DAMQT 3: Advanced suite for the analysis of molecular density and related properties in large systems

Contents lists available atScienceDirect

Computer Physics Communications

www.elsevier.com/locate/cpc

DAMQT 3: Advanced suite for the analysis of molecular density and related properties in large systems ^{✩ , ✩✩}

Anmol Kumar

^a

, Rafael López

^b,∗

, Frank Martínez

^b

, Guillermo Ramírez

^b

, Ignacio Ema

^b

, David Zorrilla

^c

, Sachin D. Yeole

^d

, Shridhar R. Gadre

^e

aSchoolofPharmacy,UniversityofMaryland,Baltimore21201,MD,USA

bUniversidadAutónomadeMadrid,FacultaddeCiencias,DepartamentodeQuímicaFísicaAplicada,Módulo14,Spain cUniversidaddeCádiz,FacultaddeCiencias,DepartamentodeQuímicaFísica,Spain

dDepartmentofChemistry,BhusawalArtsScienceandP.O.NahataCommerceCollege,Bhusawal425201,India eInterdisciplinarySchoolofScientificComputing,SavitribaiPhulePuneUniversity,Pune411007,India

a rt i c l e i n f o a b s t r a c t

Articlehistory:

Received25March2022

Receivedinrevisedform21June2022 Accepted27June2022

Availableonline8July2022

Keywords:

Electrondensity Electrostaticpotential Moleculardensitytopology Sigma-hole

ElectrostaticsforIntermolecular Complexation

Hellmann-Feynmanforces

AnewversionoftheDAMQTpackagespeciallydevelopedforlargesystemsisreported.Thegraphicalpart hasbeenentirelyredesigned,usingnewOpenGLlibraries(versions3.3orhigher)for3Ddisplay.Several 2Dplottersand3Dviewerscanbelaunchednowinthesamesessionandmorethanonemoleculecan beloadedinthesame3Dwindow.Algorithmshavebeenrescaledandmodifiedtoworkwithdensities comingfrom ZDOcomputationsin verybig molecularsystems(upto thousandsof atoms)at avery moderate cost.Newfunctionalities have been addedincludingcomputation ofmolecular electrostatic potential over a molecular surface determined as a user-defined density isosurface. The method of ElectrostaticsforIntermolecularComplexationhasbeenaddedto thepackagetoserveas anauxiliary toolforclustergeometryoptimization.Examplesareprovidedwhichprovethegoodperformanceofthe algorithms.

Programsummary ProgramTitle: DAMQT_3

CPCLibrarylinktoprogramfiles: https://doi.org/10.17632/2rxvgbsnhx.2 Licensingprovisions: GPLv3

Programminglanguage: Fortran90,C++andPython

Supplementarymaterial: Quick-startguideand User’s manualin PDF formatincluded inthe package.

User’smanualisalsoaccessiblefromtheGUI.

Externalroutines/libraries: Qt(5.10orhigher),OpenGL(3.3orhigher),ffmpeg(3.4orhigher),OpenBabel (2.3orhigher,optional)

Natureofproblem: Analysis andvisualization ofthemolecular electrondensity,electrostaticpotential, critical points, gradient paths, atomic basins, electric field and Hellmann-Feynman forces on nuclei, clustersoptimizationwithEPIC.

Solutionmethod: Molecularelectrondensityispartitionedinto(pseudo)atomicfragmentsbymeansof the method of DeformedAtoms in Molecules [1]. Electron densities of the fragments are expanded as a series of spherical harmonics times radial factors. The partition is used for defining molecular densitydeformationsandforthefastcalculationofseveralpropertiesassociatedwithdensity,including electrostaticpotential,electricfieldandHellmann-Feynmanforcesovernuclei.Explorationofdensityand potentialtopologyisfacilitated,andthecomputationofelectrostaticpotentialoveranisodensitysurface isimplemented.ClusteroptimizationfacilitywithEPICisalsoimplemented.

Additionalcommentsincludingrestrictionsandunusualfeatures: DensitymatrixmustcomefromanLCAO calculation(anycomputationallevel)withspherical(notCartesian)SlaterorGaussianfunctions.

✩ ThereviewofthispaperwasarrangedbyProf.N.S.Scott.

✩✩ ThispaperanditsassociatedcomputerprogramareavailableviatheComputerPhysicsCommunicationshomepageonScienceDirect(http://www.sciencedirect.com/ science/journal/00104655).

*

Correspondingauthor.

E-mailaddresses:[email protected](A. Kumar),[email protected](R. López),[email protected](F. Martínez),[email protected] (G. Ramírez),[email protected](I. Ema),[email protected](D. Zorrilla),[email protected](S.D. Yeole),[email protected](S.R. Gadre).

https://doi.org/10.1016/j.cpc.2022.108460

0010-4655/©^{2022TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense} (http://creativecommons.org/licenses/by-nc-nd/4.0/).

TheprogramcontainsanOPENstatementtobinaryfiles(stream)inseveralfiles.Thisstatementdoesnot haveastandardsyntaxinFortran90.Twopossibilitiesareconsideredinconditionalcompilation:Intel’s ifortandFortran2003standard.Thislatterisappliedtocompilersotherthanifort(gfortranusesthisone, forinstance).

References

[1] J.FernándezRico,R.López,I.Ema,G.Ramírez,J.Mol.Struct.,Theochem727(2005)115.

©^{2022TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-ND} license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

The reported suite is a thoroughly renewed version of the DAMQTpackage,aimed asausefultoolfortheanalysisofmolec- ular electron density (MED) and related properties. The package is based on the partition of MED into pseudo-atomic fragments following the prescription of the Deformed Atoms in Molecules (DAM)method [1,2].

The partitionofMED isfollowedby an expansionofthefrag- ments’densitiesasaseriesofradialfactorstimesregularspherical harmonics. Radial factors are numerically computed and piece- wisefittedtosuitableauxiliaryfunctions.Theexpansionsfacilitate the very efficient computation of MED itself, aswell asthe cal- culation of related properties like MED deformations, molecular electrostaticpotential (MESP),electricfield,MED andMESPgradi- ents andhessians,criticalpoints, basinsandbonding paths,Hell- mann-Feynmanforcesonnuclei,andMESPsigma-holes [3].Cluster optimization with Electrostatics for Intermolecular Complexation (EPIC)benefitsalsofromtheefficientcomputationofMESP.

The partition of density accomplished with DAM method re- tains the image of atoms in molecules as point nuclei sur- rounded by almost spherical clouds, slightly distorted by the molecular environment, and is an alternative to other partition- ingschemes [4–16].

ElectrondensitycomputedwithintheLCAO(linearcombination ofatomicorbitals)framework, canbe expressedintermsofden- sitieswhichareproductsofthefunctionsofthebasissetusedin thecalculation,{

χ

i}^m_i=1^:

ρ (

r

) =



m

j=1



m

k=¹

ρ

_jk

χ

j

(

r

) χ

_k

(

r

)

(1)

wherem standsforthenumberofbasisfunctions,and

ρ

jkarethe elementsofthedensitymatrixinthebasisset.

Inthisworkwewillconsiderbasisfunctionsconsistingofprod- uctsofradialfunctions, R(^rA),eitherofGaussian orSlatertypes, timesunnormalizedrealsphericalharmonics,z^m_l (θA,φA):

χ

_a^A_,l,m

(

r_A

) =

R

(

r_A

)

z^m_l

(θ

A

, φ

A

)

(2)

The subindex a labels the functions at center A and r_A ≡ (x_A,y_A,z_A)= (^rA,θA,φA) are thecoordinates ofapoint ofspace with respect to that center, i.e. rA≡^r−^RA= (^x−^XA,y−^YA, z−^ZA),r isthepositionofagenericpointinthemolecularframe, andRA thatofcenterA alsointhatframe.

The(unnormalized)realsphericalharmonicsaredefinedas:

z^m_l

(θ, φ) = (−

¹

)

^mP_l^|m|

(

cos

θ )



cos m

φ (

m

≥

⁰

)

sin

|

^m

|φ (

^m

<

0

)

⁽³⁾

P^|_l^m|(z) being the associated Legendre functions (see [17] eq.

8.751.1).

Thus,eq. (1) canbewrittenas:

ρ (

r

) =



N

A=¹ mA



a=¹ mA



a^=1

ρ

aa^

χ

a

(

rA

) χ

a^

(

rA

)

+



N

A=¹



N

B=¹ B=^A

mA



a=¹ mB



b=1

ρ

ab

χ

a

(

rA

) χ

b

(

rB

)

(4)

where N isthenumberofnuclei, andm_I isthe numberofbasis functionsofatom I(=^A,B).

DAMpartitionassignstoeachatom A alltheone-centercharge distributions

χ

a(rA)

χ

a^(rA) centered at its nucleus, and part of eachtwo-centerdistribution

χ

a(r_A)

χ

b(r_B)involvingitsbasisfunc- tions.

Two-centerdistributions:

χ

_a^A

(

rA

) χ

_b^B

(

rB

) =

d_ab^A

(

rA

) +

d_ab^B

(

rB

)

(5) arepartitionedfollowingacriterionbasedonthefastconvergence ofthelong-rangeexpansionofthepotentialgeneratedbythefrag- mentsd_ab^A,d_ab^B towardsthatofthefulldistribution

χ

_a^A

χ

_b^B [18,19].

Sincethetheoreticalfoundationofthemethodisessentiallythe sameasthatreportedinthepreviousversionsofthepackage [20, 21],herewewilljustoutlinethemathematicalaspects.Detailsof the mathematical developmentsand technicalaspects havebeen thoroughlycollectedinref [22],andcanbeconsultedtherein.

DAMpartitionallowsustowritethemolecularelectrondensity asasumofpseudo-atomiccontributions:

ρ (

r

) = 

A

ρ

^A

(

r_A

)

(6)

withtheatomicfragments,

ρ

^A,givenby:

ρ

^A

(

r_A

) = 

a



a^

ρ

aa^

χ

a

(

r_A

) χ

a^

(

r_A

) +

²



B=^A



a



b

ρ

abd_ab^A

(

r_A

)

(7)

These fragments are further expanded in spherical harmonics timesradialfactors:

ρ

^A

(

rA

) =



∞ l=⁰



l

m=−^l

z^m_l

(

rA

) ρ

_lm^A

(

rA

)

(8)

z^m_l (r) beingthe unnormalized sphericalharmonics of theregular solid:

z^m_l

(

r

) =

^rlzm_l

(θ, φ)

(9)

The infinitesum on l willbe actually truncatedto a suitable order,lmax,whatimpliesanapproximationtotheexactvalue.

The radial factors,

ρ

_lm^A(r), are piecewise fitted to products of exponentialstimesChebyshevT polynomials(see[17] sec.8.94):

ρ

_lm^A

(

r_A

) ≈

^e−ξirA

n_i



k=⁰

c⁽_kⁱ⁾

(

l

,

m

)

T_k

(

t

)

(10)

inasetofintervals,λi−1≤^rA≤ λi;i=¹,...n,ofthevariablet:

t

≡

^2rA

− λ

i−1

λ

_i

− λ

i−1

−

^{1 (11)}

Asithasbeenshownpreviously,theefficientcomputationofMED andMESP,andtheirderivativesaswell,isnoticeablyfacilitatedby DAMpartition/expansionscheme [23,22].

2. MESPsigmaholeonaMEDisosurface

Afeature addedtothisnewreleaseofDAMQT isthe efficient computationofMESPonaMEDisosurface,usuallytakenasanap- proximationtothelooseconceptofmolecularsurface.Theanalysis of this property [24] has revealed a fertile field in the theoreti- cal interpretation of intermolecularbonding [25–29] and reactiv- ity [30],eitherintermsofsigma andpi holesintroducedbyClark et al. [31–33],orbeyondasclaimedbyZhanget al. [34].

Furthermore, statistics derived from MESP on the (pseudo) molecular surface have provedto be a very valuabletool for the investigationoftherelationshipsbetweenmolecularstructureand physicochemicalproperties [35–39] andsuccessfulcorrelationsbe- tweenthesepropertiesandstatisticalparametershavebeenfound fordifferentfamiliesofcompounds [40,41].Thenewversionofthe packagealsoimplementsthecomputationofthesestatistics.

Histograms of MESP on the surface are computed, providing a means to characterize molecular behavior in a similar way as COSMO-RS sigma profile does [42] and, likewise, properties as molecular polar character or hydrogen bonding behavior can be inferredalsofromthesehistograms.Furthermore,contributionsto extremavaluesofMESPonsurfacearesplittedwhencomingfrom differentmolecular regions, todistinguishthose casesinwhich a singleregionofthemoleculeisresponsibleforthehydrogenbond donor(oracceptor)character,fromthoseinwhichseveralregions contributetoit.

Thesehistogramsareexpectedtobeusefulasapossibleaidin pre-screeningorscreeningprocessesinmolecularengineeringand drugdesign [43,44],analternativecomplementarytootherMESP- based techniquesfor theanalysisof molecular similarity [45–47]

andmolecularrecognition [48].

Spectrographs of MESP values in MED isosurface can be dis- played in the 3D viewer, together with their local 2D critical points.MESPhistogramscanbedisplayedinthenew2Dplotter.

3. EPICforclusterbuilding

The most valuable novelty in the package regarding appli- cations is the facility for cluster optimization. This release of DAMQTimplementsElectrostaticsforIntermolecularComplexation (EPIC) [49–53] model for rapid geometry optimization of non- covalentlyinteractinglargemolecular systems.Quantumchemical optimizationoflargemolecularsystemssuchasmolecularclusters andweaklyinteractingmolecularcomplexes,becomesincreasingly time consuming because of the high scaling of the methods in- volved,poorconvergenceandlargenumberofcloselyspacedlocal minimaintheirpotentialenergysurface.EPICmodelallowsrapid geometryoptimizationofweakly interactingsystemsby minimiz- ing thepotentialenergyofguestsysteminthepresenceofMESP of the host system. The methodology employed in the original EPIC model [49,53] required MESP of the host systemon a grid alongwithMESPcriticalpoints (CPs).TheMESPCPswereusedas a guide for optimalplacement of the guest system. For building energeticallyfavorablestructures,thepositivelychargedatom/sof the guestsystemwas/wereplaced nearthedeep negative-valued

minimai.e.(3,+^{3) CPintheMESP ofthehostsystem. Theopti-} mizationroutinerotatedandtranslatedthemoleculeinallpossible directionsto findthe orientation of thecomplex withmaximum electrostaticinteraction.Intersectionofvander Waals(vdW)sur- faces of the monomeric units was avoided during optimization.

Thismodel has beensuccessfully usedfor buildingand optimiz- ing DNAbase-pairsand trimers [51,52], understanding molecular hydrationprocess [54],hydration ofDNAbase-pairs [55],andop- timizingnon-covalentlybondedmolecularclusterssuchas(ZnS)_n, (C6H6)n, (H2O)n [56], and (Ag)_n [57] clusters. Despite successful applicationofthis EPIC model,the actual work-flow was a com- binationofdiscretecalculationsandinvolveduseofatleastthree differentsoftwaresi.e. aQMengine,EPICoptimizerandamolecu- larvisualizerwithmoleculareditingcapabilities.

ThecurrentfeaturesofDAMQT provideahotbedforcomplete integrationofEPIC modelwithenhanced efficiency, usability and broaderapplicability. The 3D viewer nowallows usplacementof guestsystem nearthe host in presence orabsence of MESP CPs of the latter. Geometric parameters (distances, angles and dihe- drals) can be displayed on the canvas to assist the build up of thestartingstructure.ThenewEPICmoduleintegratedhereinalso allowsautomated placement ofguestsystemby utilizingits par- tialchargedistributionandthetopologicalinformationofthehost system. The ease of buildinggood initial molecular arrangement reduces the manual effort and accelerates the optimization pro- cess. To further simplify the functioning of EPIC optimizer, use ofMESP-derived point chargesof guestsystemis madeoptional.

User-defined charges can be supplied in a file containing atoms names in one column and corresponding partial charges in the following column. In the case of building a homo-dimer, partial chargesoftheguestmoleculecanalsobeobtainedfrom.mltmod filecontaining the moduliof theatomicmultipolemoments (see UserandQuickStartGuideformoredetails)ofhostmolecule,gen- eratedbyDAMSTO/DAMGTOprograms(invokedunderAtomicden- sitiestabinDAMQT-GUI).Asanauxiliaryprotocol,theEPICroutine utilizes various charge models available in OpenBabel [58,59] to obtain partial charges [60] on the guest molecule, which can be used forEPIC optimization. Thisprotocol avoids therequirement ofanyQM-calculation forcharge estimation.However, for higher accuracyofoptimizationprocedures,ESPderived chargesare bet- tersuited [56].InteractionenergyinEPICisgivenby

EE P I C

= 

i

VA,i

,

qB,i (12)

wherein,V_A,i istheMESPvalueofhostmoleculeatthei^th atomic position ofthe guest molecule, andq_B,i is the partial charge on i^th atom of the pertaining guest molecule. Ability of DAMQT to provideMESPvalueandrelatedgradientsatanygivenpointelim- inatestheneedofpre-calculatedMESPgriddata,thusmakingthe algorithmconsiderablyfaster.RapidmappingofMESPanditscrit- ical points along with parallel computing capabilities of DAMQT removesall hurdles inthe usability of EPIC optimizerand facili- tatesitsapplicationtolargeandrelevantsystems.

EPICoptimizationstartswithrotationofguestgeometrytofind itsmostenergeticallyfavorable orientation inthe electricfieldof hostmolecule.Thisisfollowedbysingletranslationstepinthedi- rectionofnetelectrostaticforceactingontheguestmolecule.The step-sizeusedfortranslationisscaledby thenormalizedcompo- nentofthenetforce-vector.Aftereachtranslationstep,arotation step is performed to obtain optimal orientation at the updated position. Consequently, EPIC optimization ends with the rotation step.Ifmorethanoneguestgeometryneeds tobe optimized,the subsequentgeometriesareoptimizedinthepresenceofbothQM- derived ESPofhostmolecule andpoint-charge-derivedESP ofall

Fig. 1. ComparisonbetweenEPICoptimizedgeometriesandQMoptimizedgeometries(denotedbyCatomsinblueandgreen,respectively)forfivedimers(a)H2O-dimer,(b) CO2-dimer,(c)C2H2-dimer,(d)C2H4-C2H2,(e)C6H6-dimer.RMSDscoresobtainedbetweenthetwogeometriesarealsoshown.Seetextformoredetails.(Forinterpretation ofthecolorsinthefigure(s),thereaderisreferredtothewebversionofthisarticle.)

the previously added guest molecules. During each optimization step,scaled vdWradii oftheatoms(defaultscaling factor= ^0.7) areusedtocheckifmolecularvdWsurfacesareintersectingeach other.The final geometryobtainedafter eachrotation ortransla- tion step issaved ina trajectory file. After optimization ofguest geometry,the trajectoryfile canbe usedto developanimation of EPIC optimization process. The animation builderutilizes quater- nion interpolation tocreate smoothertransitionbetween thege- ometries saved in the trajectory file. The animation can also be recorded andplayed back on the canvas, asshownin the movie included inthesupplementary material.Ifthe endgoalis toob- tainQMoptimizedgeometryofthecomplex,DAMQTnowprovides a QM input writer for various different QM packages (Gaussian, Gamess, Molpro, Mopac, Nwchem,Psi4) which automatically uti- lizescoordinatesofEPICoptimizedgeometryasstarting pointfor QMoptimization.IftheabovementionedQMenginesareinstalled on the same machine which is used to launch DAMQT session, the QM calculation can be directly executed from DAMQT-GUI.

This feature greatly reduces the time consumed in building and growing energetically favorable molecular clusters. Furthermore, DAMQT also preparesthe job submission scripts forsome of the popular job schedulersviz. SLURM, PBEandSGE tofacilitate the QMcalculationonavailableHPCfacility.

It must be recalled that, ifthe output of the QM calculation is to be used for the density analysis with DAMQT, the calcula- tionmustbedoneusingbasisfunctionswithsphericalharmonics (notCartesian).Thisistakenintoaccountintheinputfilesgener- ated withthe templatesby includingthepertaining optionwhen required.

We demonstratethe useofEPICmoduleintegratedinDAMQT 3forbuildingfewmoleculardimersastest-case.QMoptimization ofthehostmolecule was performedatMP2/aug-cc-pvDZ levelof theory in Gaussian09 program. The atomic expansion of density withmultipolarexpansion(l=^{15)wasderivedfromtheformatted} checkpointfileandwassavedintodamqt anddmqtv files.Theop- timizedcoordinatesofthehostmoleculewasprojectedonthe3D viewer canvasalongwithcoordinatesoftheguestmolecule using

“Addmolecule”button.Theguestmoleculewas thenshiftednear the host systemusing mouse clicksand keyboard shortcuts (see User and Quick Start Guide for more details). EPIC optimization wasinitiatedusing“Optimizecluster”buttonwhichconsidersfirst molecule withassociateddamqt fileasthehostandthefollowing molecules as guests. User can change this default consideration.

AfterEPICoptimization,“QuantumMechanics”buttonwasusedto generateGaussian09inputfilesforQMoptimizationofclusterge- ometries atMP2/aug-cc-pvDZ levelof theory andbasis-set, with the5D,7Foptionforsphericalbasisset.Ultimately,QMoptimized geometrieswere comparedtotheEPIC optimizedgeometries.The reliabilityofEPICmethodisexemplifiedbysmallrootmeansquare

deviation(RMSD) betweenCartesian coordinatesofEPIC andQM optimized geometries (see Fig. 1) for different types of molecu- larsystems.RMSDiscalculatedasthesquarerootofthemeanof thesquare ofthe distances betweenthe atomswith same index inthetwosuppliedstructures.Waterdimershowssmallestdiffer- encebetweenEPIC andQMoptimizedgeometry(RMSD=⁰.178).

Obtainingcorrectorientationandintermoleculardistanceofwater dimerisofspecialsignificancebecauseofthetetrahedraldistribu- tionofelectronicchargearoundwatermolecule.CO2-dimer,C2H2- dimerandC₆H₆-dimeralsoshowhighresemblancebetweenEPIC andQMoptimizedgeometries.Themolecularinteractionbetween C2H4 and C2H2 hetero-dimer is also well-represented. The close resemblance of EPIC optimized geometry with their QM analogs emphasizestheuseofEPIC modelforreliablygeneratingmolecu- larclustersoflargersize.

4. Changesin2Dplotterand3Dviewer

Improvementsin DAMQT 3 also includethe entirelynew im- plementationsof2Dplotter and3D viewerin theGraphicalUser Interface(GUI) –seeFig.2.Now,several2Dplotsand3Ddisplays canbe opened ina session.They aredeployed outside theGUI’s mainwindow,andeach2Dplotteror3Ddisplayhasitsownmenu attachedtotheviewer.Thesemenuscanbeundockedtoincrease thewidthofthecanvas.

Manynewfunctionalitieshavebeenaddedinbothcases.Thus, 2Dplotter allowsusto loadanddisplaydifferenttypesoffigures together(i.e.isosurfaces,fieldlinesandcriticalpoints),andanew type of plot forhistograms of MESP on a densityisosurface has beenincluded.

Incaseof3D viewer,changes areeven moresignificant. Now, morethan one molecule can be loaded in the samecanvas, and functionalitiesareimplementedtohandlesinglemoleculesaswell as the set of loaded molecules as a whole. Geometry parame- ters(distances, angles anddihedrals) can be now computedand displayed bothforsingle molecules andbetweenmolecules. EPIC clusteroptimizationcanbe launchedfromtheviewer andthere- sultscanbevisualized andanimatedonthecanvas.Spectrograms ofMESP over an isodensity surface can be visualized, aswell as theirlocal2Dcriticalpoints.

3D viewer has been implemented using the new OpenGL li- braries (versions 3.3 orabove) to take full advantage of modern GPUscapabilities. Thismeansthat,to visualizethe3D structures, boththesystemhardware,librariesanddriversmustconformthis requirement. The lackof a suitable version of anyofthese com- ponentsmaylead toan errorin execution,orjust causethatthe objectswillnotbevisible.When thishappens,itisconvenientto look at the standard output where a message with the OpenGL versionactuallytakenisdisplayed.

Fig. 2. Graphical User interface, 2D plotters and 3D viewers of DAMQT 3.

Fig. 3. Structure of DAMQT 3.

Thenumberof2Dplottersand3Dviewersthatcanbelaunched inonesessionislimitedonlybythesystemresources.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompetingfinan- cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Dataavailability

Nodatawasusedfortheresearchdescribedinthearticle.

Appendix A. Newstructureofthepackage

DAMQT3hasthemodularstructureshowninFig.3.Thestart- ingpointisamolecularcalculationwithastandardpackageatany levelofcalculation (HF, DFT, CI,CAS,MRDCI, ...)within theLCAO framework.

Severalinterfaces are included in the package to read output filesofsome popularsuitesformolecular calculationsandcreate suitableinputfilesforDAMQT.Forprogramslackingofsuitablein- terfaces,instructionsaregiveninthemanualtocreatethesefiles.

Thegeometryandbasissetfiletogetherwiththemolecularor- bitalsfilearesufficienttocomputethevaluesofmolecularorbitals

overa2Dor3DgridbymeansofDAMORB320program(oritsmpi versionDAMORB_mpi320).

To perform DAM analysis ofthe molecular density, it is nec- essary to carry out the partition by running the DAMSTO320 module, in case of Slater functions, or DAMGTO320, for Gaus- sians (DAMSTO320_mpi and DAMGTO320_mpi with mpi). These modulesalsorenderchargesandmultipolesassociatedtopseudo- atomicfragments.

Oncethe partition isdone, differentmodules can beaccessed tocompute MED,MED deformations [61],MESPandelectricfield (MEF), Hellmann-Feynman forces,radial factors of fragments ex- pansion and locally oriented multipoles. Topology of MED and MESPcanbestudiedbycomputingCPs,gradientpathsandatomic basins. 2D and3D grids canbe generatedforalltheseproperties andvisualizedwiththebuilt-inviewers.Toaccomplishthesetasks, thefollowingprocedureshavebeenimplementedinthepackage:

•^DAMDEN320:computationofthedensityanddensitydeforma- tionsforthewholemolecule,atomicfragmentsandfunctional groups.2Dand3Dgridscanbegeneratedforplottingandvi- sualizationwithDAMQT3built-inviewers.Gradient,laplacian andsecondderivativescanbealso(optionally)computed.

•DAMDENGRAD320:computationofMEDgradientlines.

•DAMISODEN320: computation of MED isosurfaces and their normals.

•^DAMPOT320: computation of the electrostatic potential in- cluding 2D and 3D grid generation. Same comments as in DAMDEN320alsoholdhere.

•DAMISODEN320: computation of MESP isosurfaces and their normals.

•DAMTOPO320:analysisofMEDandMESPtopology.Computa- tion of critical points (CPs), hessian eigenvectors and eigen- valuesat CPs,gradient pathandatomicbasinsis carriedout usingDAMpartition/expansion.

•DAMFIELD320:fastcomputationofelectricfieldlinesincluding filegenerationfor3Dplotting.

•DAMFIELDPNT320:computation ofelectricfieldlines onuser- definedsetsofpoints.

•DAMFORCES320:Hellmann-Feynmanforcesonnuclei.

•DAMFRAD320: tabulation of radial factors andtheir first and secondderivatives.

•DAMMULTROT320:tabulationofatomicmultipolarmomentsin alocallyorientedframe.

•^{DAMORB320: 2D and 3D grid} computation for molecular or- bitals.

•DAMSGHOLE320:computationofMESPonaMEDisosurface.

•DAMZERNIKE320: computation of one-center MED expansion inaballintermsofCanterakis-ZerkineorJacobifunctions.

•DAMMESPIMIZER320:clusteroptimizationwithEPIC.

AlltheseprogramscanberundirectlyfromtheGraphicalUser Interface(GUI) –seeFig.2 –or,alternatively, ascommands ona consoleterminalorinbatch. Inthesecases,theGUIcanbe used togeneratesuitableinputfiles.Parallelversionswithmpiarealso includedforthemosttime-consumingprograms.

InterfacescanberuneitherfromtheGUIoutside.Runningfrom the GUIonly requiresdouble clicking on asuitable file.A quick- startguideandausermanual,bothinPDFformat,areincludedin the package.The manual canbe also accessedwiththe helpkey intheGUI.

An updated version ofthe package can be downloaded freely from:https://github.com/chemtopotools/DAMQT.git.

Appendix B.Supplementarymaterial

Supplementarymaterialrelatedtothisarticlecanbefoundon- lineathttps://doi.org/10.1016/j.cpc.2022.108460.

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