Multiwfn is an extremely powerful program for realizing electronic wavefunction analysis, which is a key ingredient of quantum chemistry. Multiwfn is free, open-source, high-efficient, very user-friendly and flexible, it supports almost all of the most important wavefunction analysis methods.

Multiwfn is maintained by Tian Lu (卢天) at Beijing Kein Research Center for Natural Sciences (http://www.keinsci.com, 北京科音自然科学研究中心). Multiwfn is always in active development, the original paper is *J. Comput. Chem.*, **33**, 580-592 (2012) (corresponding to a very old, completely out-of-date version 2.1.2).

Reporting bug, seeking help or providing suggestion, please post messages on Multiwfn forum (http://sobereva.com/wfnbbs), I always reply any question regarding Multiwfn timely.

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**Input files supported by Multiwfn**Multiwfn accepts several kinds of files for loading wavefunction information: .wfn/.wfx (Conventional / Extended PROAIM wavefunction file), .fch (Gaussian formatted check file), .molden (Molden input file), .31~.40 (NBO plot files) and .gms (GAMESS-US or Firefly output file). Other types such as Gaussian input and output files, .cub, .grd, .pdb, .xyz and .mol files can be used for specific functions.

Briefly speaking, Multiwfn can perform wavefunction analyses based on outputted file of almost all well-known quantum chemistry programs, such as Gaussian, ORCA, GAMESS-US, Molpro, NWChem, Dalton, xtb, PSI4, Molcas, Q-Chem, MRCC, deMon2k, Firefly, CFour, Turbomole ...

**Special points of Multiwfn**- Very comprehensive functions. Almost all of the most important wavefunction analysis methods have been well supported by Multiwfn.
- Extremely user-friendly. Multiwfn is designed as an interactive program (but can also run silently), prompts shown on screen in each step clearly tell users what should input next. Multiwfn also never prints obscure messages, therefore there is no any barrier even for beginners. In addition, all wavefunction analysis theories are very detailedly documented, and there are more than one hundred of well-written examples in the manual, which are very helpful for new users. Moreover, The developer always very timely and patiently replies users' questions in Multiwfn official forum.
- High flexiblity. The design of the overall framework, functions and user interface of Multiwfn is rather flexible, but this does not sacrifice ease of use. Different modules of Multiwfn are organically integrated together to make numerous analyses that single module cannot realize feasible.
- High efficiency. All codes of time-consuming steps of Multiwfn were substantially optimized. Most parts have been parallelized by OpenMP technology.
- Results can be visualized directly. A high-level graphical library DISLIN is invoked internally by Multiwfn for visualizing results, most plotting parameters are controllable in interactive interface. This feature remarkably simplified wavefunction analysis, especially for studying distribution of real space functions.

**Major functions of Multiwfn**- Showing molecular structure and viewing orbitals (MO, NBO, natural orbital, NTO, LMO, etc.). Speed of generating orbitals is extremely fast.
- Outputting all supported real space functions as well as gradient and Hessian at a point. Value can be decomposed to orbital contributions.
- Calculating real space function along a line and plot curve map.
- Calculating real space function in a plane and plot plane map. Supported graph types include filled-color map, contour map, relief map (with/without projection), gradient map and vector field map.
- Calculating real space function in a spatial scope, data can be exported to Gaussian-type cube grid file (.cub) and can be visualized as isosurface.
- For the calculation of real space functions in one-, two- and three-dimensions, user can define the operations between the data generated from multiple wavefunction files. Therefore one can calculate and plot such as Fukui function, dual descriptor and density difference very easily. Meanwhile promolecule and deformation properties for all real space functions can be calculated directly.
- Topology analysis for electron density (AIM analysis), Laplacian, ELF, LOL, etc. Critical points (CPs) and gradient paths can be searched and then be visualized in 3D window or plotted as plane graph. Interbasin surfaces can be drawn. Values of all supported real space functions can be calculated at critical points or along topology paths. CP properties can be decomposed as orbital contributions.
- Checking and modifying wavefunction. For example, print orbital and basis function information, manually set orbital occupation number and type, translate and duplicate system, discard wavefunction information from specified atoms.
- Population analysis. Hirshfeld, Hirshfeld-I, VDD, Mulliken, Löwdin, Modified Mulliken (including three methods: SCPA, Stout & Politzer, Bickelhaupt), Becke, ADCH (Atomic dipole moment corrected Hirshfeld), CM5, CHELPG, Merz-Kollmann, RESP (Restrained ElectroStatic Potential), AIM (Atoms-In-Molecules) and EEM (Electronegativity Equalization Method) are supported. Electrostatic interaction energy of two given fragments can be calculated based on atomic charges.
- Orbital composition analysis. Mulliken, Stout & Politzer, SCPA, Hirshfeld, Hirshfeld-I, Becke and natural atomic orbital (NAO) methods are supported to obtain orbital composition.
- Bond order analysis. Mayer bond order, multi-center bond order in AO or NAO basis (up to 12-centers), Wiberg bond order in Löwdin orthogonalized basis and Mulliken bond order are supported. Mayer and Mulliken bond order can be decomposed to orbital contributions. Wiberg bond order can be decomposed to contribution from various natural atomic orbital pairs.
- Plotting total, partial, overlap population density-of-states (TDOS, PDOS, OPDOS). Up to 10 fragments can be very flexibly and conveniently defined. Local DOS (LDOS) can also be plotted for a point as curve map or for a line as color-filled map.
- Plotting IR (infrared), normal/pre-resonance Raman, UV-Vis, ECD (electronic circular dichroism), VCD (vibrational circular dichroism) and Raman optical activity (ROA) spectra. Not only harmonic spectrum, but also anharmonic fundamental, overtone and combination bands can be plotted. Spin-orbit coupling effect could be incoporated. Abundant parameters (broadening function, FWHM, scale factor, etc.) can be customized by users. Many data process functions are supported (e.g. finding maximum and minimum of the spectrum). Total spectrum can be decomposed to individual contribution of each transition. Spectrum of multiple systems can be conveniently plotted together. Plotting conformational weighted spectrum can be very easily realized.
- Quantitative analysis of molecular surface. Surface properties such as surface area, enclosed volume, average value and std. of mapped functions can be computed for the whole molecular surface or for local surface; local minima and maxima of mapped functions on the surface can be located.
- Processing grid data (can be loaded from .cub/.grd or generated by Multiwfn). User can perform mathematical operations on grid data, set value in certain range, extract data in specified plane, plot integral curve, etc.
- Adaptive natural density partitioning (AdNDP) analysis. The interface is interactive and the AdNDP orbitals can be visualized directly.
- Analyzing real space functions in fuzzy atomic spaces (defined by Becke, Hirshfeld or Hirshfeld-I partitions). These quantities can be computed: Integral of selected real space function in atomic spaces or in overlap regions of atomic spaces, atomic multipole moments, atomic overlap matrix (AOM), localization and delocalization index (DI), condensed linear response kernel, multi-center DI, as well as four aromaticity indices, namely FLU, FLU-pi, PDI and information-theoretic index.
- Charge decomposition analysis (CDA) and extended CDA analysis. Orbital interaction diagram can be plotted. Infinite number of fragments can be defined.
- Basin analysis. Attractors can be located for any real space function, corresponding basins can be generated and visualized at the same time. All real space functions can be integrated in the generated basins. Electric multipole moments, orbital overlap matrix, localization index and delocalization index can be calculated for the basins. Atomic contribution to basin population can be obtained.
- Electron excitation analyses, including: Visualizing and analyzing hole-electron distribution, transition density, transition electric/magnetic dipole moment and charge density difference; calculating Coulomb attractive energy between hole and electron (exciton binding energy); calculating Mulliken atomic transition charges and TrEsp (transition charge from electrostatic potential); decomposing transition dipole moment to MO pair contribution or basis function/atom contribution; analyzing charge-transfer by the method proposed in
*JCTC*,**7**, 2498; plotting atom/fragment transition density matrix, transition dipole moment matrix and charge transfer matrix as heat maps; calculating △r index (*JCTC*,**9**, 3118) and Λ index (*JCP*,**128**, 044118) to reveal electron excitation character; calculating transition dipole moments between excited states; generating natural transition orbitals (NTOs); calculating ghost-hunter index (*JCC*,**38**, 2151); calculating amount of interfragment charge transfer via IFCT method; generating natural orbitals for a batch of excited states. - Orbital localization analysis: Pipek-Mezey (based on Mulliken or Löwdin population) and Foster-Boys localization methods are supported. Composition, energy and dipole moment of the resulting LMOs can be derived, shape and center of the LMOs can be easily visualized. Furthermore, based on the LMOs, oxidation states can be evaluated via LOBA method (
*PCCP*,**11**, 11297). - Visual study of weak interaction: RDG/NCI method (
*JACS*,**132**, 6498), aNCI method (noncovalent interaction analysis in fluctuating environments,*JCTC*,**9**, 2226), DORI method (*JCTC*,**10**, 3745), independent gradient model (IGM) method (*PCCP*,**19**, 17928). Scatter map can be directly plotted, volume enclosed by isosurface of related real space function can be integrated for quantitative analysis. Becke and Hirshfeld surface analyses, as well as fingerprint analysis are also supported. - Energy decomposition analysis (EDA): EDA based on UFF/AMBER/GAFF molecular force fields, as well as simple energy decomposition (relies on Gaussian).
- Other useful functions or utilities involved in quantum chemistry studies (incomplete list): Integrating a real space function over the whole space by Becke's multi-center method; evaluating overlap integral between alpha and beta orbitals; evaluating overlap and centroid distance between two orbitals; generating Gaussian input file with initial guess from converged wavefunction or multiple fragment wavefunctions; calculating van der Waals volume; calculating HOMA and Bird aromaticity indices; calculating LOLIPOP index; calculating intermolecular orbital overlap; Yoshizawa's electron transport route analysis; calculating atomic and bond dipole moment in Hilbert space; plotting radial distribution function for real space functions; plotting iso-chemical shielding surface (ICSS); calculating overlap integral between orbitals in two different wavefunctions; parsing output of (hyper)polarizability task of Gaussian; calculating polarizability and 1st/2nd/3rd hyperpolarizability by sum-over-states (SOS) method; outputting various kinds of integrals between orbitals; evaluating the first and second moments and radius of gyration for a real space function; exporting loaded structure/wavefunction to many popular formats such as .wfn, .wfx, .molden, .fch, NBO .47, .pdb, .xyz and yield input file for a lot of known quantum chemistry codes; calculating bond polarity index (BPI); Domain analysis (obtaining properties within isosurfaces defined by a real space function); calculating electron correlation indices; automatically detecting pi orbitals; evaluating molecular diameter and length/width/height; perform biorthogonalization between alpha and beta orbitals to maximally pair them; Evaluating interatomic connectivity and atom coordination numbers based on geometry; Evaluating core-valence bifurcation (CVB) index.

**Real space functions supported by Multiwfn**

Real space function analysis is one of the most powerful features of Multiwfn, more than one hundred of real space functions are supported and listed below, detailed descriptions can be found in Section 2.6 and 2.7 of the manual:- Electron density
- Gradient norm of electron density
- Laplacian of electron density
- Value of orbital wavefunction
- Electron spin density
- Hamiltonian kinetic energy density
*K*(**r**) - Lagrangian kinetic energy density
*G*(**r**) - Electrostatic potential from nuclear / atomic charges
- Electron localization function (ELF) defined by Becke and the one defined by Tsirelson
- Localized orbital locator (LOL) defined by Becke and the one defined by Tsirelson
- Local information entropy
- Electrostatic potential (ESP)
- Reduced density gradient (RDG) with/without promolecular approximation
*Sign*(*λ*_{2})**ρ*(product of the sign of the second largest eigenvalue of electron density Hessian matrix and electron density) with/without promolecular approximation- Exchange-correlation density, correlation hole and correlation factor
- Average local ionization energy
- Source function
- Electron delocalization range function EDR(
**r**;d) and orbital overlap distance function D(**r**) (Related code was kindly contributed by Arshad Mehmood) - The δ
*g*function defined in Independent Gradient Model (IGM) - Others (incomplete list): potential energy density, electron energy density, strong covalent interaction index (SCI), shape function, local temperature, bond metallicity, linear response kernel, local electron affinity/electronegativity/hardness, ellipticity of electron density, eta index, on-top pair density, numerous forms of DFT exchange-correlation potential, numerous forms of DFT kinetic energy density, Weizsäcker potential, Fisher information entropy, Ghosh/Shannon entropy density, integrand of Rényi entropy, steric energy/potential/charge, Pauli potential/force/charge, quantum potential/force/charge, PAEM, density overlap regions indicator (DORI), region of slow electrons (RoSE), PS-FID, single exponential decay detector (SEDD), electron linear momentum density, electric/magnetic dipole moment density, local electron correlation function, magnitude of electric field.

Implementing a new real space function into Multiwfn is extremely easy, as illustrated in Section 2.7 of the manual.

**Things that Multiwfn can do**

The analyses that Multiwfn can realize for different topics are briefly listed below, you can easily find corresponding introduction and examples by searching manual. Do not forget to ask question in Multiwfn forum when you are confused!- Visualizing various kinds of orbitals generated by various programs in various forms
- Characterizing chemical bonds: Various form of AIM analyses; studying real space functions (ELF, LOL, ▽
^{2}*ρ*, kinetic/potential energy density, valence*ρ*, fragment density difference, deformation density, source function, bond ellipticity, bond degree, eta index, V(r)/G(r), SCI, DORI, PAEM, IGM...); various kinds of bond orders analysis (Mayer, Laplacian, Mulliken, Wiberg, Fuzzy and multi-center bond orders, as well as decomposition analysis for Mayer, Mulliken and Wiberg bond orders); localization/delocalization index; orbital localization analysis; various methods of measuring bond polarity and bond dipole moment; charge decomposition analysis (CDA); overlap population density-of-states (OPDOS); energy decomposition analysis and so on. See Section 4.A.11 of manual for an overview. Variation of various properties of chemical bonds during scan and IRC processes can also be easily studied via shell scripts, see Section 4.A.1. - Characterizing electron distribution and variation: Atomic charges (AIM, Mulliken, SCPA, Hirshfeld, Hirshfeld-I, Voronoi, Löwdin, ADCH, CM5, EEM, CHELPG, MK, RESP... ); total and spin population analyses for basis functions/shells/atoms/fragments; atomic dipole and multipole moment analysis; plotting / basin analysis / domain analysis for density difference; charge displacement curve
- Aromaticity and electron delocalization analysis: ICSS; AdNDP; ELF-σ/π; LOL-σ/π; HOMA; Bird; multi-center bond order; NICS; Shannon aromaticity; FLU and FLU-π; PDI; ATI; PLR; ∆DI; density curvature perpendicular to ring plane and so on. See Section 4.A.3 for an overview
- Characterizing intramolecular and intermolecular weak interactions: AIM analysis; visual analyses (NCI, IGM, DORI); plotting and quantitative molecular surface analysis for electrostatic potential (ESP); energy decomposition analysis based on forcefield; Hirshfeld/Becke surface analysis; LOLIPOP; mutual penetration distance and penetration volume analysis; atomic charge and multipole moment analysis; charge transfer analysis (density difference map, CDA, variation of population ...); ELF and core-valence bifurcation (CVB) index and so on. See Section 4.A.5 for an overview
- Electron excitation analysis: Analysis of hole and electron (distribution, atom/fragment/orbital contribution, centroid position, displacement and overlap, exciton binding energy); charge transfer analysis (IFCT, density difference...); NTO; overlap and centroid distance between crucial MOs; plotting atom/fragment transition density matrix and charge transfer matrix; ∆
*r*index and Λ index; decomposition of transition dipole moment to basis function/atom/fragment/MO pair contributions; transition dipole moment between various excited states; transition atomic charge; ghost-hunter index; revealing variation of electronic structure (bonding and population) during excitation and so on. See Section 4.A.12 for an overview - Prediction of reactive sites: ESP and ALIE analyses on molecular surface; Fukui function and dual descriptor as well as their condensed forms; atomic charges; orbital composition analysis for frontier molecular orbitals; population of π electron; orbital overlap distance function analysis. See Section 4.A.4 for an overview
- Prediction properties of molecular condensed phase: Using ESP distribution on vdW surface to empirically predict heat of vaporization, heat of sublimation, density of molecular crystal, boiling point, heat of fusion, surface tension and so on. See Section 3.15.1
- Plotting IR, Raman, UV-Vis, ECD, VCD and ROA spectra based on output file of quantum chemistry codes
- Characterizing molecular structure: Evaluating molecular volume, length/height/weight, diameter, interatomic connectivity and atomic coordination number, average bond length of atomic cluster, cavity volume and so on
- (Hyper)polarizability study: Parsing Gaussian output file of "polar" task; plotting (hyper)polarizability density; obtaining atomic contribution to (hyper)polarizability; calculating (hyper)polarizability by means of sum-over-states method
- Many others: Teaching structure chemistry; converting file formats; studying electron correlation effect; realizing ELF-tuning and LOL-tuning for DFT functionals; evaluating oxidation state by LOBA method; electric conduction analysis (TDOS and PDOS; orbital overlap analysis between neighbouring monomer; Yoshizawa's transport route analysis); Studying distribution of real space functions (in terms of radial distribution function, centroid, first and second moments, integral over whole space and local region...) and so on

The author sincerely thanks following users (in no particular order), who provided valuable suggestions or reported bugs, users' feedbacks are very important for the development of Multiwfn.

Jingbai Li; stecue; Henry Rzepa; Théo Piechota Gonçalves; lip; Tsuyuki Masafumi; + - * /; Jingsi Cao; Jean-Pierre Dognon; Shubin Liu; Shuchang Luo; Xunlei Ding; Daniele Tomerini; Sergei Ivanov; Cheng Zhong; Can Xu; GuangYao Zhou; HaiBin Li; jsbach; Beefly; Emilio Jose Juarez-Perez; YangChunBaiXue; XinYing Li; Yang Yang; Andy Kerridge; junjian; JinYun Wang; Zhuo Yang; LiYan Wang; DongTianLiDeJiaoYang; FangFang Zhou; YingHui Zhang; ShuChang Luo; YuYang Zhu; Arne Wagner; Dongdong Qi

The following donators are greatfully acknowledged (in no particular order):

Yi Mu (穆毅); Fugui Xiao (肖富贵); Qing Song (宋青); Yifan Yang; Changli Cheng; Min Xia; Hanwen Cao

Arshad Mehmood is sincerely acknowledged for his contribution to all analysis codes of electron delocalization range function (EDR) and overlap distance (D).

Specially thanks to my wives Mio Akiyama (秋山澪) and Azusa Nakano (中野梓) in nijigen world and Sell-moe-kun in real world!