Researchintroduction
Economic development and industrialization cause a significant increase inconcentration of gases emitted into the environment Therefore, air pollution is oneof the hottest topics which attracts a lot of attention Increasing amount of carbondioxide (CO 2 ) in the air is the main factor that significantly affects the greenhouseeffect.TheenhancingapplicationsofsupercriticalCO2(hereafterdenotedb y scCO2) in manufacturing industries help to partially solve emission problems, whilealsosaveotherresources.ScCO2hasattractedmuchattentionduetoitsenvironmentallyfriendly applications,ascomparedtotoxicorganicsolvents 1 Compressed CO2h a s i n d e e d b e e n w i d e l y u s e d a s a s o l v e n t f o r e x t r a c t i o n p u r p o s e sor in organic solvent elimination/purification processes, also as an antisolvent inpolymerization of some organic molecules and precipitation of polymers With theaim of finding the new materials and solvents which preferred CO2, it is essential toclarifyinteractionsbetweenCO2andfunctionalorganiccompoundsandtheirelectroniccharacter isticsatmolecularlevel.Theseunderstandingsrequireasystematicstudy combiningtheexperimentsandmodelling,andimportantly,aquantumcomputationalapproach.
Uptonow,variousexperimentalresearchesontheinteractionsbetweensolutes and scCO2s o l v e n t h a v e b e e n u n d e r t a k e n t o b e t t e r i n v e s t i g a t e t h e s o l u b i l i t yinscCO2.Ingeneral,somefunctionalorganiccompoundsincludinghydroxyl,carbonyl, thiocarbonyl, carboxyl, sulfonyl, amine, … are considered as CO2- philicones.Furthermore,theuseofpolarizedcompoundsasH2O,smalla l c o h o l s (CH3OH,
C2H5OH) as cosolvents was reported to affect the thermodynamic andeven kinetic properties of reactions involving CO2 Addition of H2O into scCO2solvent helps to increase the solubility and extraction yield of organic compounds.Therefore, the systematic research on interactions between
CO2, H2O and organicfunctionalcompoundswillopenthedoorstothenatureandroleofformedinteractions,thee ffectofcooperativityinthesolvent–cosolvent–solutesystem.
The achieved results are hopefully to provide a more comprehensive look at scCO2applicationandalsocontribute totheunderstandingoftheintrinsic characteristic sofweaknoncovalentinteractions.
Objectandscopeof the research
- Research object: Geometrical structure, stability of complexes involving
- Scopes:complexesoffunctionalorganiccompoundsincludingdimethylsulfoxide,acetone, thioacetone, methanol, ethanol, ethanethiol, dimethyl ether and itshalogen/methylsubstitution withsomemoleculesofCO 2 and/or H2O.
Noveltyandscientificsignificance
Overviewoftheresearch
Human emissions of CO2and other greenhouse gases are the primary driverof climate change which is one of the present world’s most pressing challenges Therelation between the cumulative CO2emissions and global temperature has beenclearly discovered.2It is said that CO2is the key atmospheric gas that exerts controlover the strength of the greenhouse effect Innovating the use of CO2is an urgentmissionwiththeaimofdecreasingitsconcentrationinambientair.C O2i sabundant, reusable and non-toxic, and it reaches a supercritical point at an easilycontrolledt e m p e r a t u r e a n d p r es s u r e S c C O 2is a w e l l - k n o w n e f f e c t i v e s o l v e n t f o r the development of green chemical reactions instead of conventional toxic organicsolvents.
ScCO2is used in extensive applications in nanomaterials, food science,pharmaceuticals, especially in separation and synthetic processes 3,4 The effectiveuse of scCO2i n e x t r a c t i o n a n d f r a c t i o n a l p r o c e s s e s o f s e p a r a t i o n h a s b e e n r e p o r t e din many previous works 3,5,6 Nevertheless, the solvent has drawbacks in solute polarorganic compounds and high molecular-mass ones Thus, many efforts have beenmadetofindouttheinteractingspeciesandeffectivethermodynamicreactionconditionsaimingto enhancethesolubilityinscCO2.Fluorocarbons,fluoropolymers, and carbonyl-based compounds are previously considered as
CO2-philic functional groups 7,8,9 While high cost and toxicity are the limitations of thefirst two compounds, carbonyl-based compounds have been paid much attentionthankstotheirsimplesynthesisprocessandlowercost.Effortsforenhancedapplicability of scCO2with the use of CO2-philes have been pursuedviaseries ofexperimentalandtheoreticalworks.10,11,12,13,14,15
Dimethyls u l f o x i d e ( D M S O ) i s a c o m m o n s o l v e n t i n b i o l o g i c a l a n d physicochemicalstudies,whichiswidelyusedinsupercriticalantisolventprocesses, 16,17 withman yvaluableapplicationssuchasmicronizationofpharmaceuticalcompounds,polymers,catalysts,s uperconductorsandcolouringmaterials.18TheuseofthemixtureofDMSOandCO 2i n PCA(Pre cipitationwitha
CompressedAntisolvent)processtoprecipitateproteinsandpolarpolymersconfronts some difficulties in both operation regions that are below and upper thecritical pressure of the DMSO-CO2mixture Some experimental studies suggestedthe use of water as a cosolvent of DMSO to modify the phase behaviour of DMSO-CO2and solve limitations of the PCA process.19In this approach, water moleculeshelptoshapeparticlemorphologybychangingthemechanismofp a r t i c l e formatio n Experimental phase equilibrium data on binary mixtures of DMSO-
H2Oweremeasured.20,21Walleneta l 9reportedthatDMSOinteractsstronglywithCO2,andthe complexstrengthiscontributed by both the S=O∙∙∙CLewis acid-base interactionand the C–H∙∙∙O HB, inwhichthemorecrucialroleoftheformerwassuggestedbyTrungetal 22 Intermolecularinteractiono fDMSOandH2OwasclassifiedintotheclassofO−H∙∙∙O red-shifting and C−H∙∙∙O blue-shifting hydrogen bonds by Kirchner andReiher 23 Leiet al.revealed that the weak C−H∙∙∙O and strong O−H∙∙∙O contactsrepresent a consistent concentration dependence in interaction between DMSO andH 2 O, implying a cooperative effect between two hydrogen bonded types.24Overall,the phase behaviour of these binary and ternary mixtures can be controlled when theinteractions and stability of DMSO with both H 2 O and CO2a t t h e m o l e c u l a r l e v e lareelucidated.
Manyexperimentalinvestigationsshowedthattheadditionofas m a l l amount of cosolvents into the scCO2solvent resulted in an increase in the solubilityof solutes.25,26,27In particular, some alkanes were added to scCO2to dissolve thenonpolar compounds, whereas functional organic compounds or H2O were used forthepolarones 28,29,30 Alcoholsincludingmethanol,ethanol,andpropanolwereextensivelyusedasco solventstoimprovebothsolubilityandselectivityprocesses 27,30,31 AccordingtoHosseinietal.,thep resenceofalcoholsasa cosolventaffectstheshapeofcomplexesformed,inwhicheachalcoholh a s different impacts on the aggregation of CO2around the drugs.30The solubility ofDisperseRe d 8 2 a n d m o d i f i e d D is p e rs e Y e l l o w 1 1 9 i n c re as es s u b s t a n t i a l l y up t o
25-fold by adding 5% of ethanol cosolvent to the scCO2.31Vapor-liquid equilibriaand critical properties of the CO2ãããethanol binary mixture were experimentallyinvestigatedusingavarietyofexperimentaltechniquesandequipment.32,33,34,35Beck eretal.reportedthattheadditionofCO2t opureethanolleadstoareductionof interfacial tension in the liquid phase.32The addition of H2O into scCO2solventwasreportedthatinducesanincreaseinthesolubility andextractionyieldo f organiccompounds 36,37
From the theoretical viewpoint, it is important to elucidate the interactions,stabilityandstructuresofcomplexesbetweenorganiccompoundsandCO2with/without H2O at molecular level The mechanism of the CO2capture could alsobe understoodviathe investigation into CO2complexes In which, the intrinsicstrength of the noncovalent interactions between CO2and adsorbents is determinedas a key to demanded captured abilities. Furthermore, a systematically theoreticalinvestigation into complexes between organic compounds and CO2with/withoutH2Oatmolecularlevelcouldgiveinformationforsolvent- soluteandsolvent-cosolventinteractions in systemsinvolvingCO2.
Aspreviously mentioned,themoleculescontainingcarbonylgrouph a v e been paid much attention Indeed, they have been pursued by series of experimentalandtheoreticalworks.15,38,39,40,41,42,43,44,45,46,47Thestructuresofcomplexesandstrength sofintermolecularinteractionshavebeenreportedthroughnumerousstudiesonsystemsboundby
CO2andvariousorganiccompounds:simplealcohols, 48,49 formam ide, 50 isopropyl amine, 51 2- methoxy pyridine, 52 …Accordingtoabinitiocalculations, threetypes ofgeometriesw e r e r e p o r t e d a s p r e s e n t e d i n Fig 1.1 The conventional structure is supported by theoretical and experimentaldata, whereas two remaining ones are less favoured The parallel geometry (alsocalled non-conventional structure)is similar to the (CO 2 )2dimerand carbonyl- carbonylarrangementsincrystallographicstructures.However,thisstructureisrarelyreported,wit htheexceptionofmethylacetate-CO2c o mp le x e s Forcarbonyl complexes,C ã ã ã O t e t r e l b o n d ( p r e v i o u s l y c a l le d L e w i s a c i d - b a s e i n t e r a c t i o n ) w a s addressedas the bonding feature.
Conventionalstruc tures T-shapedstructures Non- conventionalstruct Figure1.1 Threetypesof CO2complexes ures
In 2002, Raveendran and Wallen reported the cooperative effect of C- HãããOhydrogenbondinsystemsofCO 2with differentorganicmoleculesincludingformaldehyde, acetaldehyde, acetic acid, and methyl acetate, as model carbonylcompounds, and dimethyl sulfoxide as a model system for the sulfonyl group 9 Inwhich the hydrogen atom attaches to the carbonyl carbon or the-carbon directlyinteracted with oxygen one of CO 2 However, the investigations that were combinedbyab initiocalculations and experimental infrared spectra showed that the complexof dimethyl ether and CO2is stabilized by C∙∙∙O tetrel bond with the C ssymmetry andwithout theadditional contribution ofCHãããOhydrogenbond 47,53 a) Stable structures of complexesformedbycarbonylcom poundsandCO 2 (Ref.44) b) Stable structures of complexesformed by ethanol and
CO2(Ref.48) Figure1.2 Stable geometriesof complexesinvolving CO2
Similarly, the principal role of CãããO tetrel bond was detected in complexesof
CO2with CO54, HCN55, H2O56, C2H5OH, CH3OH, … In systems of formamideand CO2,the C∙∙∙O over the C∙∙∙N tetrel bond is the primary factor in stabilizing thecomplexes 50 Manyr o t a t i o n a l datawerereportedforthenatureofinteractions between CO2and partner molecules, from solvent or lattice effects The rotationalspectra using the high-resolution Fourier transform microwave (FTMW) revealsinformation on intermolecular interactions and geometrical structures, which is usedto compare with obtained results taken from theoretical calculations.46,49,50,52Forcomplexes of simple alcohols with CO 2 , many works proposed the primary role ofCãããO tetrel bond with additional contribution of CHãããO hydrogen bond 48 ,49FortheaggregationofCO 2around ethanol,moleculardynamicsimulationsofethanol∙∙∙64
CO2systemundersupercriticalconditionsshowedt h e h i g h e r probability of CO2around the lone pairs of oxygen atom in ethanol.57Anotherinvestigation into structures of ethanol and 1-4 and 6 molecules of CO2in 2017 alsogives the same result that the CO2molecules preferably locate around the oxygenatomofethanol 58
It is useful to compare features of compounds containing oxygen and sulurelement.ApreviouslycomparativestudyoninteractionsbetweenCO 2and compoundsfuncti onalizedby>S=Oand>S=Sgroups reported thelargerstabilityof
(CH3)2(S=O)∙∙∙CO2complexes as compared to (CH3)2(S=S)∙∙∙CO2ones, which isdue to a larger contribution of the attractive electrostatic interaction of the
>S=Orelativetothe>S=S.22ThecomplexesofCO2withthioformaldehydeanditshalogen/methyl- derivatives were exclusively reported to be slightly less stable thanthosewithsubstitutedformaldehydes 42 Differentwiththegreatattentiono f carbonyl compounds, thiocarbonyl ones have been rarely studied in searching for aneffective cosolvent in scCO2 Thiocarbonyl compounds have been used in synthesesand have provided several unique organocatalysts thanks to their higher reactivityand less polarity in comparison with carbonyl ones 59 Moreover, the compoundsinvolving >C=S group are predicted to be key functions in molecular materials andbiologicallyrelevantsubstrates 60 Accordingly,understandingofinteractionsofthioacetone (acs) with popular solvents and cosolvents used in synthesis, extraction,separationprocessessuchas scCO2a n d / o rH2Oisessential.
Up to now, most of studies concentrated on the geometries, stability andinteractions of binary complexes involving CO2 Nevertheless, the aggregation andgrowth mechanism of complexes with more CO2molecules, which are important tounderstandt h e a b s o r p t i o n p r o c e s s e s a n d t h e i r p r o p e r t i e s , h a v e n o t b e e n r e p o r t e d yet.Besides,thesolvationstructuresandstabilityofcomplexesformedbyinteractions of organic compounds with a small number of CO2and H2O moleculeshavenotyetbeendiscovered.
From perspective of noncovalent interactions, the behaviour and origin ofweak interactions such as hydrogen, tetrel, chalcogen, and halogen bond have beenwidelyinvestigatedbecauseoftheirconsiderableinfluenceoncrystalpacking,materialstructure s,andbiologicalsystems.61,62,63,64,65,66,67Hydrogenbond(HB),especially blue-shifting HB has extensively been reported thanks to its ubiquity andsignificance in crystal engineering and biochemical processing.42,68,69,70A generalscheme that can unravel the origin of blue-shifting
Objectivesoftheresearch
Thiswork hasfourmainobjectives detailed as follows:
1) To determine stable structures and to compare the strength of the complexesformed by interaction of basic organic compounds functionalized by variousgroups with CO 2 and H2O molecules, and also to find out functional groupsthat interact strongly with CO2as valuable candidates in searching of novelmaterialstoadsorbCO2gasphase.
2) Tospecifytheexistenceandtheroleofnoncovalentinteractionsi n stabilizingthec omplexes,tounraveltheircooperativity,especiallythecooperativity of hydrogen bonds and tetrel bonds; and also to gain furtherinsights into the origin of noncovalent interaction Furthermore, this researchwasinvestigatedtoclarifyroleofH 2 Oinstabilizationofnoncovalentintera ctionsandcomplexes,whichleadstoaclearerunderstandingofimportanceofH2O ascosolventinsupercriticalCO2.
3) To investigate the effect of different substitution groups including halogenand methyl on the geometry and stability of complexes formed by interactionoffunctional organiccompoundswithCO 2 and/orH2O.
4) Todiscoverthetrendofgeometricalstructuresandcharacteristicofnoncovalent interactions when increasing number of CO2/H2O molecules.This gives information ofthe aggregation of CO2aroundorganic compounds,with/withoutH2O.
Researchcontent
In order to obtain the aims of research project, the complexes of functionalorganic molecules including (CH3)2SO, (CH3)2CO, (CH3)2CS, (CH3)2O, (CH3)2S,CH3OH, C2H5OH,
C2H5SH with nCO2and/or nH2O (n=1-2)were investigated.Additionally,theeffectofmethylandhalogensubstitutionisalsoexamined.
- Choosing the computational methods along with basis sets which are suitablefor both monomers and complexes based on available experimental data, or reliableresultsreportedin theliterature.
- Simulating the structures of monomers and complexes, and then optimizingthese structures to obtain stable geometries with minima of energy on potentialenergysurfaces.
- Calculating infrared spectra of monomers and complexes, and estimating thechange of C(O)−H bond lengths, its stretching vibrational frequencies and infraredintensities in the complexes compared to the relevant monomers with purpose ofclassifyingwhichtypeofhydrogenbondformed.
- Calculating interaction energy of complexes and comparing their strength.Many electronic analysed tools including MEP, AIM, NBO and NCIplot were usedto specify existence and stability of the noncovalent interactions in the complexes,and then along with PA, deprotonation energy DPE to unravel their cooperativity tostability of complexes Besides, the contribution of separate components of energyto the complex stabilisation on the basis of SAPT2+ approach was also estimated togainaclearerviewinthecooperativityofinteractionsinthecomplexes.
- Estimatingcooperativeenergyofternarycomplexestoevaluatethecooperation between noncovalent interactions in complexes The effect of additionanotherCO 2 orH2Omoleculeintocomplexeswillbeexplored.
- Investigating the effect of DPE and PA to the formation of blue-shiftingHBinvolving C−H covalent bond, in order to give more elucidation of origin of blue-shifting HB on the basis of PA of proton acceptor and DPE of C−H bond in theisolatedmonomers.
Researchmethodology
InvestigationintocomplexesoffunctionalorganicmoleculesandCO2with/without H2O at molecular level was carried out using high level computationalchemicalmethods.Inthisstudy,theresearchobjectsaremostlysmallsystems,and are made up by C, H, O, S (and/or halogen atoms: F, Cl, Br) atoms For moreaccuracy,thesecond-orderperturbation(MP2)methodinconjunctionwith6-311+
+G(2d,2p) Pople basis set was used to perform all optimization calculations ofcomplexesinvestigated.Forsinglepointenergycalculations,theMP2/aug-cc-pVDZ or MP2/aug-cc-pVTZ or even CCSD(T)/aug-cc-pVTZ which depends on thesizeofinvestigatedcomplexes,wasusedtogivethereliableresults.
Vibrational frequency analyses were performed at the same level to specifyminimum and estimate the zero-point energy Interaction energies and cooperativeenergiesarecorrectedforZPEandtheBSSE.Thedepthofintermolecularinteractions wasdiscoveredwithwavefunctioncalculationsatMP2/6-311++G(2d,2p)orMP2/aug-cc- pVTZ.NBOanalyseswithB97X-DorMP2method was used to quantitatively determine the charge-transfer effects and thecharacteristicsofnoncovalentinteractions.Tofurtheridentifythenoncovalentbehaviours, interactions between carbon dioxide and ethanol were assessed withNCIplotatMP2/6-311+ +G(2d,2p).MEPofisolatedmonomerswasplottedatMP2/aug-cc-pVTZ All quantum calculations mentioned above were carried outviatheGaussian09package.
The SAPT2+ analysis executed by PSI4 program was applied to decomposetheinteractionenergyintophysicallymeaningfulcomponentsincludingelectrostatic, induction, dispersion and exchange terms SAPT2+ calculations areperformedwithdensity- fittedintegralswith thestandardaug-cc-pVDZbasisset.
Besides, software such as Molden, Gaussview, Origin and Excel will beemployedtohelpinanalysingcalculatedresults.Researchmethodologyandtechniquesappropr iateforeachissuearedescribedmoredetailinthenextchapter.
Initial Field corrected for each core electron Solutions of Wave Equation for core electrons
Distribution of Charge Final Field
THEORETICAL BACKGROUNDS ANDCOMPUTATIONALMETHODS
Theoreticalbackgroundofcomputationalchemistry
The origin of Hartree-Fock (HF) method existed soon after the discovery ofSchrửdinger'se q u a t i o n ( 1 9 2 6 ) I n 1 9 2 8 , H a r t r e e i n t r o d u c e d f o r t h e f i r s t t i m e a procedure called theself-consistent field(SCF) method to calculate approximatewavefunctionsandenergiesforatomsandions 79 Hartreeassumedthattheappropriate potential for a core electron is total potential of the nucleus and thewhole electronic distribution of charge Another assumption in Hartree’s originalpaper is that the distribution of charge for a closed shell electron configuration iscentrallysymmetricalandthenucleustogetherwiththeelectronsformedaspherically symmetric field The following diagram briefly expresses the process ofSCF method.
AccordingtoHartree'sapproach, 79 SCFmethodgivessolutionstoSchrửdinger'sequationf orsystemswithindividualelectrons1,2,3,…inthestates
1,2,3, … The electronic wave function of system is separated into product ofwave functions of the individual electrons(r), is known asHartree product.Withthefullsetofcoordinates,theHartree productbecomes
el 1 (x 1 ) 2 (x 2 ) N (x N ) This method attracted much attention and was independently modified bySlater andFock in 1930 The Hartree product which assumes that electrons areindependent did not satisfy theanti-symmetric requirement Theanti-symmetry ofthewavefunctioncan beachieved bybuildingitfromSlaterdeterminants. i A
In order to derive the HF equation, the expression of energy of a single Slaterdeterminantisneededtobedescribed.BasedontheBorn-Oppenheimerapproximation, it is allowed that the wave functions of atomic nuclei and electronsinamoleculecanbetreatedseparately:
Here, the first term is the kinetic energies of electrons The second one is theattractionofelectronstonuclei.Twofirsttermsdependononlyoneelectroncoordinate.Thethirdter misrepulsionbetweenelectronsanddependsontwoelectrons The repulsion between nuclei is added onto the energy at the end of theequation The last term does not depend on electronc o o r d i n a t e s a n d i s a c o n s t a n t for a given nuclear geometry These operators may be collected according to thenumberofelectronindices(usedatomicunitstoshortentheequation): h ˆ1 2
Accordingtovariationalt he ore m, theideaofH F method istofind ou tthe minimumofE el when i i j (ishandled bymeansofLagrange multipliers). One of the advantages of the method is that it breaks the many-electronSchrodinger equation into many simpler one-electron equations Each one-electronequation is solved to yield a single-electron wave function which called an orbital;and energy, called an orbital energy The orbital describes the behaviour of anelectronin the net fieldof all the other electrons. fˆ i (x 1 ) i (x 1 ) Wherefis Fock operator, i (x i )is a set of one-electron wave functions, calledtheHFmolecularorbitals.
Incomputationalchemistry,thesimplifiedalgorithmicflowchartofHFmethod is described in Fig 2.1 The Hartree-Fock algorithm produces the optimalsingle-determinant electronic configuration for any set of nuclear coordinates Fromthis, the Fock matrix is constructed and diagonalized After that, it solves the eigenvalueproblembasedontheobtainedFockmatrix.Anewdensitymatrixisconstructed, andthisprocesswill berepeated untiltheconvergencetestissatisfied.
ThemaindefectoftheHFmethodisthatitdoesnottreate l e c t r o n correlation properly: each electron is considered to move in an electrostatic fieldcomposing by the average positions of the other electrons, whereas the fact is thatelectrons avoid each other better thant h e m o d e l p r e d i c t s , s i n c e a n y e l e c t r o n A really sees any otherone Basamovingparticle and the twomutually adjust(correlate)theirmotionstominimizetheirinteractionenergy.Theelectroncorrelationistreat edbetterinpost-HFmethods,whicharerepresentedinthefollowingsection.
There is a number of different methods that go beyond HF calculations,called post- Hartree-Fock methods They add electron correlation which is a moreaccurate way of including the repulsions between electrons than in the HF methodwhererepulsionsareonaveraged.Oneofthewidelyusedapproachesi s perturbation theory.
In perturbation theory, the HF solution is treated as the first term in aTaylor series One of the most common forms of perturbation was developed byMứller and Plesset 80 Because it is a perturbational treatment, Mứller-Plesset (MP)theorycanbeappliedconsideringtheperturbationseriestoincludedifferentnumber s of terms (i.e., to different orders) Second order MP theory (MP2) is oftenused for geometry optimizations and fourth order (MP4) for refining calculatedenergies.Thesecondorderperturbation was utilizedinthepresentwork.
Substitutingt hese e x p a n s i o n s i n t o t h e S c h r ử d i n g e r e q u a t i o n an d c o l l e c t i n g termsaccordingtopowersofyields
There are a number of other techniques to include electron correlation thatcan potentially provide very accurate results, such calculations can however becomevery time consuming and at present they tend to be used for small molecules Suchtime-consuming methods are used to calculate single-point energy in some smallcomplexesinthepresentwork.
Couple cluster (CC) method takes the basic HF molecular orbital methodandconstructsmulti- electronwavefunction usingtheexponentialclusteroperator to account for electron correlation The wave function of the coupled-cluster theoryiswrittenasanexponentialansatz:
Where0ist h e r e f e r e n c e w a v e f u n c t i o n w h i c h i s t y p i c a l l y a S l a t e r d e t e r m i n a n t constructedfromHFmolecularorbitals,and T ˆ isc l u s t e r o p e r a t o r T h e c l u s t e r operatoris writteninthe Taylorexpansionform:
Where ˆi s theoperator o f a ll singleexcitatio ns, ˆi s theoperatorofalldouble excitations,andsoforth.Forthedeterminationofthe amplitudes,thewavefunction(2.1)is inserted intheSchrửdinger equation:
N isintroducedthe firsttimeandcalled thenormal orderHamiltonian, whichconsistsoftheone-electron(fˆ)andtwo-electron(Wˆ
E cooris denotedforelectroncorrelationenergy.Duetoitscomplexity andtheresulting computational effort the coupled-cluster problem is normally not solved inavariationalmanner.Bymultiplicationfromtheleftofequation(2.2),iti s projected onto the reference determinant as well as onto all excited determinants.The couple cluster energy is thus considered as the expectation value of a similaritytransformedHamiltonian.
Theclassificationoftraditionalcoupled-clustermethodsrestsonthehighest numbero f e x c i t a t i o n s a l l o w e d i n t h e d e f i n i t i o n o f T ˆ T h e a b b r e v i a t i o n s f o r coupled-clustermethodsusuallybeginwiththeletters"CC"andfollowby:
S – for single excitations (shortened to singles in coupled-cluster terminology),D– fordouble excitations(doubles),
Termsinroundbracketsindicatethatthesetermsarecalculatedbasedonperturbationtheory.Forex ample,theCCSD(T)methodmeans:
- An estimate to the connected triples contribution is calculated non- iterativelyusingmany-bodyperturbationtheoryarguments.
The CCSD(T) method is often called the “gold standard” of computationalchemistry, because it is one of the most accurate methods applicable to reasonablylargemolecules.
Configuration interaction (CI) solves the problem of electron correlationby consideringmore than a single occupation scheme for theMOsand by mixingthe microstates obtained by permuting the electron occupancies over the availableMOs.Initssimplestform,aCIcalculationconsistsofapreliminarySCFcalculati on, which gives the MOs that are used unchanged throughout the rest of thecalculation. Microstates are then constructed by moving electrons from occupiedorbitals to vacant ones according to preset schemes However, the problem is that ifyou want to consider every possible arrangement of all the electrons in all the MOs(a full CI), the calculationswillbecome far too large even formoderate-sizedmoleculeswith a large basis set Thus,twotypes ofr e s t r i c t i o n a r e u s u a l l y u s e d : only a limited number of MOs are included in the CI, and only certain types ofrearrangement (excitation) of the electrons are used The most economical form isthat in which only one electron is promoted from the ground state to a virtual orbital(single excitations) This is abbreviated as CIS and has traditionally been used forcalculatingspectra.Addingalldoubleexcitations(inwhichtwoelectronsarepromoted) givesCISD,andsoon.
To sum up:ab initiocalculations, in general, give very good qualitativeresults and can yield increasingly accurate quantitative results as the molecules inquestion become smaller.The advantage ofab initiomethods is that they eventuallyconverge to the exact solution once all the approximations are made sufficientlysmallinmagnitude.Ingeneral,the relativeaccuracyofresultsis:
HFMP2CISDMP4CCSDCCSD(T)CCSDTFullCI Inab initiocalculations, there are four sources of error including the Born-
Thedisadvantageofabinitiomethodsisthattheyarecomputationalexpensive These methods often take enormous amounts of computer CPU time,memory, and disk space The
HF method scales as N 4 , where N is the number ofbasisfunctions.This mea ns thatacalculationtwiceasbigtakes 1 6timesaslong
(2 4 )tocomplete.Correlatedcalculationsoftenscalemuchworsethanthis.Inpractice,extremelyaccura tesolutionsareonlyobtainablewhenthemoleculecontains a dozen electrons or less However, results with an accuracy rivalling thatofmanyexperimentaltechniquescanbeobtainedformoderatesizedorganicmolecules The minimally correlated methods, such as MP2, are often used whencorrelationis important to the description ofmolecules.
The initial work ondensity functional theory (DFT) was reported in twopublications:t he f i r s t is o f H o h e n b e r g a n d K oh n, 1 9 6 4 81 a n d t h e ne xt i s of K o h n an dSham,1965 82 DFTisanalternativeapproachtothetheoryofelectronicstructure, in which the electron density distributionp(r), rather than the many-electronwave function,plays a central role.
According to DFT theory, the kinetic energy of the non-interacting electrondensityiscalculatedandcorrectedtotherealenergyininteractingsystemapproximately.
The correction to the non-interacting kinetic energy is known as theexchange correlation
(XC) energyand is calculated as a function of the electrondensity As the electron density itself is a function, the XC energy is a function of afunction,whichisknownasafunctional;hencethename“density functionaltheory” Its basic principles are describedmore fully by Kochand Holthausen(2001) 83
Computationalapproachestononcovalentinteractions
The interaction energy (Eint) of each investigated complex is determined byusing the supermolecular approach as the difference in total energy between thecomplex and the sum of energies of the relevant monomers at the selected suitableleveloftheory.
Eint=E complex-(E monomer 1+E monomer 2+…) Themorenegativeinteractionenergy indicatesthemorestablecomplexformed,andviceversa.Thesupermolecularapproachhasani m p o r t a n t disadvantage in that the final interaction energy is usually much smaller than thetotal energies from which it is calculated, and therefore contains a much largerrelative uncertainty In the case where energies are derived from quantum chemicalcalculationsusingfiniteatom-centeredbasisfunctions,basissetsuperposition errors can also contribute some degree of artificial stabilization The detail of basissetsuperpositionerrorsispresentedinlatersection.
It is becoming increasingly apparent that cooperative interaction involvingseveral molecules is an important component of intermolecular interactions Thecooperativity of hydrogen bond turns out to play a key role in controlling andregulatingtheprocessesoccurringinlivingorganisms.Theimportanceofcooperativityin noncovalent interactionswasreported inmanyworks.78,87,88,89
Toevaluatethecooperativeeffectexistedintheternarycomplexes,cooperativity energies are calculated as the difference between the complexationenergy of the ternary system and sum of the complexation energy of its constituentbinary systems The positive cooperativity implies that the sum of at least twointeractions is larger than the simple addition of the individual interactions Theequation 90
Ecoop=Eint-E 2 whereEinttermcorrespondstotheinteractionenergyoftheconsideredcomplexesandE 2 isenerg yofcorrespondingpairwiseinteractions.
Negative value of cooperative energy indicates that noncovalent interactionswork cooperatively, strengthen each other and make the complex stronger, while apositivevalueindicatesthat these interactions workanti-cooperatively.
In all systems treated in this work, molecules get closer and approach eachother to form complexes by intermolecular interactions This means the basis setsallocated to each of them are going to overlap This overlapping gives electronsgreater freedom to localize and can result in a reduction of the total electronicenergy This reduction in energy would not have occurred if the basis sets had beeninfinitelylarge.Thisenergyreductionisthereforeanartifactofworkingw i t h limitedbasissets. This problemis called thebasissetsuperpositionerror(BSSE).
(2.3) int AB AB AB A B where, at the right hand side of the equation, the subscript denotes the geometry ofthe system and the superscript the used basis sets Eintdenotes the interaction energyof the system The energy of the separate atoms does not depend on the interatomicdistance, while the basis set superposition error varies with the interatomic distance.TheinteractionenergyinEq. (2.3)isinneedforacorrectionontheBSSE.
Boys and Bernardi introduced the counterpoise correction to correct for theBSSE 91 In the counterpoise correction, the artificial stabilization is countered byletting the separate atoms improve their basis sets by borrowing functions of anempty basis set To realize such an empty basis set, a ghost atom is used The ghostatom has the basis set of the according atom, but no electrons to fill it Performingthis procedure for both atoms on the grid will correct for the BSSE Hence, theinteractionenergywith counterpoisecorrection
E CP (r)E AB (r)E AB (r)E AB (r) (2.4) int AB AB AB A AB B AB
Note that in Eq 2.4 the energy of the separate atoms depends on a distance – thedistancebetweentheatomandtheghostatom.
Naturalbondorbital(NBO)methodologyisintrinsicallybasedonthequantumwavefunctio nanditspracticalevaluation(tosufficientchemicalaccuracy) using modern computational technique Unlike the conventional valencebond(VB)ormolecularorbital(MO)viewpoints,NBOtheorymakesn o assumption about the mathematical form of Instead, the NBO bonding picture isderived from variational, perturbative or DFT approximations of arbitrary form(basedonchance)andaccuracy,uptoand including theexact.
The concept ofnaturalorbital was first introduced by Per-Olov Lửwdin in1955todescribetheuniquesetoforthonormal1-electron functions 92
The NBOs are one of a sequence of natural localized orbital sets that includenaturalatomic(NAO),hybrid(NHO),and(semi-)localizedmolecularorbital(NLMO)s e t s , i n t e r m e d i a t e b e t w e e n b a s i s A O s a n d c a n o n i c a l m o l e c u l a r o r b i t a l s
Inputbasis(NOs)→NAOs→NHOs→NBOs→NLMOs→MOs
The input NOs are required to be orthonormal set by using the occupancy- weightedsymmetricorthogonalizationprocedure.AsoriginallyintroducedinLửwdin,thenatural
(spin)orbitals{ i }aretheeigen-orbitalsof one-electrondensity operator(1)satisfying 1 i n i i
Wheren irepresents thepopulationoftheeigen-function ifor theone-electron densityoperator.
NAOs{ i A }arelocalized1-centerorbitalsthatcanbedescribedastheeffective "natural orbitals of atom
A" in the molecular environment The NAOsincorporate two important physical effects that distinguish them from isolated-atomnaturalorbitalsaswellasfromstandardbasisorbitals:
(i) The spatial diffuseness of NAOs is optimized for theeffective atomicchargeinthemolecularenvironment(i.e.,morecontractedifAissomewhatcationi c; more diffuse ifA is somewhatanionic).
(ii) The outer fringes of NAOs incorporate the important nodal features duetosteric(Pauli)confinementinthemolecularenvironment(i.e.,increasingoscillatory featuresandhigherkineticenergyasneighboringNAOsbegintointerpenetrate,preservin gtheinteratomicorthogonalityrequiredbythePauliexclusionprinciple).
NaturalBondOrbitals(NBOs)arelocalizedfew- centerorbitals("few"meaningtypically1or2,butoccasionallymore)thatdescribetheLewis- like molecular bonding pattern of electron pairs (or of individual electrons in the open- shellcase)ino pt im al ly co m p a c t form.Mo re precisely, NB Osa re an orthonormal s eto f l o c a l i z e d " m a x i m u m o c c u p a n c y " o r b i t a l s w h o s e l e a d i n g N/2 members(orNmembers in the open-shell case) give the most accurate possible Lewis- likedescriptionofthetotalN-electron density.
However, the general transformation to NBOs also leads to orbitals that areunoccupiedintheformalLewisstructureandthatmaybeusedtodescribenoncovalencyeffects. Themostimportantof thesearetheantibonds* AB
NLMOs {ωi} can be described assemi-localized alternatives to the ordinary("canonical") CMOs for representing the electron pairs of MO-type wave functions.EachNLMOωicloselyresemblesa"parent"NBOΩi(strictlylocalized)b u t capturesth eassociateddelocalizationsneededtodescribethedensity ofafullelectron pair, thereby becoming a valid (non- canonical) solution of the HF (or DFT- type)SCFequations.ComparedtoCMOs,theNLMOsarefreefromt h e superfluous constraints of overall symmetry adaptation NLMOs therefore adopt thecharacteristicbondingpatternofalocalizedLewisstructure,avertingthesymmetry- imposedm i x i n g s ( e v e n b e t w e e n r e m o t e g r o u p s , b e y o n d e m p i r i c a l v a n derWaals separation)thatlimittransferabilityandinterpretabilityofCMOs.
NBOType centers shell L/NL label corec A 1-c core L CR nonbonded (lonepair)n A 1-c valence L LP bondΩAB 2-c valence L BD antibondΩ*AB 2-c valence NL BD*
Rydbergr A 1-c Rydberg NL RY ij
Figure2.3.Perturbativedonor- acceptorinteraction,involvingafilled orbitalandanunfilledorbital*
In this study, the NBO theory along with NBO 5.G program 93 was employedtoquantitativelyevaluatethechargetransferinteractionsbetweeni n d i v i d u a l orbi talsandtheunitcharges 94
Allpropertiesofmatterbecomeapparentinthechargedistribution,itstopology that delineates atoms and the bonding between them It is possible todefine the structure of molecules quantum mechanically with the help of Bader’sQuantumTheoryofAtomsin Molecules(QTAIM) 95,96,97
The AIM theory rests on analysing the variation from place to place in amoleculeoftheelectrondensity function(electronprobability function,chargedensityfunction,chargedensity),.
It is the probability of finding an electron in the infinitestimal volume dvcentered on the point (x, y, z) This probability is the same as the charge indvif wetake the charge on an electron as unit of charge, hence the electron density functionisalsoconsideredas thechargedensity.
Sincenucleioftheatomsaretheonlysourceofpositivecharge,theelectron density has its maxima at or near the nuclei (attractors of electrons) The change indensity between two attractors (i.e.two atoms) is described in terms of a gradientvector.
Using the topology of electron density, QTAIM divides molecular space intoatomicsubspaces.Startingfromagivenpointinspace,onemaymoveininfinitesimalstepsalongt hedirectionofthegradientuntilanattractorisencountered The part of space from which all gradient paths end up at the samenuclei is called the basin of atom (Figure 2.4) The border between two atomicbasinsidentifyingatomsinmoleculesiscalledzerofluxsurface.Oncet h e molecular volume is divided up, the electron density is integrated within each of theatomicbasinsandtheatomiccharges,dipoles, andmultipolescanbe determined.
The zero flux surface in the gradient vector field of electron density is notcrossedbyanyofthegradient vector(r)at anypoint.
The points at which the density gradient ((r)) has a zero value are calledcriticalpoints(CPs).InQTAIM,theexistenceofCPdefineswhetherabondbetweentwoatomse xistornot.Indetail,
For the existence of CP, it does not bring any information about the nature ofbonds.Inordertodefineitsnature,theanalysesofthesecondderivativeso f electrond e n s i t y ( 2 (r))a r e r e q u i r e d I n t h r e e - d i m e n s i o n a l s p a c e , t h e r e a r e n i n e secondd e r i v a t i v e s w h i c h a r e a r r a n g e d i n a s q u a r e m a t r i x f o r m , c a l l e d
The Hessian is real symmetric matrix, thus it can be diagonalized to be adiagonalized one If1,2and3are the eigenvalues of the Hessian matrix whichrepresent curvature of the density with respect to the three principal axesx’,y’,z’,theLaplacianofthedensityis:2ρ(r)=1+2+3
(Theredballsbetweenbond are the bond criticalpoints)
0, the CP is a maximum Thus, a positive value of Laplacian represents a localchargedepletionandanegativevalueofLaplacianmeanslocalchargeconcentration.AtBCP(
(r)=0),thesignof 2 ρ(r)providesinformationfornatureof the bond Specially, the negative value implies a covalent bond, while a positiveoneindicatesanionicbondoravanderWaalsinteractions.
The rank (), and signature () are used to classified different types of CPs,which are symbolized as (,) Rank is the rank of Hessian matrix of 2 ρ(r) and iscalculatedbythenumbernonzerocurvatures().Signatureisthealgebraicsumof
Nucleus critical point (NCP): (3,- 3)Ring critical point (RCP): (3,+1)Cage critical point (CCP):
(3,3)Bondcriticalpoint(BCP):(3,-1) Itisevidentfromliteraturethatthereareotherimportantrelationshipsbetweenenergetictop ologicalparametersandthe 2 ρ(r)atCPs.Oneoftheimportantrelationshipsisthelocalformofviria ltheorem:
To be more specific, the positive values of Laplacian ( 2 ρ(r)) and electronenergy density (H(r)) imply that the kinetic electron energy density (G(r)) is greaterthan the potential electron energy density (V(r)) and hence such interactions arecharacterized as closed shell or noncovalent in nature.If|V(r)|isonet i m e m o r e than theG(r) then∇ 2 ρ(r) is positive andH(r) is negative In this situation, theinteractionisclassifiedaspartlycovalentinnature.
NCIplot is an effective tool to detect noncovalent interactions in the realspacebasedonelectrondensityandreducedgradientdensity(s((r)) 98,99 Thereduceddensitygrad ientis asfollow: s((r))
(r) 4/3 When a weak inter- or intramolecular interaction is present, there is a crucialchange in the reduced gradient between the interacting atoms, producing densitycritical points between interacting fragments Troughs appear ins((r)) associatedwith each critical point. The combination ofsandallows a rough partition of realspace intobonding regions: high- slow-rcorrespondst o n o n - i n t e r a c t i n g d e n s i t y tails,low-shigh- rtocovalentbonds,andlow-slow-rto noncovalent interactions.
Noncovalentinteractions
Noncovalentinteractionshaveaconstitutiveroleinthescienceofintermolecular relationships In nature, these interactions are the foundation of thelife process itself, the ultimate function articulation, both
E mechanical and cognitive.In synthetic chemistry, interactions between rationally designed molecular subunitsdrivetheassemblyofnanoscopicaggregateswithtargetedfunctions.
Complexescontainingnoncovalentinteractionsareidentifiedandcharacterizedinisolati oninthegasphasebyrotationalandvibrational spectroscopy.Thepropertiesoftheseisolatedcomplexessuchass t r e n g t h , geometry,etcare confirmed bytheabinitiocalculations.
The term tetrel bond (TtB) was coined recently to describe the noncovalentinteractions involving group IV The atoms of group IV act as the electrophilic sitewhich seek for the nucleophile one of another molecule.67The carbon atom of CO 2is an electrophilic center, forming tetrel bond with another component containingfreeelectronpairsor π-electron ofa Lewis base.
ComplexofCO2withHCl Complexes of CO2withHBr Figure2.7 DifferenceingeometryofcomplexesCO2-HCland CO2-HBrobtained fromexperimental spectroscopy The term tetrel bond was first suggested by Frontera and co-workers recentlyin2013 101 Nevertheless, the first complex involving TtB was investigated in 1992byWittigandco-workers.ItisthecomplexesofCO 2and HBr,whichi s dramatically different from complexes of CO2with HF and HCl (Figure
2.7).102TheOatomsofCO2i salsoanucleophileregiontointeractwithelectron- deficientsiteof partner molecules Indeed, the interactions of CO2with HF and HCl result in alinearconfigurationbyOCO2ãããH−F/Clhydrogenbond.103,104However,goingt o HBr, the geometrical structure is stabilized by interactions of CCO2ãããBr tetrel andOãããHhydrogenbonds,asaring.
The tetrel bond begins with the electronegative nonmetal C, then moves tosemimetals
Si and Ge, after which it includes the Sn and Pb metals All of theseatoms have been shown to be capable of engaging in a TtB, similar to other typesincludinghydrogenbond,halogenbond,chalcogenbond,…Untilnow,theIUPAC has not recommended the definition of tetrel bond If the definition of tetrel bondparallelsthatofchalcogenbond,thatis
A tetrel bond occurs when there is evidence of a net attractive interactionbetween an electrophilic region associated with a tetrel atom in a molecular entityand a nucleophilic region (e.g a n-pair or p-pair of electrons) in another, or thesame,molecularentity.
The tetrel bond stabilizing complexes formed involving CO2was concludedas the noncovalent bond 67 Tetrel bonds are also reported to be comparable strengthto hydrogen bonds and other-hole-based interactions, they are highly directional,and might serve as a new possible molecular linker 101 The importance of TtBs inbiology, particularly those involving C, was emphasized by a survey of proteinstructures105which placed emphasis on the CF3parallel of the methyl group Theauthors stressed the importance of these bonds in such systems as the NADP + -dependent isocitrate dehydrogenase enzyme and its interaction with an aspartateresidue, as well as a triazine-based inhibitor of enasidenib Calculations showedstrong TBs between the CF3group and a variety of bases Later surveys extendedtheseTBstotheunsubstitutedmethylgroup.
Hydrogenbond(HB)isprobably themoststudiedandanalysedamongnoncovalentinteractions.Itsimportancehasbeenm o r e c o m p r e h e n s i v e l y recognized when the presence of HBs involving C−H∙∙∙O/N had been discovered inproteins,DNAdoublehelix,RNA…
Itisoperativeindeterminingmolecularconformation, molecular aggregation, and the function of a vast number of chemicalsystems ranging from inorganic to biological In terms of modern concepts, the HBis understood as a very broad phenomenon, and it is accepted that there are openborderstoothereffects.Dissociationenergiesspanmorethantwoordersofmagnitude(about0 240kcal.mol 1 ).Withinthisrange,thenatureoftheinteractionisnotconstant,butit’selectrostatic, covalent,anddispersioncontributionsv a r y i n t h e i r r e l a t i v e w e i g h t s T h e H B h a s b r o a d t r a n s i t i o n r e g i o n s that merge continuously with the covalent bond, the van der Waals interaction, theionicinteraction,andthecation-interaction.
The hydrogen bond is an attractive interaction between a hydrogen atomfrom a molecule or a molecular fragment X–H in which X is more electronegativethan H, and an atom or a group of atoms in the same or a different molecule, inwhichthereisevidenceofbondformation.
The forces involved in the formation of a hydrogen bond include those of anelectrostaticorigin,thosearisingfromchargetransferbetweenthedonorandacceptor leading to partial covalent bond formation between H and Y, and thoseoriginating fromdispersion.
The atoms X and H are covalently bonded to one another and the X–H bondis polarized, the HY bond strength increasing with the increase in electronegativityofX.
The X–HY angle is usually linear (180º) and the closer the angle is to 180º,thestrongeristhe hydrogenbondandtheshorteristheHYdistance.
The length of the X–H bond usually increases on hydrogen bond formationleading to a red shift in the infrared X–H stretching frequency and an increase in theinfraredabsorptioncross-sectionfortheX–Hstretchingvibration.
The greater the lengthening of the X–H bond in X–HY, the stronger is theHYbond.
The X–H∙∙∙Y–Z hydrogen bond leads to characteristic NMR signatures thattypically include pronounced proton deshielding for H in X–H, through hydrogenbondspin–spincouplingsbetween XandY,andnuclearOverhauser enhancements.
The Gibbs energy of formation for the hydrogen bond should be greater thanthethermalenergyofthesystemforthehydrogenbondtobedetectedexperimentally.
Hydrogen bonds exist with a continuum of strengths Nevertheless, it can beuseful for practical reasons to introduce a classification, such as “weak”,
“strong”,andpossiblyalso“inbetween”.FollowingthesystemdescribedbyJ e f f r e y (1997), 107 HBs are called moderate if they resemble those between water moleculesor in carbohydrates (one could also call them “normal”) and are associated withenergies in the range 4-15 kcal.mol -1 HBs with energies above and below this rangearetermedstrongandweak,respectively.
AconventionalhydrogenbondA−H∙∙∙Borred-shiftinghydrogenbond(RSHB) is accompanied by an elongation of A−H bond together with a decrease ofitsstretchingvibrationalfrequency.Itsoriginiswell-understood,thatisanelectrostatic interaction between H and B However, in some systems, a hydrogenbond occurs to have opposite characteristics with RSHB including a shortening ofA−H bond, increasing in its stretching vibrational frequency, so-called blue- shiftinghydrogenbond(BSHB).BSHBhasoftenbeenrevealedinsystemswhereahydrogen atom bonded to a carbon atom forms a HB with either an electronegativeatom or a region with an excess of electron density BSHB has often been observedin systems where a hydrogen atom bonded to a carbon atom forms a hydrogen bondwith either an electronegative atom or a region with an excess of electron density Anumber of hypotheses and models have been proposed to explain the origin of bothHBtypes.108,109,110,111,112.
The interest of halogen bond has surged because of the fact that this bondexists biological materials, like proteins, nucleic acid, and interactions of drug withbiological objects 113 Furthermore, X-bonds are found to be essential architecturalelements in supramolecular systems, liquid crystal engineering, nanomaterial designand nanowire formation, and so on and so forth 114,115 The widely range applicationof halogen bond leads to a great attention of both experimental and theoreticalscientists.DefinitionofhalogenbondaccordingtoIUPAC 116
A halogen bond occurs when there is evidence of a net attractive interactionbetween an electrophilic region associated with a halogen atom in a molecularentityand anucleophilic regionin another, or thesame, molecular entity.
A typical halogen bond is denoted by the three dots in R–X∙∙∙Y R–X is thehalogen bond donor, X is any halogen atom with an electrophilic (electron-poor)region, and R is a group covalently bound to X In some cases, X may be covalentlybound to more than one group Y is the halogen bond acceptor and is typically amolecular entity possessing at least one nucleophilic (electron-rich) region Somecommon halogen bond donors and acceptors are itemized below Some features thatare useful as indications for the halogen bond, not necessarily exhaustive, are listedbelow.Thegreaterthenumberoffeaturessatisfied,themorereliablethecharacterizationofan interactionasa halogenbondis.
• The halogen bond strength decreases as the electronegativity of X increases, andtheelectron-withdrawingabilityofRdecreases.
• Theforcesinvolvedintheformationofthehalogenbondareprimarilyelectrostatic, but polarization, charge transfer, and dispersion contributions all playanimportantrole.
• The analysis of the electron density topology usually shows a bond path (a
• The infrared absorption and Raman scattering observables of both R–X and Y areaffected by halogen bond formation; new vibrational modes associated with theformationofthe X∙∙∙Ybondarealsoobserved.
• TheX ∙ ∙ ∙ Y h a l o g e n b o n d u s u a l l y a f f e c t s t h e n u c l e a r m a g n e t i c r e s o n a n c e observablesofnucleiinbothR–XandY,bothinsolution andinthesolidstate.
The chalcogen bond has a venerable history It appears to have been used forthe first time in 1998 in a theory paper by Minyaev and Minkin who predictedOchalcogenandNchalcogenbondsincomplexessuchasH2COSH2ofstrength comparable to that of a strong HB 117 Certainly by 2011 the term chalcogenbond was in commonusage An investigation of the Protein DataB a n k r e v e a l e d that SãããO interactions are common in proteins, and they can play important roles intheir functions, stability, and folding 118 For instance, SãããO and SeãããO interactionswere demonstrated that they stabilize the final molecular conformations of somethiazole and selenazole nucleosides possessing antitumor activity, and affect theirbiologicalactivityandtheirbindingto atargetenzyme 119
Following the IUPAC Recommendation 2019, 120 the definition of chalcogenbondiswrittenas:
Chalcogenbond (ChB) is the net attractive interaction betweenanelectrophilicregionassociatedwithachalcogen atominamolecularentity andanucleophilic regioninanother, orthesame,molecularentity.
Atypicalchalcogenbondisdenoted b ytheth ree dotsinR–ChãããA, whereCh is the ChB donor, being any chalcogen atom (possibly hypervalent) having anelectrophilic (electron-poor) region, R is the remainder of the molecular entity R–
ChcontainingtheChBdonor,andAistheChBacceptorandistypicallyamolecularentitypossessin gatleastonenucleophilic(electron-rich)region.Chalcogen atoms can concurrently form one or more than one chalcogen bond.Chalcogen atoms of a molecular entity give rise to a variety of interactions withdifferentelectronic andgeometric features Thetermchalcogenbondm ust notb e usedforinteractionswherethechalcogen(frequentlyoxygen)functionsasanucleophile.
Computationalmethods oftheresearch
To achieve the objectives along with research contents specified above, wearegoingtousethequantumchemicalmethodsavailableinthepackagesGAUSSIAN09,AIM2 000,NBO5.G,SAPT2012.2,Psi4,NCIplot…Suitable quantum-chemical methods including the molecular orbital theory (MO) and DFTmethods with high basis sets will be utilized, depending on investigated systems.Besides,thesoftwaresuchasMolden,Gaussview,OriginandExcelwillbeemployed to support for analysing calculated results Research methodology andtechniquesappropriate foreachissuearedescribedin moredetailasfollows:
Calculating for geometry optimization, energy and infrared spectra will becarry out by using the Gaussian 09 suite of programs Geometries and harmonicvibrational frequencies of the monomers and complexes are obtained by MP2 incombinationwithhighbasissets6-311++G(2d,2p).Harmonicvibrationalfrequencies are subsequently calculated to ensure that the optimized structures arelocal minima on the potential energy surfaces, to estimate zero-point energy and toidentify red-shift andb l u e - s h i f t o f t h e f o r m e d H B s T h e d e p t h o f t h e p o t e n t i a l energy for the small complexes and isolated monomers is further examined byperformingsinglepointcalculationsatCCSD(T)/6-311++G(2d,2p)forsmallcomplexes to obtain more accurate energy while MP2/aug-cc-pVTZ is used in casesoflargercomplexes.Indetail,
- SystemsusingMP2/aug-cc-pVTZforsingle-pointenergycalculations:
Complexes of CH3OCHX2withnCO2and/or nH2O(n=1-2)
The interaction energy of each complex investigated is determined by usingthesupramolecularapproachasthedifferenceintotalenergiesb e t w e e n t h e complex and the sum of energies of the relevant monomers at the selected suitablelevel of theory. The interaction energy is corrected by ZPE and BSSE, which iscomputedusingthefunctioncounterpoiseprocedureofBoysandBernardi 91
The AIM analyses at the MP2/6–311++G(2d,2p) level are applied to find thecritical points and to calculate electron densities and their Laplacians A topologicalanalysis of the electron density will be carried outusing the program packageAIM2000a n d Q T A I M 121 T h e e n e r g i e s o f e a c h h y d ro g e n b o n d w i l l b e e v a l u a t e d b y the empirical Espinosa-Molins-Lecomte formula 122 based on the electron densitydistributionattheBCPofthehydrogenbonds.
NBO analysis represents one of the most frequently used tools for analysingnoncovalent interactions The GenNBO 5.G program will be used to perform theNBO calculations, which is extensively applied to investigate chemical essences ofhydrogen bonds, and can provide information about natural hybrid orbitals, naturalbond orbitals, natural population, occupancies in NBOs, hyperconjugation energies,rehybridizationandrepolarization.Inthepresentstudy,NBOanalysisisalsoperformed at MP2/6-311++G(2d,2p) orB97XD/aug-cc-pVTZ to determine thechangesofelectrondensitiesinanti- bondingorbitals,toidentifydirectionsofelectrondensitytransferbetweenmonomers followingcomplexation.
Furthermore, the total stabilization energy of the complex is decomposed intothedifferentenergycomponentsincludingelectrostatic,induction,exchange-repulsion and dispersion energies The SAPT2+ approach with the consistent basisset is applied, which is calculated by the PSI4 packages Additionally, the molecularelectrostatic potential (MEP) 123 diagram of isolated monomers was evaluated atMP2/aug-cc-pVTZ To further identify the noncovalent behaviours, intermolecularinteractionswereassessedwithNCIplot athighleveloftheory 98,99
InteractionsofdimethylsulfoxidewithnCO 2a n d n H 2 O(n=1-2).46 1 Geometries, AIM analysis and stability of intermolecularcomplexes
The stable complexes of interactions of DMSO with nCO2and nH2O (n=1-2)molecules are shown in Fig 3.1 Intermolecular distances (Å) and intramolecularangles (degree) of the complexes derived from MP2/6-311++G(2d,2p) geometriesare also displayed in Fig 3.1, while selected parameters of BCPs corresponding tointermolecularinteractionsarecollectedinTablesA1a,A1bandA1cofAppendix.
Addition of either a CO2or a H2O molecule into binary complexes to formrelevantternarycomplexesleadstotheemergenceofO∙∙∙Oi n t e r a c t i o n o f CO 2 ∙∙∙CO2i nTC-DMSO-1andTC-DMSO-2, O−H∙∙∙O interaction of H2O∙∙∙H2O inTH-DMSO-1,TH-
DMSO-2andTH-DMSO-3, and O∙∙∙O interaction of CO2∙∙∙H2OinTCH-DMSO-2.
Besides,TH-DMSO-3possesses the O14−H15∙∙∙S9 interactionascomparedtotheS9∙∙∙O11interactioninDH-DMSO-
3.Remarkably,thecomplexesTH-DMSO-1,TH-DMSO-2,TH-DMSO-3andTH-DMSO-5of theDMSO∙∙∙2H 2 O system found in this work were not reported in previous study of thecooperativity between red-shift and blue-shift HBs in DMSO aqueous solution 125 All H∙∙∙O(S), S∙∙∙O, C∙∙∙O and O∙∙∙O contact distances are in the range of 1.81−2.84,3.21, 2.68−2.84 and 3.20−3.25 Å, respectively, which in general are close to thesums of van der Waals radii of relevant atoms This suggests the real existence ofthese intermolecular interactions., in which the existence of H6∙∙∙O12 contact inTC-DMSO-1( 2 8 4 Å ) ,H 2 ∙ ∙ ∙ O 1 5 i nTC-DMSO-2(2.76Å ) a n d O ∙ ∙ ∙ O i nTC-
DMSO-1, TC-DMSO-2andTCH-DMSO-1(3.20−3.25 Å) may result from anadditionalcooperativecontributionoftheremaininginteractions.
DC-DMSO-1 DC-DMSO-2,C s DC-DMSO-3 TC-DMSO-1
TC-DMSO-2 DH-DMSO-1 DH-DMSO-2 DH-DMSO-3
TH-DMSO-1 TH-DMSO-2 TH-DMSO-3 TH-DMSO-4,Cs
TH-DMSO-5 TCH-DMSO-1 TCH-DMSO-2 TCH-DMSO-3
Figure 3.1 Geometries of stable complexes formed by interactions of DMSO withCO2a n d H 2OatMP2/6-311++G(2d,2p) Furtherevidenceforformationofintermolecularinteractionsinthesecomplexescanbefou ndincomparingvariationsofanglesinCO2andH2Omolecules Following complexation, a decrease of 2−3° for∠OCO in CO2and anincreasein0.3−1.3°for∠HOHinH2Oareindeedobserved.Formationofintermolecular contacts is also confirmed by the presence of BCPs (red small ballssurroundedbybluecircle)showninFig.A1ofA p p e n d i x.TheC∙∙∙O distances of
2.77 Å inDC-DMSO-1and 2.69 Å inDC-DMSO-3are in line with those reportedbyT r u n ge t a l 22 u s i n g t h e s a m e t h e o r e t i c a l m e t h o d T h e H 1 2 ∙ ∙ ∙ O 1 0 d i s t a n c e s o f
1.87 Å inDH-DMSO-1, 1.82 Å inDH-DMSO-2and 1.88 Å inTH-DMSO-4arealso in good agreement with the work of Liet al.at the MP2/6-31++G(d,p) level(1.88, 1.83 and 1.87 Å respectively) 125 All values ofρ(r) and 2 ρ(r) at the BCPs ofH∙∙∙Ocontactslocatedrangefrom0.004to0.035au,and0.017to0.117au,respectively,exceptfor theBCPofH15∙∙∙O10contactinTH-DMSOwitharelatively high electron density of 0.038 au. They all fit within the criteria forformation of HB 126 As a result, H∙∙∙O(S) intermolecular contacts are considered asHBs The positive values of both 2 ρ(r) (0.017−0.048 au) andH(r)
(0.0007−0.0014au) for the C−H∙∙∙O HBs at these BCPs confirm that these HBs are weak interaction.On the contrary, the O−H∙∙∙O interactions are partly covalent in nature as indicatedby 2 ρ(r) > 0 andH(r) ≤ 0, except for the O−H∙∙∙O(S) HBs inTH-
DMSO-3andTH-DMSO-4withvaluesofH(r)>0(0−0.0008au).
The S(O)∙∙∙O and C∙∙∙O intermolecular contacts are named as ChB and TtB,respectively.AsshowninTableA1a-A1c,thepositivevaluesofboth 2 ρ(r)
(0.021−0.055au)andH(r)(0.0009−0.0014au)fortheS(O)∙∙∙OandS=O∙∙∙Cinteractions at theseBCPs suggest that theseintermolecularcontactsareweaknoncovalentinteractions.127,128,129
There is an increase in electron density at the BCPs of the interactions in theorder of O∙∙∙O < C−H∙∙∙O ≈ S∙∙∙O < S=O∙∙∙C < O−H∙∙∙O(S) (cf.Tables A1a- c).Accordingly,theS=O∙∙∙CTtBappearstoplay amoreimportantrolethantheC−H∙∙∙O HB and O∙∙∙O ChB in stabilizing DMSO∙∙∙1,2CO2, while complexes ofDMSO∙∙∙1,2H2O are mainly stabilized by O−H∙∙∙O(S) HBs along with an additionalrole of C−H∙∙∙O HB and S∙∙∙O ChB.
This observation will be confirmed by
NBOanalysesfollows.InthecaseofDMSO∙∙∙1CO2∙∙∙1H2O,themagnitudeo f interactions contributing to their stability increases in the ordering going from O∙∙∙OChB to C−H∙∙∙O HB to
S=O∙∙∙C TtB and finally to O−H∙∙∙O HB In an attempt tofigureo u t a r e l a t i o n s h i p b e t w e e n H B e n e r g i e s (E HB )a n d t h e i r e l e c t r o n d e n s i t i e s
−H∙∙∙O,agoodlinearcorrelationofE HBa n d ρ(r)issubsequentlyfound(Fig.3.2)asexpressedinthef ollowingequation:
Figure3.2.Alinear correlationbetweenindividualE HB andρ(r)valuesatBCPs
For the binary system DMSO∙∙∙1CO2,DC-DMSO-2with formation of twoC−H∙∙∙O HBs and one S=O∙∙∙CT t B i s c o m p a r e d t o t h e e x i s t e n c e o f o n e
C − H ∙ ∙ ∙ O HB and one S=O∙∙∙C TtB inDC-DMSO-1,and only one S=O∙∙∙C TtB inDC-
DMSO-3 Theρ(r) values at BCPs of these contacts are approximate in magnitude(0.006 au for the C−H∙∙∙O HBs and 0.012−0.014 au for the S=O∙∙∙C TtBs), implyingthat it is possible to evaluate stabilization effect of these three complexes just bycomparing the number of relevant interactions Accordingly, we can predict that thestability of these complexes increases in going fromDC-DMSO-3toDC-DMSO-1toDC-
DMSO-2 In the caseofDMSO∙∙∙2CO2,TC-DMSO-2i s e x p e c t e d t o b emore stable thanTC-DMSO-1as theE HBvalues of three C−H∙∙∙O HBs in TC-DMSO-2(from -4.5 to -5.9 kJ.mol -1 ) are more negative than that of one C−H∙∙∙OHB inTC-DMSO-1(-3.5 kJ.mol -1 ) (cf Table A1a) A decrease of electron densityat BCPs andE HB negative value of C(O)−H∙∙∙O HBs in the ordering ofDH-DMSO-2toDH-DMSO-1toDH-DMSO-
3forDMSO∙∙∙1H2O(cf.TableA1b)impliesthat thestabilityofthecomplexestendstodecreasealongthistrend.
Ternary complexesTH-DMSO-1,TH-DMSO-2,TH-DMSO-4andTH-
DMSO-5with a presence of two O−H∙∙∙O HBs are likely to be more stable thanTH- DMSO-3, where only one O−H∙∙∙O HB is involved There is an increase inelectron density at BCPs and the strength of O−H∙∙∙O HBs in the ordering ofTH-DMSO- 4Zww-4(Z=O,S) TheOww-
1with Eintof -8.6 kcal.mol-1has beenreported for the first time to be the most stable structure of aco∙∙∙2H2O instead ofOww-2intheLiao’swork 138 FromZw-1toZww-
1,thebindingenergyisremarkably increased by 4.9 kcal.mol -1 forZ=Oand 4.1 kcal.mol -
1forZ=S Foracz∙∙∙CO 2 ∙∙∙H2O system, the more negative Einto f 1 k c a l m o l-1indicates thatZcw-1is more stable thanZcw-2 The obtained results show that all energetically preferredcomplexes belong to the cyclic geometries in which sub-molecules interact mutual.This gives evidence that cyclic structures reinforce the stability upon complexation.Itisexpectedanexistenceofpositivecooperativitybetweenintermolecularinteract ionsinaco/ acsternarycomplexes.Similarto1,2CO2systems,theaco∙∙∙1,2H2Oa n d a c o ∙ ∙ ∙ 1 C O2∙∙∙1H2Oc o m p l e x e s a r e a l s o f o u n d t o b e m o r e s t a b l e than the corresponding derivatives of acs This observation is clarified on the basisofobtainedresultsfromAIManalysis.TheE HBvalues ofOH∙∙∙OHBsaresignificantlymorenegat ivethanthoseofOH∙∙∙Sones,implyinga s t r o n g e r strengthoftheformercomparedtothelaterHBs.TheelectrondensitiesatBCPsof these interactions also have the same trend, indicating a good linear correlation ofE HB andρ(r) in aco and acs complexes (cf.Fig A5) Moreover, individual energiesofOH∙∙∙O/S
There is a great similarity in energetic behaviour of aco and acs complexeswhen both of them interact with CO2and/or H2O guest molecules The stability ofaco complexes is typically larger than that of acs ones by 0.5-2.0 kcal.mol -1 ThisimpliesthattheinteractionsofacowithCO 2and/or H2Oaremorethermodynamicallyfa v o ra b l e t h a n t h o s e o f a c s i n g a s p h a s e A n a d d i t i o n o f o n e H 2 O molecule into aco/acs∙∙∙CO2/H2O binary complexes leads to an enhancement ofbinding energy by 3.7-4.9 kcal.mol -
1while a less binding energy increase of 1.9-2.7kcal.mol-1is estimated in adding of one
CO2molecule into these binary complexes.As a result, the addition of H2O is favored than that of CO2in stabilizing studiedcomplexes.
Interactionsofmethanolwith CO 2a n d H 2 O
Stable structures formed by interactions of CH3OH with CO2and H2O, andselected geometric parameters are presented in Fig 3.6, denoted byDX-Met-nandTCH-Met-n, whereD,Trepresent dimers and trimers, respectively;X = C,H(Cfor CO 2 , H for
H2O);n=1,2,3, … are ordinal numbers of isomers The selectedcharacteristicsatBCPs of intermolecularinteractionsarealsolistedinTable3.7.
DC-Met-1 DH-Met-1 DC-Met-2 DH-Met-2
TCH-Met-1 TCH-Met-2 TCH-Met-3
Figure3.6 Stablegeometries ofcomplexes formed byinteractionofCH3OHwith CO2and
H2OatMP2/6-311++G(2d,2p)(allintermoleculardistancesinÅ) Data in the Fig 3.6 show that the intermolecular distances between O and C,O and H are in the ranges of 2.71-2.93 Å and 1.91-2.81 Å, respectively; and most ofthem are smaller thanthe sum ofvan derWaals radii oft h e t w o r e l e v a n t a t o m s (3.22 Å for O∙∙∙C contact and 2.72 Å for O∙∙∙H one) This result supports for thepresenceofO∙∙∙C=OTtBsandO−H∙∙∙Ohydrogenonesuponcomplexation.Incontrast,the C 1− H 2∙ ∙ ∙ O8 distances i nD C - M e t - 1 a n d TCH- Met- 3 ar el ar ger t h a n the sums of van der Waals radii of the two isolated atoms The existence of theseC−H∙∙∙O HBs, however, would be proved from AIM and NBO analyses In fourstablestructuresofbinary complexes,CO2orH2Oguestmoleculearel o c a t e d around the -OH group of CH3OH host molecule WhileDC-Met-1is stabilized byO∙∙∙C=O TtB and C−H∙∙∙O HB,DH-Met-1is obtained by the formation of O−H∙∙∙OHB BothDC-Met-2andDH-Met-2complexes are strengthened by O−H∙∙∙O HBsinvolving-
OHgroupofmethanolandOatomofCO2orH2Omolecule.Theobtainedg e o m e t r i c a l p a r a m e t e rs a r e i n g o o d a g r e e m e n t w i t h t h e p r e v i o u s s t u d i e s forCH 3 OH∙∙∙CO2andCH3OH∙∙∙H2Ohet erodimers.40,140,141Theintermolecularinteractionsi n t h r e e s t a b l e s t r u c t u r e s o f t h e C
H3OH∙∙∙CO2∙∙∙H2Os y s t e m a r e mutuallyassociatedwhichisdescribedbythepresenceofringcriticalpointsfromAIMtop ologies Also, an O∙∙∙OChBisfoundinTCH-Met-3geometry.
Table3.7.SelectedparametersattheBCPsofintermolecularcontactsinco mplexesofmethanolwithCO2and/orH2OatMP2/6-311++G(2d,2p)
From Table 3.7, all the values ofρ(r) and 2 ρ(r) at BCPs of interactions arein the ranges of 0.006-0.029 au and 0.022-0.096 au, respectively; and most of H(r)values at BCPs are positive (0.0005-0.0019 au) These results indicate that most ofthem are noncovalent weak interactions 132 It is interesting that the O−H∙∙∙O HB inTCH-Met-1(with the highest values ofρ(r) andE HB ) behaves a slightly negativetotalelectronenergydensityimplyingasmallcovalentpartinnature.Fromoptimized structures in Fig 3.6, it is distinguished three types of O−H∙∙∙O HBs:O−H∙∙∙O m , O−H∙∙∙Owand O−H∙∙∙Ocin which Om, Owand Ocare denoted for oxygenatomofCH3OH,H2OandCO2,respectively.Basedonρ(r)andE HBn e g a t i v e values, it is predicted that the stability of these interactions decreases in order ofO−H∙∙∙O m > O−H∙∙∙Ow> O−H∙∙∙Oc, which is in good agreement with Filetiet al.140Indeed,t h eρ(r)a t B C P a n dE HBv a l u e s o f O − H ∙ ∙ ∙ Oma r ei n t h e r a n g e s o f 0 0 2 6 -
0.029 au and 28.0-31.9 kJ.mol -1 , respectively;w h i c h a r e s l i g h t l y h i g h e r t h a n t h o s e ofO − H ∙ ∙ ∙ Ow( 0 0 2 3 - 0 0 2 4 a u , 2 4 3 - 2 6 3 k J m o l -1)a n d c o n s i d e r a b l y h i g h e r t h a n
O−H∙∙∙Oc(0.012-0.013 au, 11.5-12.3 kJ.mol-1) It is also provedviadistances ofintermolecular contacts, while the lengths of H∙∙∙Omcontact range from 1.89 to 1.91Å,thedistancesofH∙∙∙Ow/
Ocarehigherandintherangeof1 9 5 - 2 2 3 Å Considered to the remaining interactions, theρ(r) values of 0.008-0.013 au forO m /Oc∙∙∙C=O TtBs are smaller than those for C−H∙∙∙O HBs (0.004-0.006 au) andO∙∙∙O ChBs (0.007 au) In short, the strength of intermolecular interactions in theexamined complexes are predicted to decrease in order of O−H∙∙∙O m > O−H∙∙∙Ow>O−H∙∙∙Oc>Om/Oc∙∙∙C=O>O∙∙∙O≈C−H∙∙∙O.
Basedonobtainedstrengthsofintermolecularinteractionsabove,t h e stabilityofbinaryan dternarycomplexescouldberevealed.Particularly,thestability of CH3OH∙∙∙CO2and
CH3OH∙∙∙H2O could be sorted increasingly asDC-Met-2