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Akef

Member

Registered: 2023-07-15

Posts: 10

How to get electron density, Laplacian of electron density and ELF?

Dear Sir
I have a question regarding the data presented in the attached image table below for MgH2. I tried to obtain the precise values for the first three entries in the attached image table (Columns 3-5) as indicated in the accompanying information. Unfortunately, my attempts were unsuccessful, and I am unsure of the source of the issue, despite using the same optimized geometry for this compound as detailed in the referenced paper. Could you please provide guidance on how to accurately acquire these values? Can you also clarify the method for obtaining these values?

----------------   CP     1,     Type (3,-3)   ----------------
Corresponding nucleus:     2(H )
Position (Bohr):        0.000000000000    0.000000000000    3.234990182304
Position (Angstrom):    0.000000000000    0.000000000000    1.711883081970
Density of all electrons:  0.2859123849E+00
Density of Alpha electrons:  0.1429561925E+00
Density of Beta electrons:  0.1429561925E+00
Spin density of electrons:  0.0000000000E+00
Lagrangian kinetic energy G(r):  0.8353885372E-03
G(r) in X,Y,Z:  0.6587947594E-06  0.6587947594E-06  0.8340709477E-03
Hamiltonian kinetic energy K(r):  0.4847582783E+01
Potential energy density V(r): -0.4848418171E+01
Energy density E(r) or H(r): -0.4847582783E+01
Laplacian of electron density: -0.1938698958E+02
Electron localization function (ELF):  0.9999943697E+00
Localized orbital locator (LOL):  0.9976607255E+00
Local information entropy:  0.7946581824E-01
Interaction region indicator (IRI):  0.1377899448E-14
Reduced density gradient (RDG):  0.1000000000E+03
Reduced density gradient with promolecular approximation:  0.1000000000E+03
Sign(lambda2)*rho: -0.2859123849E+00
Sign(lambda2)*rho with promolecular approximation: -0.2859993958E+00
Corr. hole for alpha, ref.:   0.00000   0.00000   0.00000 : -0.1290013554E-03
Source function, ref.:   0.00000   0.00000   0.00000 :  0.4769002453E+00
Wavefunction value for orbital       1 :  0.5068760802E-01
Average local ionization energy (ALIE):  0.0000000000E+00
van der Waals potential (probe atom: C ):  0.2597077372E+44 kcal/mol
Delta-g (under promolecular approximation):  0.9860070603E-02
Delta-g (under Hirshfeld partition):  0.9183522735E-02
User-defined real space function:  0.1000000000E+01
ESP from nuclear charges:  0.8277109152E+03
ESP from electrons: -0.4355111772E+01
Total ESP:  0.8233558034E+03 a.u. ( 0.2240465E+05 eV, 0.5166640E+06 kcal/mol)

Note: Below information are for electron density

Components of gradient in x/y/z are:
  0.0000000000E+00  0.0000000000E+00 -0.3475952165E-15
Norm of gradient is:  0.3475952165E-15

Components of Laplacian in x/y/z are:
-0.6464031596E+01 -0.6464031596E+01 -0.6458926384E+01
Total: -0.1938698958E+02

Hessian matrix:
-0.6464031596E+01  0.0000000000E+00  0.0000000000E+00
  0.0000000000E+00 -0.6464031596E+01  0.0000000000E+00
  0.0000000000E+00  0.0000000000E+00 -0.6458926384E+01
Eigenvalues of Hessian: -0.6464031596E+01 -0.6464031596E+01 -0.6458926384E+01
Eigenvectors (columns) of Hessian:
  0.1000000000E+01  0.0000000000E+00  0.0000000000E+00
  0.0000000000E+00  0.1000000000E+01  0.0000000000E+00
  0.0000000000E+00  0.0000000000E+00  0.1000000000E+01
Determinant of Hessian: -0.2698778713E+03
Ellipticity of electron density:    0.000000
eta index:   -1.000790

----------------   CP     2,     Type (3,-3)   ----------------
Corresponding nucleus:     1(Mg)
Position (Bohr):        0.000000000000    0.000000000000    0.000000350003
Position (Angstrom):    0.000000000000    0.000000000000    0.000000185214
Density of all electrons:  0.1056968865E+04
Density of Alpha electrons:  0.5284844326E+03
Density of Beta electrons:  0.5284844326E+03
Spin density of electrons:  0.0000000000E+00
Lagrangian kinetic energy G(r):  0.1444513333E+04
G(r) in X,Y,Z:  0.4762425043E+03  0.4762425043E+03  0.4920283245E+03
Hamiltonian kinetic energy K(r):  0.7542315441E+07
Potential energy density V(r): -0.7543759954E+07
Energy density E(r) or H(r): -0.7542315441E+07
Laplacian of electron density: -0.3016348371E+08
Electron localization function (ELF):  0.9999789579E+00
Localized orbital locator (LOL):  0.9954337292E+00
Local information entropy: -0.3264601751E+03
Interaction region indicator (IRI):  0.2680475097E-16
Reduced density gradient (RDG):  0.1000000000E+03
Reduced density gradient with promolecular approximation:  0.1000000000E+03
Sign(lambda2)*rho: -0.1056968865E+04
Sign(lambda2)*rho with promolecular approximation: -0.1053504338E+04
Corr. hole for alpha, ref.:   0.00000   0.00000   0.00000 : -0.5284844326E+03
Source function, ref.:   0.00000   0.00000   0.00000 :  0.6858041181E+13
Wavefunction value for orbital       1 :  0.3547976389E+01
Average local ionization energy (ALIE):  0.0000000000E+00
van der Waals potential (probe atom: C ):  0.2176208440+148 kcal/mol
Delta-g (under promolecular approximation):  0.2069795937E-02
Delta-g (under Hirshfeld partition):  0.8373786257E-02
User-defined real space function:  0.1000000000E+01
ESP from nuclear charges:  0.4252300554E+13
ESP from electrons: -0.4006708449E+02
Total ESP:  0.4252300554E+13 a.u. ( 0.1157110E+15 eV, 0.2668361E+16 kcal/mol)

Note: Below information are for electron density

Components of gradient in x/y/z are:
  0.0000000000E+00  0.0000000000E+00 -0.5684341886E-13
Norm of gradient is:  0.5684341886E-13

Components of Laplacian in x/y/z are:
-0.1005451567E+08 -0.1005451567E+08 -0.1005445237E+08
Total: -0.3016348371E+08

Hessian matrix:
-0.1005451567E+08  0.0000000000E+00  0.0000000000E+00
  0.0000000000E+00 -0.1005451567E+08  0.0000000000E+00
  0.0000000000E+00  0.0000000000E+00 -0.1005445237E+08
Eigenvalues of Hessian: -0.1005451567E+08 -0.1005451567E+08 -0.1005445237E+08
Eigenvectors (columns) of Hessian:
  0.1000000000E+01  0.0000000000E+00  0.0000000000E+00
  0.0000000000E+00  0.1000000000E+01  0.0000000000E+00
  0.0000000000E+00  0.0000000000E+00  0.1000000000E+01
Determinant of Hessian: -0.1016437623E+22
Ellipticity of electron density:    0.000000
eta index:   -1.000006

----------------   CP     3,     Type (3,-3)   ----------------
Corresponding nucleus:     3(H )
Position (Bohr):        0.000000000000    0.000000000000   -3.234994340655
Position (Angstrom):    0.000000000000    0.000000000000   -1.711885282475
Density of all electrons:  0.2859122208E+00
Density of Alpha electrons:  0.1429561104E+00
Density of Beta electrons:  0.1429561104E+00
Spin density of electrons:  0.0000000000E+00
Lagrangian kinetic energy G(r):  0.8353883105E-03
G(r) in X,Y,Z:  0.6587804754E-06  0.6587804754E-06  0.8340707496E-03
Hamiltonian kinetic energy K(r):  0.4847579042E+01
Potential energy density V(r): -0.4848414430E+01
Energy density E(r) or H(r): -0.4847579042E+01
Laplacian of electron density: -0.1938697462E+02
Electron localization function (ELF):  0.9999943697E+00
Localized orbital locator (LOL):  0.9976607239E+00
Local information entropy:  0.7946578434E-01
Interaction region indicator (IRI):  0.4796971281E-14
Reduced density gradient (RDG):  0.1000000000E+03
Reduced density gradient with promolecular approximation:  0.1000000000E+03
Sign(lambda2)*rho: -0.2859122208E+00
Sign(lambda2)*rho with promolecular approximation: -0.2859993625E+00
Corr. hole for alpha, ref.:   0.00000   0.00000   0.00000 : -0.1290014342E-03
Source function, ref.:   0.00000   0.00000   0.00000 :  0.4768992642E+00
Wavefunction value for orbital       1 :  0.3426754725E-01
Average local ionization energy (ALIE):  0.0000000000E+00
van der Waals potential (probe atom: C ):  0.2597035026E+44 kcal/mol
Delta-g (under promolecular approximation):  0.9860027808E-02
Delta-g (under Hirshfeld partition):  0.9183479148E-02
User-defined real space function:  0.1000000000E+01
ESP from nuclear charges:  0.8277097902E+03
ESP from electrons: -0.4355107030E+01
Total ESP:  0.8233546831E+03 a.u. ( 0.2240462E+05 eV, 0.5166633E+06 kcal/mol)

Note: Below information are for electron density

Components of gradient in x/y/z are:
  0.0000000000E+00  0.0000000000E+00  0.1210105150E-14
Norm of gradient is:  0.1210105150E-14

Components of Laplacian in x/y/z are:
-0.6464026617E+01 -0.6464026617E+01 -0.6458921380E+01
Total: -0.1938697462E+02

Hessian matrix:
-0.6464026617E+01  0.0000000000E+00  0.0000000000E+00
  0.0000000000E+00 -0.6464026617E+01  0.0000000000E+00
  0.0000000000E+00  0.0000000000E+00 -0.6458921380E+01
Eigenvalues of Hessian: -0.6464026617E+01 -0.6464026617E+01 -0.6458921380E+01
Eigenvectors (columns) of Hessian:
  0.1000000000E+01  0.0000000000E+00  0.0000000000E+00
  0.0000000000E+00  0.1000000000E+01  0.0000000000E+00
  0.0000000000E+00  0.0000000000E+00  0.1000000000E+01
Determinant of Hessian: -0.2698772465E+03
Ellipticity of electron density:    0.000000
eta index:   -1.000790

----------------   CP     4,     Type (3,-1)   ----------------
Connected atoms:     2(H )   --     1(Mg)
Position (Bohr):        0.000000000000    0.000000000000    1.799889972951
Position (Angstrom):    0.000000000000    0.000000000000    0.952460755818
Density of all electrons:  0.3242341335E-01
Density of Alpha electrons:  0.1621170668E-01
Density of Beta electrons:  0.1621170668E-01
Spin density of electrons:  0.0000000000E+00
Lagrangian kinetic energy G(r):  0.2860430907E-01
G(r) in X,Y,Z:  0.9576969559E-03  0.9576969559E-03  0.2668891516E-01
Hamiltonian kinetic energy K(r):  0.3044908266E-03
Potential energy density V(r): -0.2890879990E-01
Energy density E(r) or H(r): -0.3044908266E-03
Laplacian of electron density:  0.1131992730E+00
Electron localization function (ELF):  0.9864238361E-01
Localized orbital locator (LOL):  0.2486452000E+00
Local information entropy:  0.1405307581E-01
Interaction region indicator (IRI):  0.7538512331E-15
Reduced density gradient (RDG):  0.2711741471E-15
Reduced density gradient with promolecular approximation:  0.3237883853E+00
Sign(lambda2)*rho: -0.3242341335E-01
Sign(lambda2)*rho with promolecular approximation: -0.5989863012E-01
Corr. hole for alpha, ref.:   0.00000   0.00000   0.00000 : -0.1300761270E-05
Source function, ref.:   0.00000   0.00000   0.00000 : -0.5004812549E-02
Wavefunction value for orbital       1 : -0.4562646534E-02
Average local ionization energy (ALIE):  0.0000000000E+00
van der Waals potential (probe atom: C ):  0.3924939894E+07 kcal/mol
Delta-g (under promolecular approximation):  0.6766431210E-01
Delta-g (under Hirshfeld partition):  0.5972048373E-01
User-defined real space function:  0.1000000000E+01
ESP from nuclear charges:  0.7561868498E+01
ESP from electrons: -0.6577610941E+01
Total ESP:  0.9842575571E+00 a.u. ( 0.2678301E+02 eV, 0.6176315E+03 kcal/mol)

Note: Below information are for electron density

Components of gradient in x/y/z are:
  0.0000000000E+00  0.0000000000E+00  0.1734723476E-16
Norm of gradient is:  0.1734723476E-16

Components of Laplacian in x/y/z are:
-0.4221663186E-01 -0.4221663186E-01  0.1976325367E+00
Total:  0.1131992730E+00

Hessian matrix:
-0.4221663186E-01  0.0000000000E+00  0.0000000000E+00
  0.0000000000E+00 -0.4221663186E-01  0.0000000000E+00
  0.0000000000E+00  0.0000000000E+00  0.1976325367E+00
Eigenvalues of Hessian: -0.4221663186E-01 -0.4221663186E-01  0.1976325367E+00
Eigenvectors (columns) of Hessian:
  0.0000000000E+00  0.1000000000E+01  0.0000000000E+00
  0.1000000000E+01  0.0000000000E+00  0.0000000000E+00
  0.0000000000E+00  0.0000000000E+00  0.1000000000E+01
Determinant of Hessian:  0.3522294039E-03
Ellipticity of electron density:    0.000000
eta index:    0.213612

----------------   CP     5,     Type (3,-1)   ----------------
Connected atoms:     1(Mg)   --     3(H )
Position (Bohr):        0.000000000000    0.000000000000   -1.799890864500
Position (Angstrom):    0.000000000000    0.000000000000   -0.952461227606
Density of all electrons:  0.3242329925E-01
Density of Alpha electrons:  0.1621164962E-01
Density of Beta electrons:  0.1621164962E-01
Spin density of electrons:  0.0000000000E+00
Lagrangian kinetic energy G(r):  0.2860407971E-01
G(r) in X,Y,Z:  0.9576886106E-03  0.9576886106E-03  0.2668870249E-01
Hamiltonian kinetic energy K(r):  0.3045388403E-03
Potential energy density V(r): -0.2890861855E-01
Energy density E(r) or H(r): -0.3045388403E-03
Laplacian of electron density:  0.1131981635E+00
Electron localization function (ELF):  0.9864276600E-01
Localized orbital locator (LOL):  0.2486456022E+00
Local information entropy:  0.1405303451E-01
Interaction region indicator (IRI):  0.9046249816E-15
Reduced density gradient (RDG):  0.3254105034E-15
Reduced density gradient with promolecular approximation:  0.3237890188E+00
Sign(lambda2)*rho: -0.3242329925E-01
Sign(lambda2)*rho with promolecular approximation: -0.5989838431E-01
Corr. hole for alpha, ref.:   0.00000   0.00000   0.00000 : -0.1300631321E-05
Source function, ref.:   0.00000   0.00000   0.00000 : -0.5004761017E-02
Wavefunction value for orbital       1 : -0.6578846457E-02
Average local ionization energy (ALIE):  0.0000000000E+00
van der Waals potential (probe atom: C ):  0.3924840712E+07 kcal/mol
Delta-g (under promolecular approximation):  0.6766387856E-01
Delta-g (under Hirshfeld partition):  0.5972015774E-01
User-defined real space function:  0.1000000000E+01
ESP from nuclear charges:  0.7561861147E+01
ESP from electrons: -0.6577605743E+01
Total ESP:  0.9842554040E+00 a.u. ( 0.2678295E+02 eV, 0.6176301E+03 kcal/mol)

Note: Below information are for electron density

Components of gradient in x/y/z are:
  0.0000000000E+00  0.0000000000E+00 -0.2081668171E-16
Norm of gradient is:  0.2081668171E-16

Components of Laplacian in x/y/z are:
-0.4221630767E-01 -0.4221630767E-01  0.1976307788E+00
Total:  0.1131981635E+00

Hessian matrix:
-0.4221630767E-01  0.0000000000E+00  0.0000000000E+00
  0.0000000000E+00 -0.4221630767E-01  0.0000000000E+00
  0.0000000000E+00  0.0000000000E+00  0.1976307788E+00
Eigenvalues of Hessian: -0.4221630767E-01 -0.4221630767E-01  0.1976307788E+00
Eigenvectors (columns) of Hessian:
  0.1000000000E+01  0.0000000000E+00  0.0000000000E+00
  0.0000000000E+00  0.1000000000E+01  0.0000000000E+00
  0.0000000000E+00  0.0000000000E+00  0.1000000000E+01
Determinant of Hessian:  0.3522208613E-03
Ellipticity of electron density:    0.000000
eta index:    0.213612

sobereva

Tian Lu (Multiwfn developer)

From: Athens, Greece

Registered: 2017-09-11

Posts: 2,132

Website

Re: How to get electron density, Laplacian of electron density and ELF?

Hello,

I did the calculation at B3LYP/def2-TZVP level for MgH2 using Multiwfn, the data of the (3,-1) critical point between H and Mg is shown below; as you can see, electron density, Laplacian of electron density as well as ELF, are close to the corresponding data in your screenshot.

 Note: Unless otherwise specified, all units are in a.u.
 Position (Bohr):        0.000000000000    0.000000000000    1.652486507069
 Position (Angstrom):    0.000000000000    0.000000000000    0.874458200866
 CP type: (3,-1)
 Density of all electrons:  0.5469742512E-01
 Density of Alpha electrons:  0.2734871256E-01
 Density of Beta electrons:  0.2734871256E-01
 Spin density of electrons:  0.0000000000E+00
 Lagrangian kinetic energy G(r):  0.5838181073E-01
 G(r) in X,Y,Z:  0.2148998345E-02  0.2148998345E-02  0.5408381404E-01
 Hamiltonian kinetic energy K(r):  0.3819791954E-02
 Potential energy density V(r): -0.6220160269E-01
 Energy density E(r) or H(r): -0.3819791954E-02
 Laplacian of electron density:  0.2182480751E+00
 Electron localization function (ELF):  0.1305824033E+00
 Localized orbital locator (LOL):  0.2793399011E+00
 Local information entropy:  0.2166407157E-01
 Interaction region indicator (IRI):  0.1272295350E-15
 Reduced density gradient (RDG):  0.1000000000E+03
 Reduced density gradient with promolecular approximation:  0.5597729892E+00
 Sign(lambda2)*rho: -0.5469742512E-01
 Sign(lambda2)*rho with promolecular approximation: -0.7137381609E-01
 Corr. hole for alpha, ref.:   0.00000   0.00000   0.00000 : -0.2034958334E-04
 Source function, ref.:   0.00000   0.00000   0.00000 : -0.1050999806E-01
 Wavefunction value for orbital       1 : -0.1807371941E-03
 Average local ionization energy (ALIE):  0.7497048534E+00
 van der Waals potential (probe atom: C ):  0.2621679753E+07 kcal/mol
 Delta-g (under promolecular approximation):  0.5484493944E-01
 Delta-g (under Hirshfeld partition):  0.1073760025E+00
 User-defined real space function:  0.0000000000E+00
 ESP from nuclear charges:  0.8108603916E+01
 ESP from electrons: -0.7649101948E+01
 Total ESP:  0.4595019682E+00 a.u. ( 0.1250368E+02 eV, 0.2883421E+03 kcal/mol)