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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. 64 bit Windows, Linux and Mac OS platforms are supported.

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 (corresponding to very old version 2.1.2) is *J. Comput. Chem.*, **33**, 580-592 (2012).

Reporting bug, seeking help or providing suggestion, please post message in Multiwfn forum (*highly recommended!*), or contact Multiwfn developer via sobereva[at]sina.com.

**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 output file). Other type of files such as Gaussian output file, .cub file, DMol3 .grd file, .pdb file, .xyz file and .mol file can be used for specific functions.

**Special points of Multiwfn**- Comprehensive functions. Almost all of the most important wavefunction analysis methods (except for NBO methods) are supported by Multiwfn.
- Very user-friendly. Multiwfn is designed as an interactive program, prompts shown on screen in each step clearly tell users what should do next, Multiwfn also never prints obscure messages, hence there is no barrier even for beginners. In addition, there are about 100 well-written tutorials in the manual, which are very helpful for new users.
- High efficiency. The code of Multiwfn is substantially optimized. Most parts are parallelized by OpenMP technology. For computationally intensive tasks, the efficiency of Multiwfn exceeds analogous programs significantly.
- Results can be visualized directly. A high-level graphical library DISLIN is invoked internally and automatically by Multiwfn for visualizing results, most plotting parameters are controllable in interactive interface. This remarkably simplified wavefunction analysis, especially for studying distribution of real space functions.

**Primary functions of Multiwfn**- Showing molecular structure and viewing orbitals (MO, NBO, natural orbital, 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 and gradient paths can be searched and visualized in terms of 3D or plane graph. Interbasin surfaces can be drawn. Values of real space functions can be calculated at critical points or along topology paths.
- 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 MPA (including three methods: SCPA, Stout & Politzer, Bickelhaupt), Becke, ADCH (Atomic dipole moment corrected Hirshfeld), CM5, CHELPG, Merz-Kollmann, AIM and Electronegativity Equalization Method (EEM) 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/Raman/UV-Vis/ECD/VCD spectrum. Abundant parameters (broadening function, FWHM, etc.) can be determined by users, individual contribution from each transition to the spectrum can be easily studied. Spectrum of multiple systems can be conveniently plotted together. Plotting conformational weighted spectrum is well supported.
- 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. Becke and Hirshfeld surface analysis are also supported.
- 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). 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 PLR can be computed.
- 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 analysis, 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 transition density matrix or atom-atom contribution matrix of transition dipole moment as colored matrix map; calculating Dr index to reveal electron excitation mode; calculating transition dipole moments between all excited states; generating natural transition orbitals (NTOs); calculating ghost-hunter index proposed in*JCC*, 38, 2151. - Orbital localization analysis: Pipek-Mezey (based on Mulliken or Löwdin population) and Foster-Boys localization methods are supported. Energy of the resulting LMOs can be derived. 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. - Other useful functions or utilities involved in quantum chemistry studies: 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; monitoring SCF convergence process; 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; calculating center; the first and second moments and radius of gyration for a real space function; exporting wavefunction to .wfn, .wfx, .molden, .fch, NBO .47 and yield input file for a batch of known quantum chemistry codes; calculating bond polarity index (BPI); evaluating oxidation state; Pipek-Mezey orbital localization; Domain analysis (obtaining properties within isosurfaces defined by a real space function); calculate electron correlation indices; automatically detect pi orbitals and so on.

**Real space functions supported by Multiwfn**

Real space function analysis is one of the most powerful feature 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 K(r)
- Lagrangian kinetic 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(lambda2)*rho (The 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: Such as 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 DFT exchange-correlation potential, 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.

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

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!