Validation¶

Validation methodology¶

In this section, a force field is constructed using the current version of QuickFF (i.e. 2.2.2), after which it is tested and evaluated for its ability to reproduce the ab initio input it was fitted to. The force field was constructed using the QuickFF script qff.py. The required ab initio input is contained in the file gaussian.fchk and the electrostatic partitioning in gaussian_mbis.h5. The Yaff parameter file for the electrostatic contribution is generated using

qff-input-ei.py -f –ffatypes=low –gaussian gaussian.fchk gaussian_mbis.h5:charges pars_ei_mbisgauss.txt

The config file containing the settings that are used for the force field is given by config.txt and can be viewed below. Furthermore, all required input files as well as the generated output can be found in the directory share/validation.

#IO
fn_yaff                 :   pars_cov.txt
fn_charmm22_prm         :   None
fn_charmm22_psf         :   None
fn_sys                  :   system.chk
plot_traj               :   final
xyz_traj                :   False
fn_traj                 :   None
log_level               :   medium
log_file                :   None

#Program
program_mode            :   DeriveFF

#FF config
only_traj               :   PT_ALL
ffatypes                :   low
ei                      :   pars_ei_mbisgauss.txt
ei_rcut                 :   None #default is 20 (periodic) or 50 (non-per) A
vdw                     :   None
vdw_rcut                :   20*angstrom
covres                  :   None

excl_bonds              :   None
excl_bends              :   None
excl_dihs               :   None
excl_oopds              :   None

do_hess_mass_weighting  :   True
do_hess_negfreq_proj    :   False
do_cross_svd            :   True
pert_traj_tol           :   1e-9
cross_svd_rcond         :   1e-9

do_bonds                :   True
do_bends                :   True
do_dihedrals            :   True
do_oops                 :   True
do_cross_ASS            :   True
do_cross_ASA            :   True
do_cross_DSS            :   False
do_cross_DSD            :   False
do_cross_DAA            :   False
do_cross_DAD            :   False

bond_term               :   BondHarm
bend_term               :   BendAHarm

do_squarebend           :   True
do_bendclin             :   True
do_sqoopdist_to_oopdist :   True

To evaluate the performance of the force field, it is applied to perform a basic geometry optimization followed by a normal mode analysis using Yaff and TAMkin. Finally, two validations are performed for each system:

the force field energy is compared to the ab initio energy along the perturbation trajectories that were constructed by QuickFF.
the geometry (i.e. bond lengths, bending angles, dihedral angles and ut-of-plane distances) and normal mode frequencies as predicted by the force field are compared with the given ab initio input. To this end, the following statistics are used:
- Root Mean Square Deviation (RMSD)
  
  $RMSD = \sqrt{\frac{1}{N}\sum_{i=1}^N \left(A_i - F_i\right)^2}$
- Mean Deviation (RMSD)
  
  $MD = \frac{1}{N}\sum_{i=1}^N \left(A_i-F_i\right)$
- Root Mean Square Error (RMSE)
  
  $RMSE = \sqrt{\frac{1}{N}\sum_{i=1}^N \left(A_i-F_i-MD\right)^2}$
These statistics satisfy the condition $RMDS^2=RMSE^2+MD^2$ .

Validation 1 - water¶

Force field construction¶

Averaged Atomic Charges:
------------------------
     H     0.451 +-  0.000 (N=2)
     O    -0.901 +-  0.000 (N=1)

#Fixed charges
#---------------

FIXQ:UNIT Q0 e
FIXQ:UNIT P e
FIXQ:UNIT R angstrom
FIXQ:SCALE 1 1.0
FIXQ:SCALE 2 1.0
FIXQ:SCALE 3 1.0
FIXQ:DIELECTRIC 1.0

# Atomic parameters
# ----------------------------------------------------
# KEY        label  Q_0A              R_A
# ----------------------------------------------------
FIXQ:ATOM        H  0.4506107006  0.7308000000
FIXQ:ATOM        O -0.9012712115  1.1325000000

________________/\\\_________/\\\\\\\\\\\\\\\__/\\\\\\\\\\\\\\\_________________
______________/\\\\/\\\\_____\/\\\///////////__\/\\\///////////_________________
_____________/\\\//\////\\\___\/\\\_____________\/\\\___________________________
_____________/\\\______\//\\\__\/\\\\\\\\\\\_____\/\\\\\\\\\\\__________________
_____________\//\\\______/\\\___\/\\\///////______\/\\\///////__________________
_______________\///\\\\/\\\\/____\/\\\_____________\/\\\________________________
__________________\////\\\//______\/\\\_____________\/\\\_______________________
______________________\///\\\\\\___\/\\\_____________\/\\\______________________
_________________________\//////____\///______________\///______________________

                            Welcom to QuickFF
   a Python package to quickly derive force fields from ab initio input data

                                 Written by
     Louis Vanduyfhuys(1)*, Steven Vandenbrande(1) and Toon Verstraelen(1)

         (1) Center for Molecular Modeling, Ghent University Belgium.
                   * mailto: Louis.Vanduyfhuys@UGent.be


 USER               louis
 MACHINE            Linux T085 4.15.0-39-generic #42-Ubuntu SMP Tue Oct 23 
 MACHINE            15:48:01 UTC 2018 x86_64
 TIME               2018-11-29 16:23:19.571237
 QUICKFF VERSION    2.2.1
 PYTHON VERSION     3.6.3 |Anaconda custom (64-bit)| (default, Oct 13 2017, 
 PYTHON VERSION     12:02:49) [GCC 7.2.0]
 NUMPY VERSION      1.13.3
 SCIPY VERSION      0.19.1
 MATPLOTLIB VERSION 2.1.0
 CURRENT DIR        /home/louis/build/quickff/share/validation/water
 COMMAND LINE       /home/louis/build/anaconda3/bin/qff.py -c ../config.txt 
 COMMAND LINE       gaussian.fchk

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 INIT   Initializing system
 INIT   Initializing Second order taylor reference for ai
 INIT   Initializing Yaff force field reference for EI

 INIT   Initializing program

 VAL    Initializing valence force field
 VAL    Added 2 bond terms
 VAL    Added 1 bend terms (an)harmonic in the angle, 0 bend terms with 
 VAL    1+cos(angle) potential and 0 bend terms with 1-cos(4*theta) potential.
 VAL    Added 0 Harmonic and 0 SquareHarmonic out-of-plane distance terms

 EQSET  Resetting system coordinates to ab initio ref
 EQSET  Setting rest values to AI equilibrium values for tasks EQ_RV
 EQSET  Averaging force field parameters over master and slaves

 PTGEN  Resetting system coordinates to ab initio ref
 PTGEN  Constructing trajectories

 PTEST  Resetting system coordinates to ab initio ref
 PTEST  Estimating FF parameters from perturbation trajectories

 PTPOST Averaging force field parameters over master and slaves

 VAL    Resetting system coordinates to ab initio ref

 HCEST  Resetting system coordinates to ab initio ref
 HCEST  Estimating force constants from Hessian cost for tasks HC_FC_DIAG HC_FC_
 HCEST  CROSS_ASS HC_FC_CROSS_ASA

 PTEST  Resetting system coordinates to ab initio ref
 PTEST  Estimating FF parameters from perturbation trajectories with valence 
 PTEST  reference

 PTPOST Averaging force field parameters over master and slaves

 HCEST  Resetting system coordinates to ab initio ref
 HCEST  Estimating force constants from Hessian cost for tasks HC_FC_DIAG HC_FC_
 HCEST  CROSS_ASS HC_FC_CROSS_ASA

 HCEST  Resetting system coordinates to ab initio ref
 HCEST  Estimating force constants from Hessian cost for tasks HC_FC_CROSS_ASS 
 HCEST  HC_FC_CROSS_ASA HC_FC_CROSS_DSS HC_FC_CROSS_DSD HC_FC_CROSS_DAA HC_FC_
 HCEST  CROSS_DAD


        BondHarm/H.O (kjmol/A^2  A)                                             
            fc =  4979 +- .000    rv = .9767 +- .000

        BendAHarm/H.O.H (kjmol/rad^2  deg)                                      
            fc = 346.5 +- .000    rv = 95.53 +- .000

        Cross/H.O.H/b0a (kjmol/A  A  deg)                                       
            fc =  145 +- .0    rv0 = .971 +- 0.0    rv1 = 96.0 +- 0.0

        Cross/H.O.H/b1a (kjmol/A  A  deg)                                       
            fc =  145 +- .0    rv0 = .971 +- 0.0    rv1 = 96.0 +- 0.0

        Cross/H.O.H/bb (kjmol/A^2  A  A)                                        
            fc = -110 +- .0    rv0 = .971 +- 0.0    rv1 = .971 +- 0.0

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


 TIMING Initializing                    0:00:00.041719
 TIMING Equil Set RV                    0:00:00.000183
 TIMING PT Generate                     0:00:00.210871
 TIMING PT Estimate                     0:00:00.012061
 TIMING PT Post process                 0:00:00.000409
 TIMING HC Estimate FC                  0:00:00.031958
 TIMING PT plot energy                  0:00:00.514098

__/\\\__________________________________________________________________/\\\____
  \ \\\                                                                 \ \\\
   \ \\\     End of file. Thanks for using QuickFF! Come back soon!!     \ \\\
____\///__________________________________________________________________\///__

# BONDHARM
#---------
BONDHARM:UNIT  K kjmol/A**2
BONDHARM:UNIT  R0 A

BONDHARM:PARS         H         O  4.9793007398e+03  9.7671602900e-01


# BENDAHARM
#----------
BENDAHARM:UNIT  K kjmol/rad**2
BENDAHARM:UNIT  THETA0 deg

BENDAHARM:PARS         H         O         H  3.4652118756e+02  9.5532795842e+01


# Cross
#------
Cross:UNIT  KSS kjmol/angstrom**2
Cross:UNIT  KBS0 kjmol/(angstrom*rad)
Cross:UNIT  KBS1 kjmol/(angstrom*rad)
Cross:UNIT  R0 angstrom
Cross:UNIT  R1 angstrom
Cross:UNIT  THETA0 deg

Cross:PARS         H         O         H  -1.1006640167e+02   1.4564327376e+02   1.4564327376e+02  9.7199818096e-01  9.7199818096e-01  9.6002094143e+01

Force field evaluation¶

Perturbation trajectories¶

The figures below illustrate the reproduction of the ab initio energy along the constructed perturbation trajectories. For water, there are 3 such trajectories, two bonds and one bend.

First O-H bond:

_images/trajectory-BondHarm-H.O-0_Ehc3.png

Second O-H bond:

_images/trajectory-BondHarm-H.O-1_Ehc3.png

H-O-H bend:

_images/trajectory-BendAHarm-H.O.H-2_Ehc3.png

Geometry and frequencies¶

OBSERVABLE  [UNIT]  |      RMSD      |       MD       |      RMSE      
--------------------|----------------|----------------|----------------
                    |                |                |                
GEOMETRY            |                |                |                
  Bonds         [A] |    7.214e-05   |   -7.214e-05   |    0.000e+00    
  Bends       [deg] |    5.485e-02   |    5.485e-02   |    0.000e+00    
  Dihedrals   [deg] |         -      |        -       |          -     
  Opdists       [A] |         -      |        -       |          -     
                    |                |                |                
FREQUENCIES  [1/cm] |                |                |                
  All               |    7.656e-02   |   -2.408e-02   |    7.267e-02    
     0 -  100       |         -      |        -       |          -     
   100 -  500       |         -      |        -       |          -     
   500 - 1000       |         -      |        -       |          -     
  1000 - 3000 (  1) |    7.841e-02   |    7.841e-02   |    0.000e+00   
  3000 -  inf (  2) |    7.561e-02   |   -7.533e-02   |    6.554e-03

Validation 2 - benzene¶

Force field construction¶

Averaged Atomic Charges:
------------------------
     H     0.131 +-  0.000 (N=6)
     C    -0.132 +-  0.001 (N=6)

#Fixed charges
#---------------

FIXQ:UNIT Q0 e
FIXQ:UNIT P e
FIXQ:UNIT R angstrom
FIXQ:SCALE 1 1.0
FIXQ:SCALE 2 1.0
FIXQ:SCALE 3 1.0
FIXQ:DIELECTRIC 1.0

# Atomic parameters
# ----------------------------------------------------
# KEY        label  Q_0A              R_A
# ----------------------------------------------------
FIXQ:ATOM        H  0.1314377213  0.7308000000
FIXQ:ATOM        C -0.1315514661  1.1703000000

________________/\\\_________/\\\\\\\\\\\\\\\__/\\\\\\\\\\\\\\\_________________
______________/\\\\/\\\\_____\/\\\///////////__\/\\\///////////_________________
_____________/\\\//\////\\\___\/\\\_____________\/\\\___________________________
_____________/\\\______\//\\\__\/\\\\\\\\\\\_____\/\\\\\\\\\\\__________________
_____________\//\\\______/\\\___\/\\\///////______\/\\\///////__________________
_______________\///\\\\/\\\\/____\/\\\_____________\/\\\________________________
__________________\////\\\//______\/\\\_____________\/\\\_______________________
______________________\///\\\\\\___\/\\\_____________\/\\\______________________
_________________________\//////____\///______________\///______________________

                            Welcom to QuickFF
   a Python package to quickly derive force fields from ab initio input data

                                 Written by
     Louis Vanduyfhuys(1)*, Steven Vandenbrande(1) and Toon Verstraelen(1)

         (1) Center for Molecular Modeling, Ghent University Belgium.
                   * mailto: Louis.Vanduyfhuys@UGent.be


 USER               louis
 MACHINE            Linux T085 4.15.0-39-generic #42-Ubuntu SMP Tue Oct 23 
 MACHINE            15:48:01 UTC 2018 x86_64
 TIME               2018-11-29 16:23:22.266821
 QUICKFF VERSION    2.2.1
 PYTHON VERSION     3.6.3 |Anaconda custom (64-bit)| (default, Oct 13 2017, 
 PYTHON VERSION     12:02:49) [GCC 7.2.0]
 NUMPY VERSION      1.13.3
 SCIPY VERSION      0.19.1
 MATPLOTLIB VERSION 2.1.0
 CURRENT DIR        /home/louis/build/quickff/share/validation/benzene
 COMMAND LINE       /home/louis/build/anaconda3/bin/qff.py -c ../config.txt 
 COMMAND LINE       gaussian.fchk

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 INIT   Initializing system
 INIT   Initializing Second order taylor reference for ai
 INIT   Initializing Yaff force field reference for EI

 INIT   Initializing program

 VAL    Initializing valence force field
 VAL    Added 12 bond terms
 VAL    Added 18 bend terms (an)harmonic in the angle, 0 bend terms with 
 VAL    1+cos(angle) potential and 0 bend terms with 1-cos(4*theta) potential.
 VAL    Added 6 Harmonic and 0 SquareHarmonic out-of-plane distance terms

 EQSET  Resetting system coordinates to ab initio ref
 EQSET  Setting rest values to AI equilibrium values for tasks EQ_RV
 EQSET  Averaging force field parameters over master and slaves

 PTGEN  Resetting system coordinates to ab initio ref
 PTGEN  Constructing trajectories

 PTEST  Resetting system coordinates to ab initio ref
 PTEST  Estimating FF parameters from perturbation trajectories

 PTPOST Averaging force field parameters over master and slaves

 VAL    Resetting system coordinates to ab initio ref

 HCEST  Resetting system coordinates to ab initio ref
 HCEST  Estimating force constants from Hessian cost for tasks HC_FC_DIAG HC_FC_
 HCEST  CROSS_ASS HC_FC_CROSS_ASA

 PTEST  Resetting system coordinates to ab initio ref
 PTEST  Estimating FF parameters from perturbation trajectories with valence 
 PTEST  reference

 PTPOST Averaging force field parameters over master and slaves

 HCEST  Resetting system coordinates to ab initio ref
 HCEST  Estimating force constants from Hessian cost for tasks HC_FC_DIAG HC_FC_
 HCEST  CROSS_ASS HC_FC_CROSS_ASA

 HCEST  Resetting system coordinates to ab initio ref
 HCEST  Estimating force constants from Hessian cost for tasks HC_FC_CROSS_ASS 
 HCEST  HC_FC_CROSS_ASA HC_FC_CROSS_DSS HC_FC_CROSS_DSD HC_FC_CROSS_DAA HC_FC_
 HCEST  CROSS_DAD


        BondHarm/C.C (kjmol/A^2  A)                                             
            fc =  3965 +- .000    rv = 1.394 +- .000

        BondHarm/C.H (kjmol/A^2  A)                                             
            fc =  3333 +- .000    rv = 1.087 +- .000

        BendAHarm/C.C.C (kjmol/rad^2  deg)                                      
            fc = 601.9 +- .000    rv = 119.9 +- .000

        BendAHarm/C.C.H (kjmol/rad^2  deg)                                      
            fc = 320.9 +- .000    rv = 120.1 +- .000

        TorsCheby2/C.C.C.C (kjmol  au)                                          
            fc  = 35.9 +- 0.0    sgn =  -1

        TorsCheby2/C.C.C.H (kjmol  au)                                          
            fc  = 31.4 +- 0.0    sgn =  -1

        TorsCheby2/H.C.C.H (kjmol  au)                                          
            fc  = 16.8 +- .00    sgn =  -1

        Oopdist/C.C.H.C (kjmol/A^2  A)                                          
            fc = 166.2 +- .000    rv = .0000 +- .000

        Cross/C.C.C/b0a (kjmol/A  A  deg)                                       
            fc = 49.2 +- .0    rv0 = 1.39 +- 0.0    rv1 =  120 +- 0.0

        Cross/C.C.C/b1a (kjmol/A  A  deg)                                       
            fc = 49.3 +- .0    rv0 = 1.39 +- 0.0    rv1 =  120 +- 0.0

        Cross/C.C.C/bb (kjmol/A^2  A  A)                                        
            fc =  525 +- .0    rv0 = 1.39 +- 0.0    rv1 = 1.39 +- 0.0

        Cross/C.C.H/b0a (kjmol/A  A  deg)                                       
            fc =  113 +- .0    rv0 = 1.39 +- .00    rv1 =  120 +- .00

        Cross/C.C.H/b1a (kjmol/A  A  deg)                                       
            fc =  139 +- .0    rv0 = 1.08 +- .00    rv1 =  120 +- .00

        Cross/C.C.H/bb (kjmol/A^2  A  A)                                        
            fc = 40.3 +- .0    rv0 = 1.39 +- .00    rv1 = 1.08 +- .00

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


 TIMING Initializing                    0:00:00.109844
 TIMING Equil Set RV                    0:00:00.001019
 TIMING PT Generate                     0:00:06.375875
 TIMING PT Estimate                     0:00:00.159069
 TIMING PT Post process                 0:00:00.003885
 TIMING HC Estimate FC                  0:00:00.346235
 TIMING PT plot energy                  0:00:05.643349

__/\\\__________________________________________________________________/\\\____
  \ \\\                                                                 \ \\\
   \ \\\     End of file. Thanks for using QuickFF! Come back soon!!     \ \\\
____\///__________________________________________________________________\///__

# BONDHARM
#---------
BONDHARM:UNIT  K kjmol/A**2
BONDHARM:UNIT  R0 A

BONDHARM:PARS         C         H  3.3330947115e+03  1.0876030745e+00
BONDHARM:PARS         C         C  3.9651511136e+03  1.3940024805e+00


# BENDAHARM
#----------
BENDAHARM:UNIT  K kjmol/rad**2
BENDAHARM:UNIT  THETA0 deg

BENDAHARM:PARS         C         C         H  3.2097790994e+02  1.2015408782e+02
BENDAHARM:PARS         C         C         C  6.0195059267e+02  1.1997128609e+02


# TORSION
#--------
TORSION:UNIT  A kjmol
TORSION:UNIT  PHI0 deg

TORSION:PARS         C         C         C         H  2 3.1428590550e+01  0.0000000000e+00
TORSION:PARS         C         C         C         C  2 3.5982599978e+01  0.0000000000e+00
TORSION:PARS         H         C         C         H  2 1.6841710927e+01  0.0000000000e+00


# OOPDIST
#--------
OOPDIST:UNIT  K kjmol/A**2
OOPDIST:UNIT  D0 A

OOPDIST:PARS         C         C         H         C  1.6627861970e+02  4.7922360401e-17


# Cross
#------
Cross:UNIT  KSS kjmol/angstrom**2
Cross:UNIT  KBS0 kjmol/(angstrom*rad)
Cross:UNIT  KBS1 kjmol/(angstrom*rad)
Cross:UNIT  R0 angstrom
Cross:UNIT  R1 angstrom
Cross:UNIT  THETA0 deg

Cross:PARS         C         C         H   4.0314250860e+01   1.1314941661e+02   1.3908938734e+02  1.3934733019e+00  1.0875970644e+00  1.2001586285e+02
Cross:PARS         C         C         C   5.2510973026e+02   4.9272567406e+01   4.9272567406e+01  1.3934733019e+00  1.3934733019e+00  1.2003594733e+02

Force field evaluation¶

Perturbation trajectories¶

The figures below illustrate the reproduction of the ab initio energy along the constructed perturbation trajectories. For water, there are 3 such trajectories, two bonds and one bend.

C-H bonds:

_images/trajectory-BondHarm-C.H-0_Ehc3.png

_images/trajectory-BondHarm-C.H-7_Ehc3.png

_images/trajectory-BondHarm-C.H-8_Ehc3.png

_images/trajectory-BondHarm-C.H-9_Ehc3.png

_images/trajectory-BondHarm-C.H-10_Ehc3.png

_images/trajectory-BondHarm-C.H-11_Ehc3.png

C-C bonds:

_images/trajectory-BondHarm-C.C-1_Ehc3.png

_images/trajectory-BondHarm-C.C-2_Ehc3.png

_images/trajectory-BondHarm-C.C-3_Ehc3.png

_images/trajectory-BondHarm-C.C-4_Ehc3.png

_images/trajectory-BondHarm-C.C-5_Ehc3.png

_images/trajectory-BondHarm-C.C-6_Ehc3.png

C-C-C bends:

_images/trajectory-BendAHarm-C.C.C-24_Ehc3.png

_images/trajectory-BendAHarm-C.C.C-25_Ehc3.png

_images/trajectory-BendAHarm-C.C.C-26_Ehc3.png

_images/trajectory-BendAHarm-C.C.C-27_Ehc3.png

_images/trajectory-BendAHarm-C.C.C-28_Ehc3.png

_images/trajectory-BendAHarm-C.C.C-29_Ehc3.png

C-C-H bends:

_images/trajectory-BendAHarm-C.C.H-12_Ehc3.png

_images/trajectory-BendAHarm-C.C.H-13_Ehc3.png

_images/trajectory-BendAHarm-C.C.H-14_Ehc3.png

_images/trajectory-BendAHarm-C.C.H-15_Ehc3.png

_images/trajectory-BendAHarm-C.C.H-16_Ehc3.png

_images/trajectory-BendAHarm-C.C.H-17_Ehc3.png

C-C-H-C out-of-plane distances:

_images/trajectory-Oopdist-C.C.H.C-54_Ehc3.png

_images/trajectory-Oopdist-C.C.H.C-55_Ehc3.png

_images/trajectory-Oopdist-C.C.H.C-56_Ehc3.png

_images/trajectory-Oopdist-C.C.H.C-57_Ehc3.png

_images/trajectory-Oopdist-C.C.H.C-58_Ehc3.png

_images/trajectory-Oopdist-C.C.H.C-59_Ehc3.png

Geometry and frequencies¶

OBSERVABLE  [UNIT]  |      RMSD      |       MD       |      RMSE      
--------------------|----------------|----------------|----------------
                    |                |                |                
GEOMETRY            |                |                |                
  Bonds         [A] |    3.530e-04   |   -2.392e-04   |    2.596e-04    
  Bends       [deg] |    9.492e-08   |    7.105e-15   |    9.492e-08    
  Dihedrals   [deg] |    5.371e-16   |    1.643e-32   |    5.371e-16    
  Opdists       [A] |    5.587e-18   |    4.747e-18   |    2.947e-18    
                    |                |                |                
FREQUENCIES  [1/cm] |                |                |                
  All               |    2.338e+01   |    1.057e+00   |    2.335e+01    
     0 -  100       |         -      |        -       |          -     
   100 -  500 (  2) |    1.701e+01   |    1.700e+01   |    4.160e-01   
   500 - 1000 (  8) |    1.470e+01   |   -6.089e+00   |    1.338e+01   
  1000 - 3000 ( 14) |    3.163e+01   |    3.301e+00   |    3.146e+01   
  3000 -  inf (  6) |    3.739e+00   |    3.573e-02   |    3.739e+00