VA and VCD spectra when going from one solvent to another. These sources of perturbations are (1) perturbation of the Boltzmann populations, (2) perturbation of the electronic structure, and (3) perturbation of the normal modes.</P><P><B>Graphic Abstract</B> <IMG SRC='http://pubs.acs.org/appl/literatum/publisher/achs/journals/content/jpcafh/2012/jpcafh.2012.116.issue-32/jp303891x/production/images/medium/jp-2012-03891x_0011.gif'></P><P><A href='http://pubs.acs.org/doi/suppl/10.1021/jp303891x'>ACS Electronic Supporting Info</A></P>

Counterpoise correction is not useful for short and Van der Waals distances but may be useful at long range

Sheng, Xiao Wei,Mentel, Lukasz,Gritsenko, Oleg V.,Baerends, Evert Jan Wiley Subscription Services, Inc., A Wiley Company 2011 Journal of computational chemistry Vol.32 No.13

<P><B>Abstract</B></P><P>This article investigates the errors in supermolecule calculations for the helium dimer. In a full CI calculation, there are two errors. One is the basis set superposition error (BSSE), the other is the basis set convergence error (BSCE). Both of the errors arise from the incompleteness of the basis set. These two errors make opposite contributions to the interaction energies. The BSCE is by far the largest error in the short range and larger than (but much closer to) BSSE around the Van der Waals minimum. Only at the long range, the BSSE becomes the larger error. The BSCE and BSSE largely cancel each other over the Van der Waals well. Accordingly, it may be recommended to not include the BSSE for the calculation of the potential energy curve from short distance till well beyond the Van der Waals minimum, but it may be recommended to include the BSSE correction if an accurate tail behavior is required. Only if the calculation has used a very large basis set, one can refrain from including the counterpoise correction in the full potential range. These results are based on full CI calculations with the aug‐cc‐pVXZ (<I>X</I> = D, T, Q, 5) basis sets. © 2011 Wiley Periodicals, Inc. J Comput Chem 32: 2896–2901, 2011</P>

A VCD robust mode analysis of induced chirality: The case of pulegone in chloroform

Nicu, Valentin Paul,Debie, Elke,Herrebout, Wouter,Van der Veken, Benjamin,Bultinck, Patrick,Baerends, Evert Jan Wiley Subscription Services, Inc., A Wiley Company 2009 Chirality Vol.21 No.e1

<P>Vibrational modes in an achiral molecule may acquire rotational strength by complexation to a chiral molecule, as happens for achiral solvent molecules complexed to a chiral solute. We investigate this transfer of chirality in vibrational circular dichroism for the pulegone molecule in CDCl<SUB>3</SUB> solvent from the point of view of the robustness concept introduced recently. It turns out that the transfer of chirality yields nonrobust modes, which means that, although they are observed in vibrational circular dichroism (VCD) experiments, the sign of these modes cannot be predicted reliably with standard (Density Functional Theory) VCD calculations. This limits the usefulness of the induced chirality phenomenon for obtaining information on the intermolecular interactions that give rise to it. Chirality 21:E287–E297, 2009. © 2010 Wiley-Liss, Inc.</P>