一种基于转动光谱的分子团簇结构拟合程序.pdf

CHINESE JOURNAL OF CHEMICAL PHYSICSVOLUME 36,NUMBER 3JUNE 27,2023ARTICLEA Fitting Program for Structural Determination of Molecular Clusters fromRotational SpectroscopyXinlei Chen,Guanjun Wang,Weixing LiDepartment of Chemistry,Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials,Fudan University,Shanghai 200438,China(Dated:Received on April 30,2023;Accepted on May 25,2023)The characterization of the struc-tures of molecular clusters,whichserve as building blocks for bulksubstances,providescrucialin-sightintotheinteractionsbe-tween constituent units.Chirped-pulse Fourier transform microwave(CP-FTMW)spectroscopy,com-bined with state-of-the-art quan-tum chemical calculations,is apowerful tool for characterizing the structures of molecular clusters,as the rotational spectraare directly related to the mass distribution of a molecule or cluster.However,determin-ing the structures of large or complex clusters from experimental rotational spectra remainschallenging due to their structural flexibility.Ab initio and density functional theory cal-culations for searching their stable structures could be significantly time-consuming andmethod-dependent.To address these challenges,we have developed an approach that relieson the experimental rotational constants to search for potential molecular structures withoutquantum chemical optimization.Our approach involves creating an initial set of conformersthrough either a semi-empirical sampling program or the quasi-Monte Carlo method.After-ward,the trust region reflective algorithm is utilized for structure fitting.This procedureenables us to quickly generate potential conformers and gain access to precise structural in-formation.We apply our fitting program to water hexamer and benzaldehyde-water clusters,and the resulting topological structures align extremely well with the experimental results.Key words:Molecular cluster,Microwave spectroscopy,Chirped pulse,Structure fitting,Fitting programI.INTRODUCTIONMolecular clusters are groups of molecules held to-gether by non-covalent interactions(NCIs)such as hy-drogen bonding,van der Waals forces,and dipole-dipoleinteractions.These clusters as the building blocks forPart of the special topic for“the Chinese Chemical Societys17th National Chemical Dynamics Symposium”Authors to whom correspondence should be addressed.E-mail:,bulk substances provide crucial insight into the inter-actions between constituent units,which help us un-derstand the behavior and properties of materials atthe molecular level 1.The characterization of clus-ter structures has been a long-standing research focus25.Many efforts have been dedicated to unveil thestructures of bare gas-phase clusters,which is free fromsolvent and matrix effects 68.The combination of Fourier transform microwave(FTMW)spectroscopy with supersonic-jet expansiontechniques has enabled the investigations of weaklyDOI:10.1063/1674-0068/cjcp2304042298c 2023 Chinese Physical SocietyChin.J.Chem.Phys.,Vol.36,No.3Fitting Program for Structural Determination of Molecular Clusters299bound molecular complexes 913.The primary spec-troscopic parameters,i.e.,rotational constants,ob-tained from microwave spectra,are directly related tothe mass distribution of the measured molecule.Thus,information of the molecular bond lengths and anglescan be obtained from the rotational spectra.This tech-nique combined with electrical discharge 1417,laserablation 1820,or laser photolysis 2124 has beenapplied to study the transient molecular species suchas radicals,and ions.Many molecules of astrochemical,atmospheric and biological interest have been preciselydescribed by microwave spectroscopy 2528.The developing chirped-pulse Fourier transform mi-crowave(CP-FTMW)technique has significantly in-creased the acquisition rate of broadband spectra,byraising the single-shot bandwidth of microwave spec-troscopy from approximately 0.5 MHz to more than10 GHz 29.The frequency resolution of better than10 kHz enables each spectral signal acquisition with upto 106resolution elements 10.This allows for accu-rate and definite identification of chemical species,evenwithin complex mixtures.Its high spectral resolutionenables the discrimination of closely spaced rotationalspectra of isotopologues.The primary advantage of ro-tational spectroscopy for determining molecular struc-ture lies in its ability to use isotopic substitution to de-rive the coordinates of each atom in the principal axissystem,without relying on any assumptions about ini-tial structures 30.Based on the Born-Oppenheimerapproximation,the approach assumes that the posi-tions of atoms within a molecule are not affected by iso-topic substitution.Substituting each atom with a differ-ent isotope modifies the mass distribution,resulting inchanges to the rotational constants.These alterationsto the moments-of-inertia can then be translated intothe coordinates of the atoms in the principal axis system(rs).An alternative method to obtain the structuralinformation is by adjusting certain structural parame-ters in an initial structure,which is generally obtainedfrom high-level quantum chemical calculations,to alterthe moments-of-inertia.The experimental moments-of-inertia are then duplicated in a least-squares fitting pro-cedure,resulting in a fitted structure that represents theeffective ground state structure(r0).In principle,the structure of any given molecule canbe determined from their rotational spectroscopy by themethods described above.However,the structural de-termination of a molecular cluster,especially for a largesize cluster,is highly challenging.First,the determi-nations of the experimental structures need the spec-troscopic parameters of corresponding isotopologues.But the fact that efficient production of high-densitygas phase molecular clusters in a controllable manneris hardly achieved with current technology,makes themeasurement of their isotopomers very difficult.Sec-ond,the energetically favored structures of large clus-ters are challenging to predict because they are in-fluenced by various types of non-covalent interactionswhich are subtle.As the degrees of freedom and sizesof the clusters increase,their potential energy surfacesare often characterized by numerous quasi-degenerateand shallow local minima that are difficult to calculate.Therefore,the optimization of such complex systemsbecomes time-consuming and less accurate,even withthe use of state-of-the-art DFT methods.In this study,we develop a program to search forthe possible r0structures of molecular clusters basedon experimental rotational constants.The procedurefor conformer searching involves generating a set of ini-tial conformers followed by structural fitting using theexperimental rotational constants.After structural op-timization,the resulting structures are filtered to re-move unreasonable conformations,and the remainingstructures are ranked according to their relative ener-gies.This method avoids ab initio energy calculations,and the optimization process are solely based on mathe-matical principles,making its computational cost negli-gible in comparison with ab initio or DFT calculations.Besides the rapid selection of the candidate structuresfrom plenty of structures,the other advantage of thisprogram is the accurate determination of the structuralparameters.We have tested our program on the clusters ofbenzaldehyde-water 31 and water hexamer 7.Thetest results show that our method can efficiently pro-duce the cluster structures without manual interven-tion or tuning,using only the experimental parametersas the optimization target.These advantages indicatethat our program can serve as an efficient tool for fit-ting the structures of molecular clusters from microwavespectroscopy.II.EXPERIMENTSA.Experimental methodWe have set up a CP-FTMW spectrometer at FudanUniversity recently,with a single-shot signal acquisitionDOI:10.1063/1674-0068/cjcp2304042c 2023 Chinese Physical Society300Chin.J.Chem.Phys.,Vol.36,No.3Xinlei Chen et al.FIG.1 Diagram of CP-FTMW spectrometer at Fudan University.covering 28 GHz frequency range.Its schematic dia-gram is depicted in FIG.1.In brief,a pulsed supersonicjet was produced by expanding the gas mixture into avacuum chamber,and chirped pulses covering the fre-quency range of 28 GHz were emitted into the cham-ber to interact with the molecular beam.The resultingresponse of the chirped pulse in the limit of a strongdriving field was referred to as rapid adiabatic passage(RAP)32.Once the excitation pulse dissipated,theparticle population underwent redistribution and emit-ted coherent light,ultimately producing the free induc-tion decay(FID)signal.This signal was then gatheredand examined for analysis.The rotational spectra of benzaldehyde-water clustersin the 28 GHz range were recorded by our CP-FTMWspectrometer.And the experiment was carried out asthe following:a custom-made reservoir was employed,which is designed as part of a pulsed valve(general valveseries 9)and positioned proximal to the valve orifice.This reservoir was maintained at ambient temperatureand used to hold benzaldehyde.Distilled water was heldin a second reservoir,which was located upstream of thegas pipeline,outside of the vacuum chamber.Samplesof varying H216O/H218O ratios were utilized for iso-topologues.The experimental setup employed neon gasas the carrier gas with a backing pressure of 3 bars.Thegas mixture was expanded through the nozzle with a di-ameter of 0.8 mm,generating a pulsed supersonic jet ina vacuum chamber.The frequency of the jet was set to9 Hz.After a delay of around 900 s,a horn antennabroadcast eight chirped pulses with a 4 s durationspanning the 28 GHz into the vacuum chamber.Thesechirped pulses were generated by an arbitrary waveformgenerator operating at a sampling rate of 25 GS/s andamplified by a traveling wave tube amplifier with a min-imum gain of 55 dB(300 W).The macroscopic dipolemoment of the ensemble of molecules was probed by col-lecting eight FID signals,40 s for each,using anotherhorn antenna,which were then recorded in the timedomain with a digital oscilloscope with sample rate of25 GS/s.The signals were subsequently transformedinto the frequency domain using Fourier transforma-tion with a Kaiser-Bessel window function.In order todecrease sample consumption and measurement time,a fast-frame data acquisition method was implementedthat allowed for eight or more excitation and emissioncycles during each supersonic expansion.The accuracyof the frequency measurement of the spectra was betterthan 15 kHz,and the resolution was better than 25 kHz.B.Computational methodsThe fitting program for the structures of molecularclusters was implemented using Python 3.The scriptis briefly divided into three components:preprocessingthe coordinates data,fitting the rotational constantsof the initial coordinates to the experimental ones byadjusting the initial coordinates,regenerating the coor-dinates.Initially,the input coordinates of the molec-ular cluster in the xyz format are split according toconstituted monomers.Each monomer,except for thefirst one,is represented by a transform array of lengthsix.The first three elements of this array represent theDOI:10.1063/1674-0068/cjcp2304042c 2023 Chinese Physical SocietyChin.J.Chem.Phys.,Vol.36,No.3Fitting Program for Structural Determination of Molecular Clusters301FIG.2 Structure fitting workflow.Where x0is the variable to optimize and xis the result.The function accepts x0,targetrotational constant and molecule list as variables,and calculate difference between target value and one at x0.Optimizingalgorithm is able to find xthat minimizes residual of the function.translation position,while the last three correspond tothe orientation expressed in Euler angle.These trans-form arrays are concatenated to form the input variablefor the following optimization.The core process of fit-ting program is based on trust region reflective(TRR)algorithm.TRR algorithm is a nonlinear optimizationalgorithm used to find global or local minimum of anunconstrained optimization problem.The basic idea ofthe TRR algorithm is to compute the gradient and Hes-sian matrix of the objective function at each iteration,and then construct a quadratic model.The algorithmthen seeks a minimum of the quadratic model withina trust region,which limits the search to a certain re-gion around the current point.In our case,TRR algo-rithm is implemented by least-square fit function usingscipy package.This function would optimize the inputto minimize the cost,which is expressed as the sumof related error of rotational constants in our program.The cost function accepts the overall transformation ar-ray,and transforms it to the structure of an optimizedcluster.Then the rotational constants of the clusterwith the new structure is calculated,giving the devia-tion related to the target rotational constants,which isthe objective of the optimizing function.The functionminimizes these deviations by adjusting transformationarray.During this process,the structures of individ-ual molecules remain constant.A new transformationarray is given when optimizing process is finished,andthe final cluster structure is converted to text as output.The whole process is summarized in FIG.2.A sampling program,such as CREST 33 and AB-Cluster 34,is required in our workflow,which performsstructure sampling and provides proper initial struc-tures.In our case,CREST is chosen for initial con-former generation.Random sampling is an alternativemethod to obtain initial structures.By using a quasi-Monte Carlo(QMC)35 engine to generate random setsof initial transform arrays,more comprehensive start-ing points can be obtained.However,the results fromthe QMC method require filtering the energetically fa-vored structures further,and this process is consider-ably time-consuming due to the mostly unreasonablestarting structures.III.RESULTS AND DISCUSSIONIn a previous report,water hexamer has been exam-ined in a pulsed supersonic expansion using CP-FTMW,three isomers were unambiguously identified as cage,prism,and book conformers,respectively 7.The oxy-gen coordination was deduced using isotopic rotationalconstants through the Kraitchman equation,resultingin the rsstructure.The oxygen framework of threewater hexamers was determined using 18 single18O-substituted isotopologues.Their r0structures were fit-ted using calculated restructure and experimentally ro-tational constants of isotopic species,as shown in Ref.7and FIG.3.In this work,we utilized our structural fitting pro-gram to optimize the structures of water hexamer whichhave been further compared with the experimental ones.Total 91 conformers of water hexamer are initially pro-duced by CREST.These structures have been selectedas the initial structures for the structural optimizationwith our fitting program.Totally,four prism structures,four cage structures,and seven book structures wereDOI:10.1063/1674-0068/cjcp2304042c 2023 Chinese Physical Societ