1. An introduction to multifunctional wavefunction analysis program
Multiwfn 3.0
Tian Lu
School of Chemical and Biological Engineering
University of Science and Technology Beijing
2013-MAY-15

2. Outline What is wavefunction analysis?
Basic features and usage of Multiwfn
Functions, related theories and applications of Multiwfn

3. 1
What is wavefunction analysis?

4. Wavefunction analysis
Valuable
Information
(Apart from energy, electric moments, polarizability, spectrum…)

5. Ingredients of wavefunction analysis
Population analysis
Bond order analysis
Electron localization / delocalization analysis
Charge transferation analysis
Orbital composition analysis
Basin analysis
Molecular surface analysis
...
Bader’s atoms in molecules (AIM) theory
Natural bond orbital (NBO) analysis
Frontier molecular orbital theory
Some portion of conceptual density functional theory

6. The uses of wavefunction analysis
Understanding the natural of chemical bonding
Providing deeper insights on chemical reactions
Predicting reactivity and reactive sites
Predicting molecular properties
Studying aromaticity
Characterizing charge distribution
Analyzing non-covalent interactions
Analyzing electronic excitation and transferation
etc.

7. Existing wavefunction analysis codes:
AIM2000, AIMALL, AIMPAC, Xaim, MORPHY, TopMod, TopChem, NBO, AOIM, AdNDP, CheckDen, DGrid, AOMix, NCIPlot, QMForge, CDA, GIMIC, ACID, AOSB, promolden, PAMoC, GaussSum, HiPart, InteGriTy, Bader ...
Popular quantum chemistry programs also feature a few wavefunction analysis functions

8. Shortcomings of existing codes:
Limited functions, lack of integration
Low efficiency
Poor user-interface, lack of readable manual and tutorials
Unable to visualize analysis result directly
Not free-of-charge, not open-source or distributed priviately
Not flexible enough
波函数分析被低估了，大家不懂，教材不行，没有好用的程序

9. 2
Basic features and usage of Multiwfn

10. 32/64bit Windows and 64 bit Linux platform
Multiwfn aims to be the best wavefunction analysis program in the world, and to overcome all shortcomings of existing wavefunction analysis codes
32/64bit Windows and 64 bit Linux platform
(Windows version is recommended for new users)
Free-of-charge, open source
Size: <5MB, 4 files (The program itself)
Programmed by Fortran 90/95
(Intel fortran compiler and compaq visual Fortran are formally supported)
OpenMP parallelization
尝试干掉所有其它波函数分析工具，除了NBO以外

11. Interactive, command line + GUI mixed running mode
Silent and batch mode is supported via simple shell script

12. Special points of Multiwfn A single program can do almost everything!
1. Very comprehensive functions, highly integrated
All of the most useful wavefunction analysis methods are supported
结果导入导出方便
A single program can do almost everything!

13. Special points of Multiwfn
2. High efficiency
Codes have been substantially optimized and parallized by OpenMP
3. Very easy-to-use
Friendly user-interface, well-written manual, result can be directly visualized and save to graphic file
3. Flexible
Highly adjustable parameters, abundant options, result can be imported and exported, readable code

14. Offical website of Multiwfn: http://Multiwfn.codeplex.com
Download
Older version
Manual
Executable files
Source codes

15. History of Multiwfn The first version (1.0): 2009-Nov-27
... (1.2/1.3/1.4/1.5)
Version 1.5: 2010-Oct-2
Version 2.0: 2011-Mar-9
... (16 versions)
Version 2.6.1: 2013-Jan-9
Version 3.0: 2013-Mar-24
The latest version (3.0.1): 2013-May-5
The development of Multiwfn will never be ceased!

16. (Cited by more than 50 times)
An introductory paper on version 2.1.2:
Tian Lu, Feiwu Chen, Multiwfn: A multifunctional wavefunction analyzer, J. Comp. Chem., 33, 580 (2012)
(Cited by more than 50 times)
Currently Multiwfn has been used by more than 100 publications, the users cover the whole world

17. Manual of Multiwfn 265 pages, pdf file
Clearly describes all functions and introduces all related theories
More than 60 tutorials or case studies are given in Chapter 4

18. Supported wavefunction types:
Close-shell, unrestricted and restricted open-shell HF / DFT wavefunctions
Close-shell and open-shell post-HF wavefunctions (Natural orbital formalism)
Supported wavefunction size:
Unlimited (in principle). Actual limitation is solely dependent on available memory
Supported basis functions:
Gauss type functions. Up to g angular moments

19. Input file of Multiwfn AIMPAC wavefunction file (.wfn)
Produced by Gaussian, GAMESS(US/UK), Firefly, Q-chem, Turbomole, DeMon2k
Molpro, Molcas, ORCA, Dalton (Need molden2wfn to convert format)
AIM Extended Wavefunction Files (.wfx)
Gaussian09 B.01 or later
Gaussian formatted check file (.fch/.fchk)
NBO plot file (.31~.40)
Molden input file (.molden)
Only the one produced by Molpro, ORCA, deMon2k and BDF are formally supported
PDB file format (.pdb), .xyz format
Gaussian-type cube file (.cub) and Dmol3 .grd file
Other: .chg, plain text file (including Gaussian output file)

20. Different functions of Multiwfn require different types of information!
详细内容参见手册、例子
E.g. Bond order analysis module (shown at the end of each section):

21. Efficiency comparison
Grid data generation for Laplacian of electron density
Acetic acid, 6-31G** basis-set, points
Test platform: Windows 7 64bit, Toshiba X500-01R notebook (Intel Core-i7 2630QM)

22. AIM topology analysis for C60 with 6-31G*
1. Searching (3,-1) critical points
AIM2000: 155s
Multiwfn N=1: 4.8s
Multiwfn N=4: 1.5s
2. Searching bond path from (3,-1) critical points
AIM2000: 264s
Multiwfn: 10.1s (Serial mode)

23. Functions, related theories and applications of Multiwfn3
Functions, related theories and applications of Multiwfn

24. Main functions 0 Show molecular structure and view orbitals
1 Output all properties at a point
2 Topology analysis
3 Output and plot specific property in a line
4 Output and plot specific property in a plane
5 Output and plot specific property within a spatial region
6 Check & modify wavefunction
7 Population analysis
8 Orbital composition analysis
9 Bond order analysis
10 Plot Total/Partial/Overlap population density-of-states (DOS)
11 Plot IR/Raman/UV-Vis/ECD/VCD spectrum
12 Quantitative analysis of molecular surface
13 Process grid data
14 Adaptive natural density partitioning (AdNDP) analysis
15 Fuzzy atomic space analysis
16 Charge decomposition analysis (CDA) and extended CDA (ECDA)
17 Basin analysis
100 Other functions
Main
functions

25. Visualize structure and orbital isosurface
Main function 0:
Visualize structure and orbital isosurface
Adjust Isosurface quality
Adjust isosurface style
Adjust isovalue and select orbital by one-click

26. Visualizing NAO/NHO/NBO/NLMO (and their “pre-” version) via NBO plot files
Two orbitals can be shown simultaneously to study overlapping between NBOs
Lone pair of nitrogen and anti-bonding orbital between carbon and oxygen of NH2COH. Secondary perturbation energy E(2) ≈ 60kcal/mol.

27. High quality: A few seconds 900 GTFs on 4-core PC
Low quality: only 1s
High quality: A few seconds
900 GTFs on 4-core PC
High quality
Low quality

28. Main function 1, 3, 4 and 5
Outputting all supported real space functions at a point
Outputting real space function in a line and plot it as curve map
Outputting real space function in a plane and plot it as graph
Outputting real space function in a spatial scope and plotting as isosurface
User can define the operations between the data generated from multiple wavefunction files (thus can study such as Fukui function, dual descriptor and density difference very easily

29. Supported real space functions
Electron density
Gradient norm of electron density
Laplacian of electron density
Value of orbital wavefunction
Electron spin density or spin polarization parameter
Hamiltonian kinetic energy density K(r)
Lagrangian kinetic energy density G(r)
Electrostatic potential from nuclear charges / atomic charges
Electron Localization Function (ELF)
Localized orbital locator (LOL)

30. 11 Local information entropy
12 Total electrostatic potential (ESP)
13 Reduced density gradient (RDG)
14 Reduced density gradient with promolecular approximation
15 Sign(lambda2)*rho
16 Sign(lambda2)*rho with promolecular approximation
17 Exchange-correlation density, correlation hole and correlation factor
18 Average local ionization energy
19 Source function
20 Many other useful functions, such as potential energy density, electron energy density, shape function, local temperature and linear response kernel.
Users can customize their real space functions by properly filling code in “userfunc” function in function.f90 file

31. Electron Localization Function (ELF)
Becke and Edgecombe, J. Chem. Phys., 92, 5397
Tian Lu and Feiwu Chen, Acta Phys. -Chim. Sin., 27, 2786

32. Localized orbital locator (LOL)
Schmider and Becke, J. Mol. Struct. (THEOCHEM), 527, 51

33. Output of main function 1: Real space function values at a given point
Density of all electrons: E-01
Density of Alpha electrons: E-01
Density of Beta electrons: E-01
Spin density of electrons: E+00
Lagrangian kinetic energy G(r): E-01
Hamiltonian kinetic energy K(r): E-02
Potential energy density V(r): E-01
Energy density: E-02
Laplacian of electron density: E+00
Electron localization function (ELF): E+00
Localized orbital locator (LOL): E+00
Local information entropy: E-01
Reduced density gradient (RDG): E+03
Reduced density gradient with promolecular approximation: E+01
Sign(lambda2)*rho: E-01
Sign(lambda2)*rho with promolecular approximation: E-01
Corr. hole for alpha, ref.: : E-02
Source function, ref.: : E-01
Wavefunction value for orbital : E-04

34. Average local ionization energy: 0.4652745256E+00
User function: E+00
ESP from nuclear charges: E+01
ESP from electrons: E+01
Total ESP: E-01 a.u. ( E+01 J/C, E+02 kcal/mol
Note: Below information are for electron density
Components of gradient in x/y/z are:
E E E+00
Norm of gradient is: E+00
Components of Laplacian in x/y/z are:
E E E-01
Total: E+00
Hessian matrix:
E E E+00
E E E+00
E E E-01
Eigenvalues of Hessian: E E E+00
Eigenvectors(columns) of Hessian:
E E E+00
E E E+00
E E E+00
Determinant of Hessian: D-02
Ellipticity of electron density:

35. Plotting real space function in a line
Electron density in the molecular axis of LiF

36. C Br
Fermi hole function of CH3Br, dash line indicates reference point

37. Plotting real space functions in a plane
Electron Localization Function (ELF) map of B13+ cluster

38. Localized orbital locator (LOL) map of a tile of graphene

39. Relief+filled color map of gradient of electron density of benzene

40. Contour map of two NBO orbital wavefunctions

41. Electrostatic potential map of BrCl
Blue line reveals van der Waals surface

42. Gradient vector field with contour lines of electron density of uracil in molecular plane

43. Gradient line map of electron density with contour lines of magnesium porphyrin

44. Contour map of deformation density of magnesium porphyrin

45. Animation (Third-part software is needed, e.g. ImageMagick)
Deformation density map during pushing two hydrogens with different-spin (left) and like-spin (right) electrons together

46. Animation (Third-part software is needed, e.g. ImageMagick)
LOL map during hydrogen transferation in HCN
The contour line with isovalue of 0.5 is bolded

47. Weak interaction analysis via reduced density gradient method
Sign(2)*
J. Am. Chem. Soc., 132, 6498

48. Reduced density gradient (RDG) isosurface of phenol dimer

49. Aristolochic acid
Mapping Sign(2)* on RDG isosurface by different colors
Rendered by VMD

50. Weak interaction in urea crystal

51. van der Waals interaction between two alpha-helix

52. Fukui function Dual descriptor
Predict electrophilic attacking site of phenol
Fukui function
Dual descriptor

53. Main function 2: Topology analysis
Available for electron density, Laplacian of electron density, orbital wavefunction, ELF, LOL, user-defined function
Basic functions:
Search critical points (CP)
CP: The position where the gradient norm of the selected function is vanished
Calculate value of all supported real space functions at CP
Generate topology paths and calculate value of functions along the path
Generate interbasin surfaces

54. Purple sphere: (3, -3) CP, namely local maxima
Orange sphere: (3, -1) CP
Yellow sphere: (3, +1) CP
Critical points (CP), bond paths and some interatomic surfaces of electron density of imidazole - magnesium porphyrin complex

55. A symbol of covalent bonding Lone pair
Critical points of localized orbital locator (LOL) of acetic acid

56. (3,-1) — (3,-3) topology paths of LOL of acetic acid

57. Critical points of ELF-pi (the ELF solely contributed from pi electrons) of benzene
The ELF-pi value at these (3,-1) critical points is a popular index for measuring aromaticity
J. Chem. Phys., 120, 1670 and J. Chem. Theory Comput., 1, 83

58. Main function 17: Basin analysis
Basin: The local region separated by zero-flux surface (interbasin surface), each basin uniquely encloses an attractor, namely maximum or (3,-3) CP
Illustration of electron density basin of NH2COH

59. AIM basin (basin of electron density) of hydrogen of HCN

60. NH2COH The ELF basin corresponding to N-C sigma bond
The ELF basin corresponding to lone pair of oxygen

61. The features of basin analysis module of Multiwfn
Based on near-grid algorithm (J. Phys.: Condens. Matter, 21,084204)
Capable to locate attractor, generate and integrate basins for any real space function, even for Fukui function and density difference
Much easier to use than any existing code (especially TopMod)
Basin can be visualized directly
Integrating any real space function in the basins
Calculating electric multipole moments, localization index, delocalization index, orbital overlap matrix for basins

62. Checking & modifying wavefunction
Main function 6
Checking & modifying wavefunction
Save current wavefunction to new .wfn file
Output information of GTF, basis function and orbitals
Output coefficient matrix, overlap matrix and density matrix
Set or swap information of GTFs
Translate and duplicate system
Set orbital type and occupation number
The contribution of some orbitals to real space functions can be ripped out by simply setting their occupation numbers to zero.
Remove specific atoms from wavefunction

63. Translate and duplicate system

64. Main function 7 Population analysis
Hirshfeld population
Voronoi deformation density (VDD) population
Mulliken atom & basis function population analysis
Löwdin population analysis
Modified Mulliken population defined by Ros & Schuit (SCPA)
Modified Mulliken population defined by Stout & Politzer
Modified Mulliken population defined by Bickelhaupt
Becke atomic charge with atomic dipole moment correction
Atomic dipole corrected Hirshfeld population (ADCH)
CHELPG ESP fitting charges
Merz-Kollmann (MK) ESP fitting charges
Mulliken可以分解为轨道的贡献，得到不同基函数、壳层、原子的布居数

65. Hirshfeld and atomic dipole corrected Hirshfeld population (ADCH)
Hirshfeld charge:
wHirsh is the atomic space defined by Hirshfeld (Theor. Chim. Acta (Berl.) 44, 129)
Hirshfeld charges are too small and have poor reproducibility of observable quantity (dipole moment, ESP etc.)
ADCH: Hirshfeld charges are corrected by expanding atomic dipole moments to correction charges placed at neighbour atoms.
ADCH charge is not only more reasonable but also exactly reproduces molecular dipole moment and has good reproducibility of ESP.
Original paper of ADCH: Tian Lu and Feiwu Chen, J. Theor. Comput. Chem., 11, 163
Comparison of atomic charges: Tian Lu and Feiwu Chen, Acta Phys. -Chim. Sin, 28, 1

66. Orbital composition analysis
Main function 8
Orbital composition analysis
Mulliken, SCPA, Stout-Politzer, NAOMO and Hirshfeld partition methods are supported
Outputting contributions from basis functions, shells, atoms and fragment to orbitals
A detail comparison of orbital composition analysis method is presented in
Tian Lu and Feiwu Chen, Acta Chim. Sinica, 69, 2393

67. Output of Mulliken orbital composition analysis
Threshold of absolute value: > %
Orbital: 3 Energy(a.u.): Occ: Type: Alpha&Beta
Basis Type Atom Shell Local Cross term Total
4 Y (O ) % % %
8 Y (O ) % % %
15 YZ (O ) % % %
16 S (H ) % % %
17 S (H ) % % %
21 S (H ) % % %
22 S (H ) % % %
Sum up listed above: % % %
Sum up all basis functions: % % %
Composition of each shell, threshold of absolute value: > %
Shell Type: P in atom 1(O ) : %
Shell Type: P in atom 1(O ) : %
Shell Type: D in atom 1(O ) : %
Shell Type: S in atom 2(H ) : %
Shell Type: S in atom 2(H ) : %
Shell Type: S in atom 3(H ) : %
Shell Type: S in atom 3(H ) : %
Composition of each atoms:
Atom 1(O ) : %
Atom 2(H ) : %
Atom 3(H ) : %

68. Main function 9 Bond order analysis
Mayer bond order analysis
Orbital occupancy-perturbed Mayer bond order
Multicenter bond order analysis (3~10 centers)
Wiberg bond order analysis
Mulliken bond order analysis
Decompose Mulliken bond order to orbital contributions
Fuzzy bond order analysis
Laplacian bond order

69. Mayer bond order (black) and three-center bond order (blue) of planar B13+ cluster

70. Laplacian bond order (LBO)
w is a smoothly varying weighting function proposed by Becke and represents fuzzy atomic space, hence wAwB corresponds to fuzzy overlap space between A and B
LBO well correlates with the bond polarity, the bond dissociation energy and the bond vibrational frequency
Tian Lu and Feiwu Chen, J. Phys. Chem. A, 117, 3100 (2013)

71. Plotting Density-of-States (DOS)
Main function 10
Plotting Density-of-States (DOS)
The DOS curves are artificially broadened from discrete energy levels via Gaussian, Lorentizan or Pseudo-Voigt functions
Abundant adjustable plotting options are provided
Fragments can be flexibly defined, basis functions, shells and atoms are allowed to be freely mixed
Total DOS
Partial DOS
Overlap DOS

72. Total DOS (black), partial DOS (red, blue and magneta), overlap DOS (green, between Fe and carbon Pz basis functions) map of ferrocene

73. Plot IR/Raman/UV-Vis/ECD/VCD spectrum
Main function 11
Plot IR/Raman/UV-Vis/ECD/VCD spectrum
Excitation energies and strengths can be loaded from plain text file or Gaussian output file
Many adjustable options are provided to meet professional requirement

74. Quantitative analysis of molecular surface
Main function 12
Quantitative analysis of molecular surface
Molecular surface: Defined by isosurface of electron density
E.g. =0.001 is a commonly used definition of van der Waals surface
Quantitative analysis: Locate position and obtain the value of minima and maxima of mapped function on the surface. Also calculates statistics such as average value, variance, surface area of positive part of mapped function.
Mapped function: Electrostatic potential, averaged local ionization energy (or other function provided by users)
Uses: Predict molecular properties, reactivity and reactive site. Evalute electrostatic interaction
Detail of the numerical algorithm:
Tian Lu and Feiwu Chen, J. Mol. Graph. Model., 38, 314

75. Output of quantitative analysis of ESP on vdW surface of phenol
Global surface minimum: a.u. at Ang.
Global surface maximum: a.u. at Ang.
Number of surface minima: 3
# a.u eV kcal/mol X/Y/Z coordinate(Angstrom) *
Number of surface maxima: 5 *

76. Output of quantitative analysis of ESP on vdW surface of phenol
================= Summary of surface analysis =================
Volume: Bohr^3 ( Angstrom^3)
Overall surface area: Bohr^2 ( Angstrom^2)
Positive surface area: Bohr^2 ( Angstrom^2)
Negative surface area: Bohr^2 ( Angstrom^2)
Overall average value: a.u. ( kcal/mol)
Positive average value: a.u. ( kcal/mol)
Negative average value: a.u. ( kcal/mol)
Overall variance (sigma^2_tot): a.u.^2 ( (kcal/mol)^2)
Positive variance: a.u.^2 ( (kcal/mol)^2)
Negative variance: a.u.^2 ( (kcal/mol)^2)
Balance of charges (miu):
Product of sigma^2_tot and miu: a.u.^2 ( (kcal/mol)^2)
Internal charge separation (Pi): a.u. ( kcal/mol)

77. Surface minima and maxima of ESP

78. Surface minima and maxima of averaged local ionization energy
Correctly predicted reactive site of electrophilic attack!

79. ESP distribution of Aristolochic acid
Rendered by VMD based on the surface analysis result of Multiwfn
Sergio Manzetti, Tian Lu, J. Phys. Org. Chem. (2013) DOI: /poc.3111

80. Condensed phase properties can be predicted by means of surface descriptors
(Density, boiling point, surface tension, heats of vaporization and sublimation, LogP, diffusion constant, viscosity, solubility, solvation energy and so on)
E.g. Heat of vaporization of the molecules containing C, H, N, O can be predicted via (J. Phys. Chem. A, 110, 1005)
a=2.130, b=0.930 and c= are the parameters determined by least-squares fit
Surface descriptors also have many important uses in study of biochemical systems (Review: Int. J. Quantum. Chem., 85, 676 )

81. Main function 13: Process grid data
Visualize isosurface of grid data
Export cube file
Export coordinate of specific set of grid points along with their values to plain text file
Set value for specific grid points
Mathematical operations on single set of grid data or between two sets of grid data. Operators: +, -, *, /, abs, log ...
Scale the value range of grid data
Show statistic data of the grid points in specific spatial and value range
Grid data can be loaded from .cub/.grd or produced by Multiwfn itself

82. Calculate and plot integral curve in X/Y/Z direction
E.g. in Z direction:
If p is selected as electron density difference, then I(z) is known as “charge displacement curve”, which is very useful for studying charge transfer on linear system or adsorption on solid surface
JACS, 130, 1048

83. Adaptive natural density partitioning (AdNDP)
Main function 14
Adaptive natural density partitioning (AdNDP)
A generalization of 3c-NBO searching to infinite number of centers, used to construct “semi-localized“ orbitals to exhibit local multi-center orbitals
Zubarev and Boldyrev, Phys. Chem. Chem. Phys., 10, 5207 (2008)
Prevalently used in electronic structure studies of large conjugated organic systems and clusters
Very useful but not free of ambiguity. Users must intervene the orbital searching
Multiwfn is the only public program for AdNDP analysis

84. Two four-center orbitals (4c-2e) of Li5+ cluster
Occupation number: 1.997

85. Selected AdNDP orbitals of B11- cluster
2c-2e
3c-2e
11c-2e

86. Ten 4c-2e orbitals of Au20 Cluster
The cube file was outputted by Multiwfn, the graph was rendered by VMD
Occupation number:
= Red
= Orange

87. Fuzzy atomic space analysis
Main function 15
Fuzzy atomic space analysis
Fuzzy atom: In contrary to AIM or Voronoi-like atomic space, fuzzy atomic space does not have clear boundary
Typical definition of fuzzy atom: Hirshfeld, Becke, ISA
Advantage of fuzzy atom space: Easy to be integrated at high accuracy; Overlap space can be straightforwardly defined

88. Fuzzy atomic space of carbon and fuzzy overlap space between C-N in NH2COH

89. Capacity of fuzzy atomic space analysis model
(Hirshfeld and Becke fuzzy atom are supported)
Integrating real space function in fuzzy atomic spaces
Integrating real space function in fuzzy overlap spaces
Calculating atomic multipole moments
Calculating atomic overlap matrix
Calculating localization and delocalization index
Calculating multi-center delocalization index
Calculating PDI (Para-delocalization index)
Calculating FLU (Aromatic fluctuation index)
Calculating FLU-pi
Calculating condensed linear response kernel (CLRK)
Calculating PLR (Para linear response index)

90. Charge decomposition analysis (CDA)
Main function 16
Charge decomposition analysis (CDA)
S: Overlap matrix between fragment orbitals (FOs)
C: Coefficient matrix of complex orbital in FO basis
Via orbital i of complex:
Electron donation from A to B
Back donation from B to A
Repulsive polarization
Net charge transferation = di - bi
Dapprich and Frenking, J. Phys. Chem., 99, 9352

91. The CDA formula used in Multiwfn (Generalization of original CDA by me)
Can be used for open-shell cases (covalent bonding) and when fragments are calculated by post-HF methods. See manual for detail

92. Example: COBH3 Fragment A = CO Fragment B = BH3
Orb Occ d b d - b r
......
Sum:

93. Composition of FOs in complex orbital derived by Mulliken partition
Occupation number of orbital of the complex:
Orbital of fragment 1, Occ: Contribution: %
Orbital of fragment 1, Occ: Contribution: %
Orbital of fragment 2, Occ: Contribution: %
Orbital of fragment 2, Occ: Contribution: %
MO 7 of CO (Occupied)
MO 5 of BH3 (Virtual)
MO 9 of complex

94. Orbital interaction diagram plotted by Multwiwfn

95. Other features of CDA module
Extended charge decomposition analysis (ECDA)
Separately consider charge transferation (CT) and charge polarization effect, and hence provide more accurate CT value than d – b term of CDA (J. Am. Chem. Soc., 128, 278 )
Multiple-fragments CDA analysis
Infinite number of fragments can be defined simultaneously, analysis can thus be applied for each fragment pair
Frag. 1: Pt
Frag. 2: Cl2
Frag. 3: (NH3)2

96. Other functions of Multiwfn
1 Draw scatter graph between two functions
2 Output molecular structure to a pdb file
3 Calculate molecular van der Waals Volume
4 Integrate a function in whole space
5 Show overlap integral between alpha and beta orbitals
6 Monitor SCF convergence process
7 Generate Gaussian input file with initial guess from converged wavefunction
8 Generate Gaussian input file with initial guess from fragment wavefunctions
9 Evaluate coordination number of all atoms
10 Analyze charge-transfer
11 Calculate overlap between two orbitals in whole space

97. 12 Plot transition density matrix as color-filled map
13 Calculate HOMA and Bird aromaticity index
14 Calculate LOLIPOP (LOL Integrated Pi Over Plane)
15 Calculate intermolecular orbital overlap
18 Yoshizawa's electron transport route analysis
20 Output molecular structure to Gaussian input file
21 Calculate properties based on geometry information for specific atoms
22 Detect pi orbitals and set occupation numbers
23 Fit function distribution to atomic value
24 Utility used to obtain NICS_ZZ for non-planar system

98. Integrating a function in whole space
The multi-center integration method for DFT functionals proposed by Becke is used to integrate specific function (J. Chem. Phys., 88, 2547 ). The integrand can be easily written by users themselves
E.g. Computing Weizsäcker kinetic energy
Simply filling below code to “userfunc” function in “function.f90”
userfunc=fgrad(x,y,z,'t')**2/8/fdens(x,y,z)

99. Analyze charge-transfer
J. Chem. Theory Comput., 7, 2498
Example: The first singlet excited state of
Electron density difference between ground state and excited state, complicated and unclear

100. After transformation of density difference:

102. Transferred charge (positive and negative parts): 0.844 -0.844
Barycenter of positive part in x,y,z:
Barycenter of negative part in x,y,z:
Distance of CT in x,y,z (Bohr): Norm:
Distance of CT in x,y,z (Angstrom): Norm:
Dipole moment variation (a.u.) : Norm:
Dipole moment variation (Debye): Norm:
RMSD of positive part in x,y,z: Total:
RMSD of negative part in x,y,z: Total:
H index in x,y,z (Bohr): Norm:
H index in x,y,z (Angstrom): Norm:
t index in x,y,z (Bohr): Norm:
t index in x,y,z (Angstrom): Norm:
Overlap integral between C+ and C-:
t index: The separation degree of positive and negative part of density difference
H index: Averaged diffusion degree of positive and negative part of density difference

103. Plot transition density matrix as color-filled map
Contract transition density matrix (TDM) to atomic centers
Larger diagonal term denotes larger charge variance of corresponding atom
Larger non-diagonal term implies stronger electron-hole coherence between corresponding two atoms
Example (at ZINDO level):

104. S0->S1
Ld: Transition length
Lc: Coherent span

106. Main development plan Support calculating charge transfer integral
Support Atomic-Orbital-Symmetry Based sigma, pi and delta Decomposition Analysis of Bond Orders (AOSB)
Orbital localization
Support STO basis functions, and hence support ADF and STO version of BDF
On-line version of Multiwfn
Support distributed multipole analysis (DMA)
Support first-principles calculation programs, especially VASP and Crystal 09
Improve speed of ESP calculation

107. Multiwfn website: http://Multiwfn.codeplex.com
Discussion zone of Multiwfn:
QQ group for discussing Multiwfn and computational chemistry:
Any question or recommendation about Multiwfn please contact me via

108. Related posts Multiwfn 3.0波函数分析程序的意义、功能与用途
Multiwfn入门tips
《衡量芳香性的方法以及在Multiwfn中的计算》（
《制作动画分析电子结构特征》（
《电子定域性的图形分析》（
《使用Multiwfn图形化研究弱相互作用》（
加起来有20万字

109. 《使用Multiwfn做拓扑分析以及计算孤对电子角度》（http://hi. baidu
《使用Multiwfn绘制NBO及相关轨道》（
《谈谈轨道成份的计算方法》（
《使用AdNDP方法以及ELF/LOL、多中心键级研究多中心键》（
《使用Multiwfn绘制原子轨道图形、研究原子壳层结构及相对论效应的影响》（
《使用Multiwfn的定量分子表面分析功能预测反应位点、分析分子间相互作用》（

110. 《分子间轨道重叠的图形显示和计算》（http://hi. baidu
《分子间轨道重叠的图形显示和计算》（
《绘制跃迁密度矩阵平面图分析电子跃迁》（
《使用Multiwfn做电荷分解分析(CDA)、绘制轨道相互作用图》（
《使用Multiwfn做电子密度、ELF、静电势、密度差等函数的盆分析》 （
《杂谈Multiwfn从1.0到3.0版的开发经历》 （
《回答一些关于Multiwfn的疑问以及未来Multiwfn的发展打算》（
《谈谈分子体积的计算》（
《AIM键临界点处电子密度拉普拉斯值符号判断相互作用类型失败原因的图形分析》（

111. Welcome to participate in the 1st Multiwfn workshop!
August, 2013
Hai Dian district, Beijing, China
2~3 days
《量子化学波函数分析--原理与实践》