Ab Initio Benchmark Calculations on Ca(II) Complexes and Assessment of Density Functional Theory...

Published: September 28, 2011

r 2011 American Chemical Society 11331 dx.doi.org/10.1021/jp205101z | J. Phys. Chem. A 2011, 115, 11331–11343

ARTICLE

pubs.acs.org/JPCA

Ab Initio Benchmark Calculations on Ca(II) Complexes andAssessment of Density Functional Theory MethodologiesDimas Su�arez,† Víctor M. Ray�on,‡ Natalia Díaz,† and Hayd�ee Vald�es*,†,§

†Departamento de Química Física y Analítica, Facultad de Química Universidad de Oviedo, 33007 Oviedo, Spain‡Departamento de Química Física y Química Inorg�anica, Facultad de Ciencias Universidad de Valladolid, 47005 Valladolid, Spain

bS Supporting Information

’ INTRODUCTION

Calcium ion is one of the metals most commonly found inbiological systems, playing important roles in diverse biochem-ical processes.1 Inside eukaryotic cells, Ca(II) concentrationlevels regulate muscle contraction, secretion, glycolysis, gluco-neogenesis and ion transport.2 It also participates as a signalingmediator in cell cycle regulation, proliferation and apoptosis.3Outsidecells, Ca(II) plays crucial roles in many matrix�matrix, cell-matrix and cell�cell contacts, in the mineralization of bones, inblood clotting, and in receptor structures.4 In all these cases,binding of calcium ions to proteins seems to affect their structuralstability or to modulate substrate binding and the catalytic acti-vity of enzymes.

According to the analysis of the Cambridge Structural Data-base (CSD), the calcium ion is able to interact with six, seven oreight ligands. The metal�ligand bonding is commonly consid-ered to be predominantly ionic, so the ligand disposition ismainly determined by the possibilities of packing donor atomsaround the Ca(II) cation.5�7 The calcium complexes show astrong preference to bind to oxygen atoms as the donors, whereascomplexes with nitrogen or sulfur donors are very rare.8 Inaddition, carboxylate complexes with Ca(II) show several typesof geometrical behavior (syn-monodentate, antimonodentate,and symmetrical bidentate) showing a greater tendency towardbidentate carboxylate binding. Interestingly, it has been shownthat the geometry found in all the Ca(II)-containing proteinstructures in the Protein Data Bank determined at resolutione1.6 Å, agrees with that predicted from the CSD for ligands thatare analogues of amino acid side chains in proteins.9

Binding of Ca(II) to proteins is thus a topic of great interest forwhich deeper understanding requires the proper study of the

calcium ligand abilities. A plausible way to achieve such knowl-edge is by means of computational chemistry. Then, followingthe same philosophy than in our previous paper about the Zn(II)ligand abilities,10 we have selected a set of complexes modelingthe Ca(II)�ligand interactions and proceeded similarly. In otherwords, we have first performed high-level quantum chemical cal-culations on the selected complexes in order to obtain a reliableenergetic, structural, and electronic description of the Ca(II)�ligand binding abilities. Second, we have used the data obtainedby means of the high-level quantum chemical calculations asbenchmark data to assess the performance of various densityfunctional theory (DFT) functionals. And third, we have ana-lyzed the nature of the ligand�metal bond bymeans of an energydecomposition method aiming to obtain relevant information onthe relative importance of the different electrostatic, inductionand dispersion contributions to the interaction energy.

The assessment of the performance of the DFT functionalsdeserves a special comment. Nowadays, DFT has become themost popular correlated methodology for the study of biomole-cules due to its fast computer performance and its capability fordescribing both noncovalent interactions11,12 and chemicalreactions13 as well as for providing molecular properties and des-criptors.14 However, it should not be forgotten that the versatilityof a particular functional has to be carefully tested in advance15

because many functionals have not been parametrized to fit data

Special Issue: Pavel Hobza Festschrift

Received: May 31, 2011Revised: August 11, 2011

ABSTRACT: A set of benchmark results for the geometries, binding energies, and protonationaffinities of 24 complexes of small organic ligands with Ca(II) is provided. The chosen level oftheory is CCSD(T)/CBS obtained by means of a composite procedure. The performance offour density functionals, namely, PW91, PBE, B3LYP, and TPSS and several Pople-type basissets, namely, 6-31G(d), 6-31+G(d), 6-31+G(2d,p) and 6-311+G(d) have been assessed.Additionally, the nature of the metal ligand bonding has been analyzed by means of theSymmetry Adapted Perturbation Theory (SAPT). We have found that the B3LYP hybridfunctional, in conjunction with either the polarized double-ζ 6-31+G(2d,p) or the triple-ζ 6-311+G(d) basis sets, yields the closest results compared to the benchmark data. The SAPT analysis stresses the importance of inductioneffects in the binding of these complexes and suggests that consideration of classical electrostatic contributions alone may not bereliable enough for the prediction of relative binding energies for Ca(II) complexes.

11332 dx.doi.org/10.1021/jp205101z |J. Phys. Chem. A 2011, 115, 11331–11343

The Journal of Physical Chemistry A ARTICLE

for inorganic or organometallic molecules and their applicabilityoutside the scope for which they were developed is not alwaysguaranteed. Hence, assessing the performance of the DFTfunctionals against ab initio benchmark data is always recom-mendable. Ab initio calculations are time-consuming, and con-sequently, the size of the system to be studied is considerablylimited especially when the accuracy of coupled-cluster (CC)methods combined with infinite (extrapolated to the completebasis set limit, CBS) basis sets is required. For this reason, theperformance of the DFT functionals is typically assessed againstab initio benchmark data on small model systems (for Ca(II)complexes, see for example, refs 16�22). According to thisphilosophy and as commented before, various DFT functionalsare here assessed against ab initio benchmark calculations for aconveniently chosen set of Ca(II)�ligand complexes mimickinginteractions that potentially exist in proteins. In particular, thefollowing ligands were chosen: water, methanol, formic acid,acetic acid, formaldehyde, acetone, formamide, acetamide, N-methyl acetamide (NMA), methyl acetate, ammonia, methyla-mine, methanimine, 1H-imidazole, benzene, hydrogen sulfide,methanethiol, hydroxide, methanolate, acetate, imidazolate, hy-drosulfide, methanethiolate, formate, and methyl phosphate.Note that the selected set of ligands is mainly populated bymolecules with O donor atoms in different chemical environ-ments (sp2 O, sp3 O, neutral, ionic, ...) as calcium ions in bio-logical systems show a clear preference for binding to carboxylate/carbonyl groups and water molecules. However, we have alsoconsidered other ligands with N and S donor as well as benzenebecause it is important to properly describe the whole spectrumof possible Ca(II)�ligand interactions.

The third goal of this study is the analysis of the nature of themetal�ligand bond in thesemodel complexes. Polarization inter-actions (also referred to as induction) are of utmost importancein the properties and dynamics of many biologically relevantsystems.23 However, translation of these polarization effects intoa particular model function (force field) to be efficiently used inatomistic molecular simulations is quite challenging and a matterof current debate.24�29 Most nonpolarizable force fields describenonbonded interactions by means of a pairwise additive functionthat typically includes an electrostatic and a Lennard�Jonescontribution. Regarding the electrostatic term, each atom is as-signed an effective partial (fixed) charge that is adjusted tomodel,in an average way, polarization effects in the condensed phase(we note that because polarization interactions are highly non-additive they cannot be properly described by a pairwise additivefunction). We would like to point out that this adjustment is notperformed for metal ions because most standard force fieldsretain their original integer (bare) charges [i.e., +2 for Ca(II)].The Lennard�Jones parameters are even more empirical thanelectrostatic charges because they are frequently used to com-pensate for inaccuracies in the force field.30 Thismachinery yieldsreasonable results whenever induction effects are not dominantin the system. For those cases where polarization effects cannotbe neglected polarizable force fields have to be used instead. Ascommented above, derivation of specific functions that includeinduction effects and that are suitable for biological simulations isa hot topic of current research. A second important point is toassess the magnitude and importance of polarization effects for aparticular interaction, for example the interaction between aspecific metal ion and nucleophilic ligands. To this end, quantummechanical (QM) calculations have proven very useful and, inparticular, techniques aimed to partition the interaction energy

provide a rigorous way to estimate the importance of individualinteraction energy terms (electrostatic, induction, dispersion,and exchange-repulsion).10,29,31�37 In this work, we will assessthe importance of polarization effects in Ca(II) complexes bymeans of the Symmetry Adapted Perturbation Theory (SAPT).We hope that these results, in conjunction with those providedby other research groups and partitioning schemes, will con-tribute to the improvement and refinement of polarizable mole-cular force fields. Ultimately, we hope that all this informationmay gradually help to settle the physical bases governing metalbinding in proteins.

’COMPUTATIONAL METHODS

Ab Initio Calculations. Ab initio benchmark calculations ofthe monoligand Ca(II) complexes studied in this work werecarried out assuming the frozen core approximation in all thecorrelated calculations treating the Ca(II) ions likewise thirdperiod elements (i.e., core orbitals for Ca(II) ions include only 1s,2s, and 2p). We systematically used the Dunning’s basis setaugmented with diffuse functions [aug-cc-pVnZ (n = 3�5)]38,39

for all the atoms except for the Ca(II) ion for which we used thecc-pVnZ basis sets developed by Koput and Peterson to describeboth its 4s valence and 3s3p core spaces.40 Nevertheless and forthe sake of simplicity, herein we will only use the notation aug-cc-pVnZ [n = 3�5)]. The basis sets for calcium were taken from theEMSL Basis Set Exchange.41,42 Molecular geometries and har-monic frequencies were carried out at the MP2/aug-cc-pVTZlevel of theory and electronic energies were refined by perform-ing CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ single-pointenergy calculations (coupled cluster single and double excitationaugmented with a noniterative treatment of triple excitations).43

Subsequently, electronic energies were extrapolated toward theCBS (complete basis set) limit from MP2/aug-cc-pVnZ (n = 4,5)//MP2/aug-cc-pVTZ energies using two different extrapola-tion formulas:44

En ¼ ECBS þ An�3 ð1Þ

En ¼ ECBS þ Ann � 1 þ Be�ðn � 1Þ2 ð2Þwhere n is the cardinal number of the basis set and ECBS, A, and Bare fitting parameters, with ECBS being the resulting estimate ofthe CBS limit. The average ECBS value obtained from these twoexpressions has been reported as a conservative estimate of theactual CBS limit.44 Herein, extrapolations using eqs 1 and 2 withthe aug-cc-pVnZ (n = 4, 5) basis sets were used systematically onthe MP2 correlation energies. The HF energies were not extra-polated, and the 5Z HF values were simply taken as the mostaccurate estimates of the HF limits.Although accurate, the calculation of the CCSD(T) CBS limit

here employed is in general impractical and, thus, we decided toapproximate the corresponding CCSD(T) CBS values by meansof the following “composite” formula:

ECCSDðTÞCBS≈ECCSDðTÞ=aug-cc-pVTZ þ ðEMP2=CBS � EMP2=aug-cc-pVTZÞð3Þ

Additionally, the sensitivity of the computed binding energiesand molecular properties with respect to basis set effects and/orthe method employed for geometry optimization were assessedby carrying out further ab initio calculations for some of theCa(II)�L complexes (L = OH� and H2O). For these small



complexes, molecular geometries were reoptimized at theCCSD/aug-cc-pVTZ level. Besides, the CBS limit of the CCSD-(T) energies was also estimated by means of single-point CCSD-(T)/aug-cc-pVnZ (n = 4, 5) calculations using eqs 1 and 2. Forthe sake of completeness, CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVTZ energies were also calculated. By means of the testcalculations on the [Ca(H2O)]

2+ and [Ca(OH)]+ complexes, wealso examined whether the same CBS limit is consistentlyattained from both electronic energies that included the counter-poise (CP) correction45 for Basis Set Superposition Error(BSSE) and uncorrected energies. Finally, the validity of thefrozen core approximation was assessed by carrying out full elec-tron correlation calculations on the Ca2+ water/hydroxide sys-tems. In this case, molecular geometries were optimized at theCCSD/aug-cc-pVTZ level and followed by single-point CCSD-(T)/aug-cc-pVnZ (n = 3�5). It must be noticed that in the fullelectron calculations, we used the following core�valence basissets for the Ca2+ ions: CVT+2dZ, CVQ+2dZ, and CV5Z, whichhave been developed and recommended by Martin and co-workers46 for including deep core correlation effects in Ca.Density Functional Calculations. In this work, we aim to

assess the performance of four of the most commonly used andwidely available in quantum chemistry programpackages “general-purpose” functionals. Specifically, we selected two functionalsbased on the generalized gradient approximation (GGA), PW9147

and PBE,48 one hybrid functional, B3LYP,49�52 and one meta-GGA, TPSS53 which, unlike the formers, is a nonempirical func-tional. In conjunction with these four functionals, we testedseveral basis set of double-ζ and triple-ζ quality also equallyaccessible. Consequently, we selected a “6-31G” double-ζ and a“6-311G” triple-ζ basis sets. For the main group elements thesebasis sets consists of the Pople’s 6-31G54 and 6-311G55 basis. Theonly exception is sulfur for which the 6-311G set from McLeanand Chandler56 was used. Currently, there are two double-ζ sets,usually referred to as “6-31G”, for calcium. The first one wasinitially developed by Rassolov et al. in 199857 and later improvedby the same authors in 2001, including the 3d shell in the valencespace.58 Its contraction [5s,4p,2d] or [66631,6631,31] has thesame structure as the 6-31G set for the first two rows of theperiodic table. The second available “6-31G” double-ζ basis doesnot actually have the expected “6-31G” structure because itscontraction is [5s,3p,1d] or [63311,531,3] and has been devel-oped as part of the Gaussian-2 (G2) theory in 1997.59 We wouldlike to point out that in the Gaussian03 program package thedefault 6-31G basis is the old one from Rassolov et al. (year1998), which does not include the 3d shell in the valence space.We carried out a small set of test calculations to assess theperformance of these two ‘6-31G’ basis sets. The results, availableas Supporting Information (see Tables S1 and S2), show thatboth basis sets yield similar results. We have selected the 6-31Gset from G2 theory for the present study although the conclu-sions obtained should be valid for the improved Rassolov’s 6-31Gbasis set (year 2001) as well. In the following, we will refer to the“G2” 6-31G basis simply as 6-31G. Regarding the triple-ζ basisfor the calcium atom, we selected the [8s,7p,1d] or [62111111,3311111, 3] basis set available in G03 as the default 6-311G basisfor this element.59 Similarly, this set has been developed as part ofthe Gaussian-2 (G2) theory.Both the 6-31G and the 6-311G basis sets were augmented

with sp diffuse and d polarization functions. The followingcombinations have been tested in the current study: 6-31G(d),6-31+G(d), 6-31+G(2d,p), and 6-311+G(d). The exponent of

the diffuse primitive for calcium (0.0071) as well as the exponentsof the d polarization functions �0.216 (6-31G) and 0.260(6-311G) have been taken from ref 59. Cartesian functions wereused with the 6-31G set, whereas spherical functions were usedwith the 6-311G. For the sake of completeness, geometries andbinding energies were also computed by means of the MP2method combined with these basis sets.The geometries of the tested Ca(II) complexes were fully

optimized with the above-described functionals and basis sets.Analytical frequency calculations were carried out to check thatthe optimized structures were minima on the correspondingpotential energy surfaces. The default integration grid in G03 (75radial shells and 302 angular points) was used for all the DFTcalculations. For test purposes, we also carried out calculationson the whole set of complexes using a larger (“Ultrafine”) inte-gration grid (99 radial shells and 590 angular points). Thesecalculations were performed using the B3LYP functional in con-junction with the aug-cc-pVTZ basis set.All of the wave function and density functional calculations

carried out in this work were performed with the Gaussian0360

program package.SAPT Analyses. The nature of the Ca(II)�ligand interaction

was analyzed by means of the Density Functional Theory�Sym-metry Adapted Perturbation Theory (DFT-SAPT) developed byHesselmann and Jansen61�63 and independently by Szalewiczand co-workers64,65 [in the latter case, the theory is usuallyreferred to as SAPT(DFT)]. DFT-SAPT interaction energy isexpressed as a sum of physically meaningful contributions,namely, electrostatic, induction, dispersion, and their correspon-ding exchange counterparts

EDFT-SAPTint ¼ Eð1Þelst þ Eð1Þexch þ Eð2Þind þ Eð2Þexch-ind þ Eð2Þdisp þ Eð2Þexch-disp

ð4Þwhere the superscript refers to the order in which these termsappear in the perturbation expansion. The molecular orbitals andorbital energies resulting from a DFT calculation on the frag-ments are used to compute Eelst

(1) whereas Frequency DependentDipole Polarizabilities (FDDS) are used to obtain Eind

(2) and Edisp(2) .

These three contributions are potentially exact, meaning thatthey would be exact if the exact exchange-correlation (xc)potential was used. On the other hand, the exchange terms,which cannot be expressed in terms of fragments’ properties, arecomputed using the first- and second-order density matrices,which are only approximations to the true matrices. Thus, ex-change contributions are not potentially exact. In any case, it hasbeen shown that DFT-SAPT provides indeed exchange terms,which are in good agreement with those computed using SAPT.In this work we will group the DFT-SAPT contributions in

terms arising at first- and second-order:

Eð1Þ ¼ Eð1Þelst þ Eð1Þexch ð5Þ

Eð2Þ ¼ Eð2Þind þ Eð2Þexch-ind þ Eð2Þdisp þ Eð2Þexch-disp ð6ÞIn this way, we split the interaction energy in contributionsassociated to the interaction of frozen (unrelaxed) wave func-tions of the monomers (E(1)) and those contributions associatedto the relaxation (through polarization and charge transfer) offragments’ charge densities (E(2)).We finally point out that third-and higher-order induction and exchange induction effects canbe included at the HF (noncorrelated) level computing the



difference between the SAPT noncorrelated first- and second-order energy and the supermolecular HF interaction energy:

δEHFint ¼ EHFint � Eð10Þelst � Eð10Þexch � Eð20Þind, r � Eð20Þexch-ind, r ð7ÞThe final DFT-SAPT interaction energy reads, therefore

EDFT-SAPTint ¼ Eð1Þ þ Eð2Þ þ δEHFint ð8ÞFurther details of the DFT-SAPT [and the equivalent SAPT-(DFT)] method can be found in the original references. All theDFT-SAPT calculations were performed on the MP2/aug-cc-pVTZ geometries using an aug-cc-pVTZ dimer centered basis set(DCBS). The PBE0 xc potential was used throughout. In orderto correct the wrong asymptotic behavior of the PBE exchangepotential the correction approach of Gr€uning et al. was used.66

This approach requires the calculation for each fragment of thedifference between the (exact) vertical ionization potential (IP)and the negative of the highest occupied molecular orbital(HOMO). The vertical IPs were taken from theNISTChemistrywebbook,67 whereas the HOMO energies were computed at thePBE0/aug-cc-pVTZ level. All the DFT-SAPT calculations werecarried out with the MOLPRO suite of programs.68

’RESULTS AND DISCUSSION

Ab Initio Calculations. The optimized structures for themonoligand complexes formed between Ca(II) and the neu-tral ligands (L = water, methanol, formic acid, acetic acid,

formaldehyde, acetone, formamide, acetamide, N-methyl acet-amide (NMA), methyl acetate, ammonia, methylamine, metha-nimine, 1H-imidazole, benzene, hydrogen sulfide, andmethanethiol)and anionic ligands (L = hydroxide, methanolate, acetate, imida-zolate, hydrosulfide, methanethiolate, formate, and methyl phos-phate), respectively, are collected in Figures 1 and 2. For eachcomplex shown in Figures 1 and 2, the equilibrium Ca�L dis-tance involving the Ca atom and the donor atom(s) of the ligand,the Natural Population Analysis (NPA) charge of the Ca atom,and the harmonic frequency of the stretching normal modeassociated with the Ca�L bond are also reported. As mentionedin Computational Methods, the consistency of the computa-tional scheme employed for computing the binding energies wastested in the case of the complexes of Ca(II) with water andhydroxide by using more elaborated computational schemes aswell (see Table 1). We will analyze first these validation calcula-tions, and then we will present the benchmark data for all theCa(II) complexes.ValidationCalculations on theWater andHydroxide Com-

plexes.Test calculations performed on the Ca(II)�L (L = waterand hydroxide) complexes that assess the adequacy of the variouschoices made in the computational scheme defined in eqs 1�3(i.e., “composite” approximation, MP2 geometries, valence cor-relation, CBS extrapolation, ...) are collected in Table 1. Suchcalculations have been done aiming to ensure that the benchmarkcalculations here performed are accurate and could replacemissing experimental data.

Figure 1. Geometrical arrangement of the studied Ca(II) complexes with neutral ligands along with the most important geometrical parameters, ascomputed at the MP2/aug-cc-pVTZ level of theory. For water, froze-core CCSD/aug-cc-pVTZ and full electron CCSD/aug-cc-pVTZ data are given initalics and in squared brackets, respectively. All distances are given in Å.



A first conclusion that can be drawn from the analysis of thedata collected in Table 1 is that binding energies (De) obtained

using theMP2-optimized geometries and theDunning et al. basissets combined with the “composite method” (�57.33 and

Figure 2. Geometrical arrangement of the studied Ca(II) complexes with anionic ligands along with the most important geometrical parameters ascomputed at the MP2/aug-cc-pVTZ level of theory. For hydroxide, froze-core CCSD/aug-cc-pVTZ and full electron CCSD/aug-cc-pVTZ data aregiven in italics and in squared brackets, respectively. All distances are given in Å.

Table 1. Binding Energies (in kcal/mol) for the Ca(II) Complexes with Water and Hydroxide Obtained with Different Ab InitioComputational Protocols

ligand MP2/aug-cc-pVTZ CCSD(T)/aug-cc-pVTZ MP2/CBSa composite methodb

Frozen Core, MP2/aug-cc-pVTZ Geometries

water �57.14 �56.97 �57.49 �57.33

hydroxide �338.36 �339.22 �341.81 �342.68

Frozen Core, MP2/aug-cc-pVTZ Geometries, CP-Corrected Energies

water �54.75 �54.32 �56.60 �56.18

hydroxide �334.49 �334.83 �340.40 �340.74

ligand CCSD/aug-cc-pVTZ CCSD(T)/aug-cc-pVTZ CCSD(T)/CBSa

Frozen Core, CCSD/aug-cc-pVTZ Geometries

water �56.91 �56.98 �57.23

hydroxide �339.29 �339.23 �342.83

Full Electron, CCSD/aug-cc-pVTZ Geometries, Martin’s Basis Sets for Ca

water �58.55 �55.80 �56.83

hydroxide �339.27 �339.55 �343.10

Full Electron, CCSD/aug-cc-pVTZ Geometries, Martin’s Basis Sets for Ca, CP-Corrected Energies

water �57.94 �55.16 �56.77

hydroxide �337.86 �338.03 �342.91aObtained from CBS extrapolation of the correlation energy based on eqs 1 and 2 and using the HF/aug-cc-pV5Z energies. bUsing an additivecombination of electronic energies.



�342.68 for L =H2O andOH�, respectively) are nearly identicalto those obtained at the CCSD(T)/CBS//CCSD/aug-cc-pVTZlevel of theory (�57.23 and �342.83 kcal/mol), showing, thus,that it seems reasonable to rely on the “composite method” datawhen the CCSD(T)/CBS calculations are not feasible. Therelevance of deep core�valence correlation effects was evaluatedby carrying out full electron CCSD calculations on the Ca(II)�L(L = water and hydroxide) complexes and using the aug-cc-pVnZbasis sets for the nonmetal atoms with the larger basis sets for theCa(II) ion developed byMartin and co-workers,46 which containabout 30% more Gaussian type functions than the cc-pVnZ basissets of Koput and Peterson40 in order to take into account bothouter-core valence and deep-core-valence effects in calcium. Wefound that the CCSD(T)/CBS binding energies computedwithin the frozen core approximation (�57.23/�342.83 kcal/mol for H2O/OH

�) deviate little from the corresponding De

using the all-electrons basis set, namely, �0.4 and 0.3 kcal/molfor H2O and OH�, respectively. Thus, it may be reasonable toestimate that deep core�valence correlation effects may have animpact lower than 1.0 kcal/mol in absolute value for the mono-ligand Ca2+ complexes.We have additionally extrapolated the CP corrected binding

energies to the basis set limit. The “composite method” De

energies obtained fromCP-corrected electronic energies (�56.18and �340.74 kcal/mol) are about 1�2 kcal/mol above the CP-uncorrected values (�57.33 and �342.68 kcal/mol). Notice,however, that both the CP-corrected and CP-uncorrected en-ergies using the Martin et al. basis sets are very similar to each

other (�56.77/�342.91 and �56.83/�343.10 kcal/mol, re-spectively). Most importantly, we note that the “compositemethod” energies using the CP-uncorrected data are closer tothe Martin et al. results than the “composite” CP-correctedvalues. The difference, as commented above, is smaller than0.5 kcal/mol.As mentioned in Computational Methods, we also assessed

the reliability of the CBS extrapolation scheme by computing thebinding energy change when going from MP2/aug-cc-pVQZ toMP2/aug-cc-pV5Z and from MP2/aug-cc-pV5Z to MP2/CBS.In the first case, the differences are�0.25 and�1.09 kcal/mol forH2O and OH�, respectively, whereas in the second case such dif-ferences are 0.22 kcal/mol (H2O) and �0.20 kcal/mol (OH�).When the core�valence correlation is taken into account, thesedifferences become�0.25 kcal/mol (H2O) and�0.80 kcal/mol(OH�) for the CCSD(T)/aug-cc-pVQZ to CCSD(T)/aug-cc-pV5Z and 0.21 kcal/mol (H2O) and�0.09 kcal/mol (OH�), forthe CCSD(T)/aug-cc-pV5Z to CCSD(T)/CBS.In summary, the largest factors that in principle could affect the

benchmark “composite” energies are the deep core�valence cor-relation effects and BSSE. Nevertheless, and according to thedifferentDe energies reported in Table 1, the combined effects ofthe two factors should not be larger than 1�2 kcal/mol. Con-sequently, carrying out the benchmark calculations within thefrozen core approximation without including the CP correc-tion represents a reasonable compromise between cost andaccuracy, which in turn should be close to chemical accuracy(∼1 kcal/mol).

Table 2. Binding Energies (in kcal/mol) for the Monoligand Ca(II) Complexes Obtained with the MP2 and CCSD(T) Methodsa

ligand MP2/aug-cc-pVTZ De CCSD(T)/ aug-cc-pVTZ De MP2/CBSb De composite methodc De composite methodd D0

water �57.14 �56.97 �57.49 �57.33 �55.55

methanol �67.79 �67.58 �67.63 �67.42 �66.29

formic acid �81.19 �81.62 �81.01 �81.44 �79.88

acetic acid �83.91 �84.29 �83.49 �83.87 �83.38

formaldehyde �67.22 �67.58 �66.96 �67.32 �65.74

acetone �89.11 �89.45 �88.79 �89.13 �88.25

formamide �96.01 �96.58 �96.06 �96.64 �94.36

acetamide �103.73 �104.29 �103.67 �104.23 �102.12

N-methyl acetamide �109.38 �110.00 �109.11 �109.73 �107.86

methyl acetate �89.64 �90.29 �89.30 �89.95 �88.95

ammonia �66.00 �65.86 �65.86 �65.72 �63.56

methylamine �73.43 �73.32 �72.82 �72.71 �71.33

methanimine �73.65 �73.43 �72.43 �72.21 �70.41

1H-imidazol �97.98 �98.05 �95.62 �95.69 �94.47

benzene �86.88 �86.02 �86.22 �85.36 �84.03

hydrogen sulfide �45.90 �45.61 �46.67 �46.38 �44.96

methanetiol �57.82 �57.56 �58.41 �58.15 �57.31

hydroxide �338.36 �339.22 �341.81 �342.68 �340.66

metoxi �337.03 �336.45 �339.87 �339.29 �335.56

formate �315.35 �316.13 �317.55 �318.33 �316.18

acetate �323.67 �324.20 �325.49 �326.02 �324.15

imidazolate �279.65 �279.86 �277.91 �278.12 �277.04

hydrosulfide �285.91 �285.68 �290.24 �290.01 �288.88

methanetiolate �292.57 �292.05 �295.88 �295.37 �293.73aMolecular geometries were optimized at the MP2/aug-cc-pVTZ level. bObtained from CBS extrapolation of the MP2 correlation energy based oneqs 1 and 2 and using the HF/aug-cc-pV5Z energies. cUsing an additive combination of electronic energies (CCSD(T)/aug-cc-pVTZ + MP2/CBS�MP2/aug-cc-pVTZ). dUsing an additive combination of electronic energies and including MP2/aug-cc-pVTZ ZPVE energies.



Regarding geometries, we have observed that small changes onthe equilibrium geometries of the Ca(II) water/hydroxide com-plexes affect little the binding energies. Thus, the structures opti-mized at the frozen-core or full-electron CCSD/aug-cc-pVTZlevel have slightly larger Ca�O distances, by 0.01�0.04 Å, thanthe reference MP2 structures, but very similar De values areobtained (see Table 1). Additionally, NPA charges of the Caatom computed using the MP2 and CCSD electronic densitiesare similar and the MP2 and CCSD harmonic stretching fre-quencies for the Ca�ligand bond match each other closely (seeFigures 1 (Ca(II) 3 3 3 H2O) and 2 (Ca(II) 3 3 3 OH

�)).Ab Initio Benchmark Data.Table 2 contains ab initio binding

energies for the full set of Ca(II) complexes here studiedcalculated at various levels of theory. The “composite” De values(5th column) provide the benchmark data. Notice however thatthe MP2/aug-cc-pVTZ level (2nd column) shows a good perfor-mance as compared with the “composite” energy calculations.Indeed, binding energies computed on MP2/aug-cc-pVTZ geo-metries are quite similar regardless of the correlated method(CCSD(T) vs MP2) or the basis set used to perform the corres-ponding single-point energy calculations. Also true is that in-cluding energy corrections by using higher correlated methodsand larger basis sets does not alter significantly the MP2/aug-cc-pVTZ De values. In fact, those two improvements frequently“work” in opposite directions and turn out canceling each otherto some extent implying that the average difference between theMP2/aug-cc-pVTZ calculations and the more accurate “compo-site” energy values is relatively small: the mean unsigned percen-tage error (MU%E) for neutral ligands is 0.7% (largest error forimidazole, 2.4%) and for anionic ligands 0.9% (largest error forhydrosulfide, 1.4%). Then, all these results suggest that predic-tions obtained at the MP2/aug-cc-pVTZ level of theory forCa(II) complexes should be reliable enough. Certainly, this is avery satisfactory conclusion since both CCSD(T)/aug-cc-pVTZand MP2/aug-cc-pVnZ (n = 4, 5) calculations are significantly

more computationally expensive. Table 2 also shows that most ofthe improvement when going from MP2/aug-cc-pVTZ to thecomposite values comes from the basis set extension. Thus, theMU%Es between the MP2/CBS and the composite values aremerely 0.5% for neutral ligands (largest error for benzene, 1%)and 0.2% for anionic ligands (largest error for hydroxide, 0.3%).Indeed the mean unsigned errors (MUEs) are in all cases below1 kcal/mol.For the neutral ligands, the optimized structures correspond to

monodentate Ca(II) complexes characterized by a single intera-tomic Ca�X distance of 2.12, 2.31, and 2.78 Å for X = O, N, andS, respectively (averages of the corresponding Ca�X distances).It turns out that, for a giving donor atom, the binding energycorrelates well with the Ca�X distance (e.g., the linear correla-tion coefficient, r, between the Ca�X distances and the compo-site De values amounts to 0.813 and 0.972 for X = O and N,respectively). NPA charges suggest a significant charge transferwhen Ca(II) binds to neutral ligands: within the 0.08�0.2 e�

range. The amount of charge transfer depends on the electro-negativity and hybridization of the donor X atom and we havefound that it is relatively well correlated with theDe energies (r∼�0.882 (for X = O) and r∼�0.844 (for X = N)). This suggeststhat charge-transfer interactions could also contribute to the totalbinding of these complexes. We also point out that the frequencyof the stretching motion of the Ca�X bond is uncorrelated withthe strength of the metal�ligand bond expressed in terms ofbinding energies. The strong interaction between the Ca(II)cation and the anionic ligands is reflected in the magnitude of thecomputed binding energies (from �338 to �280 kcal/mol),which is accompanied by a typical shortening of the Ca�X dis-tances within a range of 0.40�0.1 Å with respect to the neutralligands and an important charge transfer from ligand to Ca(II)(0.21�0.12 e�).For the sake of completeness, we have also derived the pro-

tonation energies (PE) of some of the ligands studied in this

Table 3. Protonation Energies (PEs in kcal/mol) for Various Acid�Base Pairs Both in Their Isolated Form and in theCorresponding Ca(II) Complexesa

Acid�Base Pair MP2/aug-cc-pVTZ CCSD(T)/aug-cc-pVTZ MP2/CBSb composite methodc

A/B

H2O/OH� �393.26 �397.15 �393.13 �397.02 (�389.01)

H2S/HS� �353.60 �355.99 �353.38 �355.77 (�349.97)

CH3OH/CH3O� �388.27 �391.13 �388.11 �390.98 (�381.09)

CH3SH/CH3S� �360.25 �362.65 �360.18 �362.58 (�356.17)

HCOOH/HCO2� �344.37 �347.41 �344.12 �347.17 (�338.79)

CH3COOH/CH3CO2� �352.52 �355.27 �352.31 �355.05 (�346.44)

1H-imidazol/1H-imidazolate �352.91 �356.78 �352.89 �356.76 (�348.01)

Ca�A/Ca�B

H2O/OH� �112.04 �114.90 �108.82 �111.68 (�103.90)

H2S/HS� �113.59 �115.92 �109.81 �112.14 (�106.05)

CH3OH/CH3O� �119.02 �122.26 �115.87 �119.11 (�111.82)

CH3SH/CH3S� �125.50 �128.16 �122.71 �125.36 (�119.75)

HCOOH/HCO2� �110.21 �112.91 �107.57 �110.27 (�102.48)

CH3COOH/CH3CO2� �112.76 �115.36 �110.30 �112.90 (�105.67)

1H-imidazol/1H-imidazolate �171.24 �174.97 �170.60 �174.33 (�165.44)aMolecular geometries were obtained at theMP2/aug-cc-pVTZ level. bObtained fromCBS extrapolation of theMP2 correlation energy based on eqs 1)and (2 and using the HF/aug-cc-pV5Z energies. cUsing an additive combination of electronic energies (CCSD(T)/aug-cc-pVTZ+MP2/CBS�MP2/aug-cc-pVTZ). Values in parentheses include the MP2/aug-cc-pVTZ ZPVE energies.



work at the different correlated levels of theory. According to thePE values reported in Table 3, the nature of the correlatedmethod (CCSD(T) vs MP2) has a more pronounced effect(∼2 kcal/mol) on the computed PEs than in the case of theCa�L binding energies, whereas the CBS limit of theMP2 PEs isvery similar to the MP2/aug-cc-pVTZ values. When comparingthe PEs of the isolated A/B pairs with those of their Ca-boundcounterparts, we see that the Ca(II) cation decreases the PEs byan amount ranging within �285, �183 kcal/mol (compositeenergy values including ZPVE) for the different acid�base pairs,respectively. Thus, the actual impact on the acid�base strengthof the Ca-ligands is quite variable, with the water/hydroxide pairbeing the most affected one.DFT Calculations. The performance of the test DFT func-

tionals will be discussed in terms of Mean Unsigned PercentageErrors (MU%Es). We point out that in our previous study onmonoligand Zn(II) complexes, wemainly discussed mean signederrors (MSEs). The reason was that for the zinc complexes alltested functionals showed a systematic bias with respect to thereference values (either underestimating or overestimating them)for a given property and basis set. For the calcium complexes, wehave not observed such systematic deviations and we havetherefore chosen MU%Es to assess the performance of thedensity functionals. We also note that, for the sake of simplicity,part of the results of the present study has been collected in thetables presented in the Supporting Information.DFT Molecular Geometries of the Ca�L complexes. For

the majority of the complexes analyzed in this work DFTmethods, when used in conjunction with Pople-type basis sets,predict the same geometry for the lowest energy structure thanthe MP2/aug-cc-pVTZ reference level. There are, however, fewexceptions that deserve to be commented. The complex Ca-(II)�CH3COOH has a C�O�Ca angle of 104� (see Figure 1)at the MP2/aug-cc-pVTZ level of theory. With the Pople-typebasis sets, particularly with the 6-31+G(2d,p) basis, this angletends to open up to 180�. Indeed, with Pople-type basis sets, bothisomers (C�O�Ca ∼ 104� and C�O�Ca ∼ 180�) are trueminima on the potential energy surface except for the 6-31+G(2d,p) basis for which the first isomer does not exist. We havenevertheless considered the MP2/aug-cc-pVTZ-like isomer(C�O�Ca ∼ 104�) for this complex, except with the 6-31+G(2d,p) basis set. The Ca(II) complexes with N-methyl acet-amide and methyl acetate show one imaginary frequency withsome functional and basis sets (the values range between 30 and70 cm�1). Appearance of this imaginary frequency is due to therotation of methyl groups and has a negligible effect in thebinding energies. We therefore considered for these complexesthe MP2/aug-cc-pVTZ geometries shown in Figure 1. TheCa(II) complex with methanethiolate has C3v symmetry at theMP2/aug-cc-pVTZ level, but Cs symmetry with the Pople-type

basis sets (also with the MP2 method). The C�S�Ca anglevaries between 130 and 170�, with B3LYP and MP2 yielding thesmaller values. We have considered these Cs symmetry structuresin this work. Finally, and in agreement with what we found in ourprevious study on Zn(II) complexes, every functional in con-junction with Pople basis sets predicts C1 symmetry for theimidazolate complexes. This is in disagreement with the MP2/aug-cc-pVTZ results, which predict that the planar Cs structure isthe true minimum on the potential energy surface. At theB3LYP/aug-cc-pVTZ level of theory, the complex has again Cs

symmetry, so it seems that the disagreement between the DFTand the MP2/aug-cc-pVTZ geometries is due to the Pople-typebasis sets. For comparison purposes, we have considered a Cs

symmetry for this complex.Table 4 collects the MU%E in the metal�ligand bond

distances of all the calcium complexes here studied. For thepresent analysis, MP2/aug-cc-pVTZ geometries have been takenas the reference ones. We point out that the MU%Es have beencomputed for the whole set of complexes including neutral andanionic ligands since similar errors were obtained for both ofthem. All the functional we have tested give, in general, metal�ligand bond distances that are shorter than the MP2/aug-cc-pVTZ reference values. With the 6-311+G(d) basis set, thedistances may be overestimated for some complexes, but this isdue to the fact that this basis yields distances very close to thereference values. The DFT/aug-cc-pVTZ distances are alsosystematically shorter than the reference. Thus, the general trendis that DFT functionals give too short Ca(II)�ligand bonddistances. This result is interesting because the Zn(II) complexesshow the opposite behavior.10 Table 4 shows, however, that theerrors for the Ca(II) complexes are not very large, the worstresults are obtained at the PW91/6-31G(d) level, and theirMU%E is 1.4%. Focusing on the different basis sets, the followingbehavior can be observed: MU%E(6-31G(d)) > MU%E(6-31+G(2d,p)) > MU%E(6-31+G(d)) > MU%E(6-311+G(d)). Theperformance of the MP2 method with these basis sets is totallydifferent since (a) MP2 overestimates the metal�ligand bonddistances with Pople basis sets, (b) MP2 metal�ligand bonddistances show larger deviation with respect to the reference onesthan those obtained with the various DFT functionals, and (c)comparison of the MU%Es obtained with the four Pople basissets show the opposite trend to that found with the DFT

Table 4. Mean Unsigned Percentage Errors (MU%Es) in theMetal�Ligand Bond Distances of the Ca(II) Complexes withRespect to the MP2/aug-cc-pVTZ Reference Values

basis set PW91 PBE B3LYP TPSS MP2

6-31G(d) 1.4 1.2 0.9 1.2 1.1

6-31+G(d) 0.7 0.6 0.4 0.6 1.7

6-31+G(2d,p) 1.3 1.2 0.8 1.1 1.2

6-311+G(d) 0.4 0.4 0.6 0.4 2.0

aug-cc-pVTZ 1.3 1.2 0.8 1.1

Table 5. Mean Unsigned Percentage Errors (MU%Es) in theBinding Energies of the Ca(II) Complexes with Neutral andAnionic Ligands


Neutral Ligands

6-31G(d) 11.1 9.8 6.4 7.9 4.1

6-31+G(d) 6.5 5.4 2.8 4.3 4.0

6-31+G(2d,p) 5.5 4.5 2.1 3.4 4.6

6-311+G(d) 5.1 4.2 2.3 3.2 5.3

aug-cc-pVTZ 6.7 5.9 3.4 4.6

Anionic Ligands

6-31G(d) 9.1 8.6 6.5 7.5 2.2

6-31+G(d) 2.8 2.5 0.9 2.1 2.8

6-31+G(2d,p) 2.8 2.4 0.8 2.0 2.6

6-311+G(d) 2.0 1.8 0.9 1.4 3.3

aug-cc-pVTZ 3.5 3.2 1.5 2.7



functionals, namely, MU%E(6-31G(d)) < MU%E(6-31+G-(2d,p)) < MU%E(6-31+G(d)) <MU%E(6-311+G(d)). Table 4also shows that the DFT/aug-cc-pVTZ results are comparable tothose obtained with the 6-31G(d) basis but worse than thoseobtained with the larger 6-31+G(d), 6-31+G(2d,p), and 6-311+G(d) basis sets. The MP2 and DFT/aug-cc-pVTZ results clearlypoint to an error cancellation between the underestimation of themetal�ligand distances by the tested density functionals andtheir overestimation by Pople-type basis sets. Let us finally pointout that geometry optimizations carried out using a larger(“Ultrafine”) integration grid at the B3LYP/aug-cc-pVTZ leveldiffer very little from the “medium” grid results: the largest dif-ference in the metal�ligand bond distances is 0.003 Å (see TableS3 in the Supporting Information).DFT Binding Energies. Tables 5 and 6 collect the MU%Es of

the DFT binding energies, corrected and noncorrected from theBSSE, with respect to the reference composite ones for thedifferent Ca(II)�L complexes here studied. Notice that we willdiscuss the DFT binding energies of the neutral and anionicligands separately because their binding energies for complexa-tion are very different in magnitude. In our previous study onZn(II) complexes,10 we noticed that all tested functionals over-shot the composite CCSD(T)/CBS energies and we related thisfact to the overestimation of polarizabilities by the densityfunctionals.69 Indeed, for the zinc complexes we showed thatinduction forces (collecting charge transfer and polarization)played a relevant role in the metal�ligand bonding interactions.As we will show here, the case of the calcium complexes isanalogous, that is, the chosen functionals tend to overestimatethe interaction energies. However, the overestimation is not solarge and, in some particular cases, even underestimations areoccasionally observed. We will see later that, in fact, inductioneffects in Ca(II) complexes are much smaller than in Zn(II)complexes. We point out in passing that the larger bindingenergies found for the Zn(II) complexes with respect to Ca(II)nicely correlate with the higher ionization energy of zinc thatshould induce a larger polarization and charge transfer from thebases to the metal cations. Taking into account the importance ofinduction effects in the binding of these complexes (recall alsothe correlation between the NPA charges and De energiescommented above), this correlation is indeed what shouldbe expected and suggests that consideration of electrostatic

contributions alonemay not be reliable enough for the predictionof relative binding energies. This suggestion will be address infurther detail below.The results of the complexes with neutral ligands will be

discussed first (see Table 5). In general, all the tested densityfunctionals overestimate the binding energies. Only for the 6-311+G(d) basis set the results are close enough to the reference values[CCSD(T)/CBS] that some underestimations are observed.Table 5 shows that, for the Pople-type basis sets, the MU%Eranges from 2.1 to 11.1%. The largest errors are found with the6-31G(d) basis set. Inclusion of diffuse and further polarizationfunctions, in particular, 6-31+G(2d,p) and 6-311+G(d), di-minishes the difference between DFT and the reference datato 2.1�5.5%. Because these two bases provide a better agreementwith the reference data than aug-cc-pVTZ, it seems that someerror compensation is taking place when using Pople-type sets.As a matter of fact, the MP2 energies do not show any improve-ment when increasing the basis set size. Regarding the assess-ment of the tested functionals, from the analysis of Table 5, itseems clear that both B3LYP and TPSS functionals, particularlythe first one, show the best performance. Because, as anticipatedabove and discussed in further detail below, induction forces arethe largest contributors to the interaction energy on these com-plexes, we believe that the more or less accurate predictionsobtained by different density functionals should be related to acorrect description of this particular intermolecular force. Asexpected, the complexes with anionic ligands, as compared to theneutral ligands, give larger absolute errors. However, relativeerrors are smaller than those previously discussed for the neutralligands (see Table 5). For instance, the B3LYP functional givesMU%E = 1.5% with the aug-cc-pVTZ basis set (for neutralligands MU%E is 3.4%) and MU%E = 0.8% when the 6-31+G(2d,p) basis set is used (for neutral ligands is 2.1%).We observeagain that Pople-type basis sets yield systematically better resultsthan the aug-cc-pVTZ basis and that the B3LYP and TPSSfunctionals perform the best. We would like to point out thatbinding energies computed with a larger (“Ultrafine”) integra-tion grid at the B3LYP/aug-cc-pVTZ level are within 0.1 kcal/mol from the “medium” grid results except for two complexes,namely, Ca(II)�acetic acid (difference: 0.34 kcal/mol) andCa(II)�methyl acetate (0.15 kcal/mol; see Table S4). Thus,larger integration grids are in principle not required for the cal-culation of binding energies in these Ca(II) complexes.Table 6 collects the MU%Es corresponding to the binding

energies corrected for the BSSE. For both neutral and anionicligands, comparison of the data shown in Tables 5 and 6 showthat the CP-corrected DFT energies are in general in betteragreement with the reference values than the uncorrected ones.This is not surprising because the tested functional overestimatesthe binding energies with errors in most cases larger than theBSSE itself. However, the improvement obtained after correctingthe binding energies from the BSSE is not very large. As a matterof fact, the average BSSE value at the B3LYP/6-311+G(d) levelfor the set of neutral ligands is not very large, 0.59 kcal/mol (thelargest value: 1.56 kcal/mol for water), and for the anionicligands, 0.93 kcal/mol (largest value: 2.58 kcal/mol for hydro-xide). As expected, the BSSE is larger at the MP2 level of theory:for the 6-311+G(d) basis set we found an average value forneutrals of 2.2 kcal/mol (largest: 3.91 kcal/mol for benzene) andfor the anionic ligands 3.95 kcal/mol (largest: 4.84 kcal/mol forhydrosulfide). Because Pople-type basis sets underestimate thebinding energies, the corrected MP2 energies show worst

Table 6. Mean Unsigned Percentage Errors (MU%Es) in theCounterpoise (CP) Corrected Binding Energies of the Ca(II)Complexes with Neutral and Anionic Ligands


Neutrals

6-31G(d) 8.6 7.4 4.3 5.8 6.0

6-31+G(d) 5.6 4.6 2.2 3.5 6.7

6-31+G(2d,p) 5.0 4.0 1.8 3.0 7.0

6-311+G(d) 4.2 3.4 1.9 2.4 7.5

aug-cc-pVTZ 3.8 1.8 2.7 2.1

Anionic

6-31G(d) 7.2 6.8 4.7 6.0 1.9

6-31+G(d) 2.4 2.1 0.8 1.7 4.0

6-31+G(2d,p) 2.3 2.0 0.6 1.6 3.6

6-311+G(d) 1.6 1.4 0.7 1.0 4.5

aug-cc-pVTZ 2.3 0.9 2.0 1.5



agreement with the reference than the uncorrected values. Onthe other hand, the tested density functionals in conjunction withthe aug-cc-pVTZ basis yield small BSSEs: the B3LYP average forneutral ligands is 0.20 kcal/mol (largest: 0.37 kcal/mol forbenzene) and for anionic ligands 0.40 kcal/mol (largest:0.65 kcal/mol for hydroxide). Thus, taking into account therelatively small effect of the BSSE on the binding energies, on theone hand, and the computational effort needed for the calcula-tion of the CP-corrected energies (which involves three addi-tional calculations: both fragments in the dimer centered basis setand the ligand in its complexed geometry with its own basis set)on the other, it seems that raw binding energies provide a betterquality/cost ratio than the CP-corrected ones. It is finally worthstressing that the CP method does not correct for basis setincompleteness errors apart from the BSSE itself. Thus, the6-31G(d) binding energies in Table 6 show again the worstagreement with the reference.In principle, computation of relative energies for ligand

exchange processes can benefit from cancellation of “systematic”errors in the computed binding energies (De). Hence, we alsoobtained the linear correlation coefficients (r) of DFT resultsversus the ab initio reference results in order to ascertain moreclearly the differences and similarities in the systematic deviationsof the computed energies (discriminating between the neutraland the anionic ligands; see Table S5 in the Supporting In-formation). Thus, we found that the DFT binding energies ofneutral ligands show quite a good correlation (r > 0.99) withrespect to the reference data for all the combinations of DFTfunctionals and basis sets used. For the anionic ligands, the linearregression fits of the binding energies tend to be less satisfactory,especially for the small 6-31G(d) basis set that has r values∼0.96�0.97. However, when the 6-31+G(2d,p) and aug-cc-pVTZ basis sets are used, the trends observed in the DFT bindingenergies of the neutral and anionic ligands match quite closelythe trends observed in the ab initio reference energies, resultingin similar r coefficients. For example, the B3LYP/aug-cc-pVTZDe values for the neutral and anionic ligands have the same r value(0.9967). Therefore, we expect that the relative energies forprocesses involving the rupture of bonds between Ca(II) andeither neutral or anionic ligands should be determined quite

accurately using a DFT method combined with a flexiblebasis set.DFT Protonation Energies. Table 7 collects the MU%Es in

the protonation energies (PEs) of the isolated acid�base pairs aswell as for the complexed anionic ligands. A first observation thatcan be made from the analysis of these data is that the former(isolated acid�base pairs) show significantly smaller MU%Ethan the latter. Indeed, unless for the 6-31G(d) basis set, MU%Esare below 2% and typically closer to 1%. The best performance ofall the functional tested is obtained, as in the case of the bindingenergies, with the B3LYP and TPSS functionals, for which theMU%Es are quite close to zero (0.3% each), particularly inconjunction with the 6-31+G(2d,p) basis set. For the complexedanionic ligands, results collected in Table 7 show MU%Es thatare clearly larger than those for the isolated ligands. Moreover,the computed protonation energies display similar or evenslightly larger MU%Es with respect to the reference than thebinding energies (compare to Table 5).We also note that for PEsthe MP2 values are in better agreement with respect to thereference results than the DFT ones. As a general conclusion, itcan be said then that one should be careful when usingcomplexed anionic ligands PEs, even those obtained with thebest levels of theory, in order to find out whether a ligand isprotonated or deprotonated when coordinated to the Ca(II)cation.DFT-SAPTAnalyses.Wewould finally like to comment briefly

on the nature of the interaction of the Ca(II) complexes withneutral ligands. Figure 3 shows the E(1) and E(2) contributions(see Computational Methods for the definitions) as well as thetotal DFT-SAPT interaction energies for the 17 Ca(II) com-plexes with neutral ligands. A complete set of numerical DFT-SAPT data has been collected in Tables S6 and S7 in theSupporting Information. Let us first comment briefly on twogeneral conclusions that can be drawn from the DFT-SAPTresults. First, it is encouraging to see that the DFT-SAPT inter-action energies are in very good agreement with the compositeones. The average percentage error for the seventeen Ca(II)complexes is a mere 2.9% being the largest deviation 6.5%(5.6 kcal/mol) in Ca(II) 3 3 3Bz. Thus, we conclude that DFT-SAPT provide for these systems fairly reliable interaction en-ergies in spite of their relatively large magnitude. Second, theδEint

HF term is not very large for these calcium complexes being inall cases smaller than 5% of the total DFT-SAPT interactionenergy (except Ca(II) 3 3 3Bz, 12.4%). We point out that for theZn(II) complexes δEint

HF represented 10�20% of the total SAPT2energy, showing that third-order contributions are far moreimportant for these systems in agreement with their largerbinding energies. The error in the DFT-SAPT interactionenergies without inclusion of the δEint

HF term is 4.0%, not muchlarger than the error obtained including this term. Indeed, for 8out of the 17 complexes, inclusion of δEint

HF slightly worsens theagreement with the reference. Explicit calculation of third ordercorrections, which is feasible within DFT-SAPT but withoutresponse, is much more computationally demanding and, takinginto account the relatively small magnitude of the δEint

HF term, hasnot been attempted in this work.Figure 3 shows that for the whole set of complexes the second-

order terms are larger than the first-order ones. Since dispersionis almost negligible for these systems (see Table S6), the DFT-SAPT results highlight the importance of charge transfer andpolarization contributions to the metal�ligand bonding in Ca(II)complexes. For the sulfur-containing ligands, E(1) is indeed

Table 7. Mean Unsigned Percentage Errors (MU%Es) in theProtonation Energies of the Isolated and Complexed AnionicLigands (L = OH�, CH3O

�, HCO2�, CH3CO2

�, Im�, HS�,CH3S

�)


Isolated

6-31G(d) 3.4 3.3 3.6 3.7 3.0

6-31+G(d) 1.8 1.8 1.3 1.0 1.8

6-31+G(2d,p) 0.8 0.8 0.3 0.3 0.6

6-311+G(d) 1.9 1.9 1.4 1.0 1.7

aug-cc-pVTZ 0.8 0.9 0.4 0.4

Complexed

6-31G(d) 6.5 6.4 2.3 3.8 3.4

6-31+G(d) 9.0 8.9 4.8 6.0 1.3

6-31+G(2d,p) 5.9 5.7 2.2 3.0 2.4

6-311+G(d) 7.4 7.3 3.3 4.3 1.2

aug-cc-pVTZ 7.1 7.0 2.9 4.2



very small and most of the binding energy comes from thesecond-order terms. In the particular case of Ca(II) 3 3 3Bz, thefirst-order contributions are almost negligible, 0.41 kcal/mol, andthe stability of the interaction comes again from the relaxation ofthe charge densities. This result highlights once more theimportance of polarization effects when an aromatic ring inter-acts with an ionic partner.70�73 The Ca(II) binding energies toformaldehyde and ammonia have been analyzed before by Corralet al.74 Interestingly, the relative binding energies of these twocomplexes (larger for formaldehyde) seem to be reversed withrespect to their protonation affinities (larger for ammonia). Theanalysis of Corral et al. lead them to conclude that the maincontribution to the binding preference of Ca(II) appear to stemfrom polarization effects. The SAPT results shown in Figure 3(see also Table S6) show indeed that the electrostatic interactionis larger for the ammonia complex but that the induction contri-butions (second, E(2) plus higher order, δEint

HF) reverse the finalinteraction energies. We therefore agree with Corral et al. in thatclassical electrostatics alone does not seem to be able to re-produce the Ca(II) binding preference for these two complexes.Interestingly, the binding energies of ammonia and formaldehyde

to Zn(II) are in agreement with their relative proton affinities.10

SAPT shows (see Table 11 in ref 10) that, for these complexes,the electrostatic contribution favors the ammonia complex by20 kcal/mol, whereas the induction forces favor formaldehyde byabout 5 kcal/mol. This is the same qualitative trend found for theCa(II) complexes. However, the electrostatic preference forammonia in the Zn(II) complex is so large that it overcomes thepreference for formaldehyde in terms of the induction forces andthe final binding energy is larger for the former. These twoexamples stress again the important role played by induction forcesand therefore suggest that models based on classical electrostaticinteractions may not be reliable enough for the prediction ofrelative ligand binding energies. We would finally like to point outthat Gresh and Garmer studied some of the complexes consideredin this work using a different partitioning scheme, the RestrictedVariational Space (RVS) procedure, and arrived to similar conclu-sions about the role of the polarization effects.75,76 We also pointout that SAPT results for the complexes with water, formaldehyde,and benzene have also been recently published.32,77

It is worthwhile to compare the Ca(II) results to those ob-tained in our previous work for Zn(II).10 In Figure 4 we compare

Figure 3. First- and second-order contributions (kcal/mol) to the interaction energy of the 17 Ca(II) complexes with neutral ligands, as obtained at theDFT-SAPT/aug-cc-pVTZ level of theory.

Figure 4. First- and second-order contributions (kcal/mol) to the interaction energy of 12 Ca(II) and Zn(II) complexes, as obtained at the DFT-SAPT/aug-cc-pVTZ level of theory.



the E(1) and E(2) contributions for 12 Ca(II) and Zn(II) com-plexes. Because the Zn(II) results had been obtained at theSAPT2/6-31+G(2d,p) level of theory,10 we have recalculatedfour representative complexes (namely, those with water, am-monia, benzene, and hydrogen sulfide) at the DFT-SAPT/aug-cc-pVTZ level just to confirm that the results obtained are verysimilar (this is not indeed an unexpected result since we alreadyshowed10 that for Zn(II) complexes the 6-31+G(2d,p) basisyielded results in good agreement to those obtained with aug-cc-pVTZ). Figure 4 clearly shows that, whereas themagnitude of thefirst-order term is similar for Ca(II) and Zn(II) complexes, thesecond-order contributions are about 2.5�3 times larger forthe later. As above-mentioned, the dissociation energies of theCa(II) complexes are about half of the corresponding Zn(II)ones. We related this fact to the higher ionization energy of zinc,which should induce a larger charge transfer from the bases to themetal cation. Figure 4 and Table S7 show that this is indeed thecase: it is the much larger polarization of the ligands’ chargedensities in the Zn(II) complexes that yields larger interactionenergies for these compounds. We would like to stress again thatthe different roles played by the second-order forces in theinteraction energy of Ca(II) and Zn(II) complexes has necessaryimplications for the description of these systems using molecularmechanics models. Indeed, it may well be that models based onclassical electrostatics alone may not yield reliable relative bind-ing energies, taking into account the importance of polarizationeffects. We would like to finish this section, stressing the impor-tance of performing rigorous bonding analysis by means ofmethodologies like SAPT such that further developments inmolecular mechanics and force fields can reflect the underlyingphysical forces that govern the interaction potentials in thesecomplexes. We point out that efforts in this direction are alreadyon the way (see, for example,refs 25 and 78).

’CONCLUSIONS

In this study we have carried out high-level ab initio calcula-tions for a set of monoligand Ca(II) complexes to provide areliable set of benchmark results on metal�ligand distances,binding energies, and protonation energies. Geometries havebeen obtained at the MP2/aug-cc-pVTZ level of theory, and a“composite” CCSD(T)/CBS scheme has been chosen as thereference method for the protonation and binding energies. Webelieve that these levels of theory should provide results reliableenough for benchmark purposes. We have, for example, esti-mated that the “composite” CCSD(T)/CBS binding energiesshould be already close to chemical accuracy (∼1 kcal/mol). Aninteresting first conclusion of this work is that MP2/aug-cc-pVTZ binding energies are very close to the “composite” ref-erence ones, the MU%E is smaller than 1%, meaning that theyshould be within 1 kcal/mol from the CCSD(T)/CBS results.We have additionally tested four widely used density functionalsand several Pople-type basis sets (including an increasing num-ber of polarization and diffuse functions). The B3LYP and TPSSfunctionals provide the closest agreement with the referencevalues, particularly the former. In conjunction with the 6-31+G(2d,p) and 6-311+G(d) basis sets, both functionals yieldMU%Es in the binding energies below 3%. Besides, we have shownthat DFT binding energies yield a very good linear correlationwhen compared to the “composite” reference results. Therefore,the computation of accurate relative energies, which are impor-tant for the study of ligand exchange processes, should provide

reliable results when using a DFT method combined with aflexible basis set.

We have additionally estimated the relative weight of thedifferent contributions to the metal�ligand bond using theSymmetry Adapted Perturbation Theory. This analysis shouldprovide useful information for the assessment of current “non-polarizable” molecular mechanics potentials and for the futuredevelopment of polarizable force fields. Our results have shownthat induction and electrostatic forces contribute similarly to themetal�ligand bond in the studied Ca(II) complexes, suggestingthat an explicit treatment of polarization is advisible to properlydescribe the coordination structure of Ca(II) complexes.

’ASSOCIATED CONTENT

bS Supporting Information. Mean unsigned percentage er-rors in the binding energies and metal�ligand bond distances forthe whole set of complexes, as obtained with Blaudeau’s andRassolov’s 6-31G basis sets, metal�ligand bond distances, andbinding energies at the B3LYP/aug-cc-pVTZ level with an“ultrafine” grid; linear correlation coefficients corresponding tothe binding energies between BFT/MP2 and the benchmarkresults, detailed SAPT contributions for the Ca(II) complexes;and comparative SAPT results for some selected Ca(II) andZn(II) complexes. This material is available free of charge via theInternet at http://pubs.acs.org.

’AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected].

Present Addresses§Departament de Fisicoquímica, Facultat de Farm�acia, Universi-tat de Barcelona, 08028 Barcelona, Spain.

’ACKNOWLEDGMENT

This research has been supported by the Junta de Castilla yLe�on (Grant VA006B07). N.D. and D.S. are also grateful to theSpanish MEC for support via Grant CTQ2007-63266. Thisarticle is dedicated to the memory of our colleague and friendDr. Miguel �Alvarez Blanco.

’REFERENCES

(1) Even€as, J.; Malmendal, A.; Fors�en, S. Curr. Opin. Chem. Biol.1998, 2, 293.

(2) Dudev, T.; Lim, C. Chem. Rev. 2003, 103, 773.(3) Berridge, M. J.; Bootman, M. D.; Lipp, P.Nature 1998, 395, 645.(4) Maurer, P.; Hohenester, E. Matrix Biol. 1997, 15, 569.(5) Harding, M. M. Acta Crystallogr., Sect. D 2000, 56, 857.(6) Rao, J. S.; Dinadayalane, T. C.; Leszcynsky, J.; Sastry, G. N.

J. Phys. Chem. A 2008, 112, 12944.(7) Tunell, I.; Lim, C. Inorg. Chem. 2006, 45, 4811.(8) Harding, M. M. Acta Crystallogr., Sect. D 1999, 55, 1432.(9) Harding, M. M. Acta Crystallogr., Sect. D 2001, 57, 401.(10) Ray�on, V. M.; Vald�es, H.; Díaz, N.; Su�arez, D. J. Chem. Theory

Comput. 2008, 4, 14.(11) Riley, K. E.; Pitonak, M.; Jurecka, P.; Hobza, P. Chem. Rev.

2010, 110, 5023.(12) Grimme, S. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2011, 1,

211.(13) Ramos, M. J.; Fernandes, P. A. Acc. Chem. Res. 2007, 41, 689.



(14) Geerlings, P.; De Proft, F.; Langenaeker, W. Chem. Rev. 2003,103, 1793.(15) Sousa, S. F.; Fernandes, P. A.; Ramos, M. J. J. Phys. Chem. A

2007, 111, 10439.(16) Alcamí, M.; Gonz�alez, A. I.; M�o, O.; Y�a~nez, M. Chem. Phys. Lett.

1999, 307, 244.(17) Corral, I.; M�o, O.; Y�a~nez, M.; Scott, A. P.; Radom, L. J. Phys.

Chem. A 2003, 107, 10456.(18) da Costa, L. M.; Carneiro, J. W. d. M.; Coelho Paes, L. W.;

Romeiro, G. A. J. Mol. Struct.: THEOCHEM 2009, 911, 46.(19) da Costa, L. M.; de Mesquita Carneiro, J. W.; Romeiro, G. A.;

Paes, L. W. C. J. Mol. Model. 2011, 17, 243.(20) Haworth, N. L.; Sullivan, M. B.; Wilson, A. K.; Martin, J. M.;

Radom, L. J. Phys. Chem. A 2005, 109, 9156.(21) Petrie, S.; Radom, L. Int. J. Mass Spectrom. 1999, 192, 173.(22) Viswanathan, B.; Barden, C. J.; Ban, F.; Boyd, R. J. Mol. Phys.

2005, 103, 337.(23) Barnes, P.; Finney, J. L.; Nicholas, J. D.; Quinn, E. E. Nature

1979, 282, 459.(24) Cieplak, P.; Dupradeau, F.-Y.; Duan, Y.; Wang, Y. J. Phys.:

Condens. Matter 2009, 21, 333102.(25) Luque, F. J.; Dehez, F.; Chipot, C.; Orozco, M. WIREs

Computational Molecular Science 2011, 1, 844.(26) Leontyev, I.; Stuchebrukhov, A. Phys. Chem. Chem. Phys. 2011,

13, 2613.(27) Lopes, P. E. M.; Roux, B.; MacKerell, A. D., Jr Theor. Chem. Acc.

2009, 124, 11.(28) Warshel, A.; Kato, M.; Pisliakov, A. V. J. Chem. Theory Comput

2007, 3, 2034.(29) Wu, J. C.; Piquemal, J.-P.; Chaudret, R.; Reinhardt, P.; Ren, P.

J. Chem. Theory Comput. 2010, 6, 2059.(30) Project, E.; Nachliel, E.; Gutman, M. J. Comput. Chem. 2008,

29, 1163.(31) de Courcy, B.; Piquemal, J.-P.; Gresh, N. J. Chem. Theory

Comput. 2008, 4, 1659.(32) Dehez, F.; Archambault, F.; Soteras Guti�errez, I.; Luque, F. J.;

Chipot, C. Mol. Phys. 2008, 106, 1685.(33) Frison, G.; Ohanessian, G. J. Comput. Chem. 2008, 29, 416.(34) Kol�ar, M.; Berka, K.; Jurecka, P.; Hobza, P. ChemPhysChem

2010, 11, 2399.(35) Zgarbov�a, M.; Otyepka, M.; Sponer, J.; Hobza, P.; Jurecka, P.

Phys. Chem. Chem. Phys. 2010, 12, 10476.(36) Piquemal, J.-P.; Chevreau, H.; Gresh, N. J. Chem. Theory

Comput. 2007, 3, 824.(37) de Courcy, B.; Pedersen, L. G.; Parisel, O.; Gresh, N.; Silvi, B.;

Pilm, J.; Piquemal, J.-P. J. Chem. Theory Comput. 2010, 6, 1048.(38) Kendall, R. A.; Dunning, J. T. H.; Harrison, R. J. J. Chem. Phys.

1992, 96, 6796.(39) Woon, D. E.; Dunning, T. H., Jr. J. Chem. Phys. 1993, 98, 1358.(40) Koput, J.; Peterson, K. A. J. Phys. Chem. A 2002, 106, 9595.(41) Feller, D. J. Comput. Chem. 1996, 17, 1571.(42) Schuchardt, K. L.; Didier, B. T.; Elsethagen, T.; Sun, L.;

Gurumoorthi, V.; Chase, J.; Li, J.; Windus, T. L. J. Chem. Inf. Model.2007, 47, 1045.(43) Raghavachari, K.; Trucks, G.W.; Pople, J. A.; Head-Gordon, M.

Chem. Phys. Lett. 1989, 157, 479.(44) Peterson, K. A.; Puzzarini, C. Theor. Chem. Acc. 2005, 114, 283.(45) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553.(46) Iron, M. A.; Oren, M.; Martin, J. M. Mol. Phys. 2003, 101.(47) Perdew, J. P.; Burke, K.; Wang, Y. Phys. Rev. B 1996, 57, 14999.(48) Perdew, J. P.; Burke, K.; Enzerhof, M. Phys. Rev. Lett. 1996,

78, 1396.(49) Becke, A. D. J. Chem. Phys. 1986, 95, 7184.(50) Becke, A. D. J. Chem. Phys. 1988, 88, 2547.(51) Becke, A. D. J. Chem. Phys. 1988, 88, 1053.(52) Lee, C.; Yang, R. G.; Parr, R. G. Phys. Rev. B 1988, 37, 785.(53) Tao, J.; Perdew, J. P.; Starovenov, V. N.; Scuseria, G. E. Phys.

Rev. Lett. 2003, 91, 146401.

(54) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab InitioMolecular Orbital Theory; Wiley: New York, 1986.

(55) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys.1980, 72, 4654.

(56) McLean, A. D.; Chandler, G. S. J. Chem. Phys. 1980, 72, 5639.(57) Rassolov, V. A.; Pople, J. A.; Ratner, M. A.; Windus, T. L.

J. Chem. Phys. 1998, 109, 1223.(58) Rassolov, V. A.; Ratner, M. A.; Pople, J. A.; Redfern, P. C.;

Curtiss, L. A. J. Comput. Chem. 2001, 22, 976.(59) Bladeau, J.-P.; McGrath, M. P.; Curtiss, L. A.; Radom, L.

J. Chem. Phys. 1997, 107, 5016.(60) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.;

Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.;Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.;Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson,G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.;Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.;Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.;Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.;Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.;Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski,V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick,D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui,Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.;Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith,T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.;Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.;Pople, J. A.Gaussian 03, Revision C.02; Gaussian, Inc.: Wallingford, CT,2004.

(61) Hesselmann, A.; Jansen, G. Chem. Phys. Lett. 2002, 357, 464.(62) Hesselmann, A.; Jansen, G. Chem. Phys. Lett. 2002, 362, 319.(63) Hesselmann, A.; Jansen, G. Chem. Phys. Lett. 2003, 367, 778.(64) Misquitta, A. J.; Szalewicz, K. Chem. Phys. Lett. 2002, 357, 301.(65) Misquitta, A. J.; Jeziorski, B.; Szalewicz, K. Phys. Rev. Lett. 2003,

91, 33201.(66) Gr€uning,M.; Gritsenko, O. V.; vanGisbergen, S. J. A.; Baerends,

J. E. J. Chem. Phys. 2001, 114, 652.(67) Lias, S. G.; Levin, R. D.; Kafafi, S. A. Ion Energetics Data. In

NIST Chemistry Webbook, NIST Standard Reference Database Number69; Linstrom, P.J.; Mallard, W.G., Eds.; National Institute of Standardsand Technology: Gaithersburg, MD, http://webbook.nist.gob.

(68) Werner, H.-J.; Knowles, P. J.; Lindh, R.; Manby, F. R.; Sch€utz,M.; Celani, P.; Korona, T.; Rauhut, G.; Amos, R. D.; Bernhardsson, A.;Berning, A.; Cooper, D. L.; Deegan, M. J. O.; Dobbyn, A. J.; Eckert, F.;Hampel, C.; Hetzer, G.; Lloyd, A. W.; McNicholas, S. J.; Meyer, W.;Mura, M. E.; Nicklass, A.; Palmieri, P.; Pitzer, R.; Schumann, U.; Stoll,H.; Stone, A. J.; Tarroni, R.; Thorsteinsson, T.MOLPRO, a package of abinitio programs; 2006; see http://www.molpro.net.

(69) Piquemal, J. P.; Marquez, A.; Parisel, O.; Giessner-Prettre, C.J. Comput. Chem. 2005, 26, 1052.

(70) Caldwell, J. W.; Kollman, P. A. J. Am. Chem. Soc. 1995, 117,4177.

(71) Cubero, E.; Luque, F. J.; Orozco, M. Proc. Natl. Acad. Sci. U.S.A.1998, 95, 5976.

(72) dehez, F.; �Angy�an, J. G.; Soteras Guti�errez, I.; Luque, F. J.;Schulten, K.; Chipot, C. J. Chem. Theory Comput. 2007, 3, 1914.

(73) Gresh, N.; Pullman, B. Biochim. Biophys. Acta 1980, 625, 356.(74) Corral, I.; M�o, O.; Y�a~nez, M.; Radom, L. J. Phys. Chem. A 2005,

109, 6735.(75) Garmer, D. R.; Gresh, N. J. Am. Chem. Soc. 1994, 116, 3556.(76) Gresh, N.; Garmer, D. J. J. Comput. Chem. 1996, 17, 1481.(77) Soteras, I.; Orozco, M.; Luque, F. J. Phys. Chem. Chem. Phys.

2008, 10, 2616.(78) Gresh, N.; Cisneros, G. A.; Darden, T. A.; Piquemal, J.-P.

J. Chem. Theory Comput. 2007, 3, 1960.

Ab Initio Benchmark Calculations on Ca(II) Complexes and Assessment of Density Functional Theory...

Documents

Transcript of Ab Initio Benchmark Calculations on Ca(II) Complexes and Assessment of Density Functional Theory...