| Chapter 28. PATH Calculation with Transition Vector | ||
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Part II. AMPAC™ 10 Examples |  |
| Chapter 28. PATH Calculation with Transition Vector | ||
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Part II. AMPAC™ 10 Examples | |
Table of Contents
The PATH algorithm in AMPAC™ is designed to follow the steepest descent path from a point on the potential surface to its conclusion. It performs this numerical task by integrating the reaction path and following the force it is supplied with or that it detects (see the section called “Integration of a Reaction Path in PATH or IRC” for a discussion on the theory of integrating reaction pathways). The PATH technique is useful for several tasks:
Following an identified T.V. to determine if the transition state that has been located corresponds to the reaction mechanism and products desired. This is also important in that the reverse of the T.V. should also be followed to reactants to ensure that it does correspond to a pathway between reactants and products. Note that the TV supplied to PATH must be the result of an LTRD calculation.
Following other negative eigenvalues to refine a transition state by eliminating spurious vibrations. PATH is very efficient at this, one of the most difficult obstacles in the computational study of transition states and reaction mechanisms.
To computationally explore the results of selectively exciting a particular vibrational mode by some experimental technique.
To locate a weak intermediate between a transition state and a minimum.
The example that will be used to illustrate the use of PATH is the three-fold dissociation of triazine into three separate HCN molecules. This is the same reaction described in the preceeding example.
In previous versions of AMPAC, the transition vector
to be followed had to be specified by the user. This PATH example utilizes the
T.V. keyword, where the user specifies the exact
transition vector to be followed in the extra input section. This is primarily for backward
compatibility and is useful only if the user wants to explicitly control the definition of the
transition vector. The subsequent IRC example utilizes
T.V.=n, where the
transition vector for the specified mode is computed automatically. (A version of this PATH example
using the T.V.=n keyword can be found in the test suite as irc/path.dat.)
am1 uhf singlet path t=auto t.v. weight gradients Triple Wammy (C3H3N3 -> 3HCN) PATH - Read in TV and Weight N 0.000000 0 0.000000 0 0.000000 0 0 0 0C 2.167880 1 0.000000 0 0.000000 0 1 0 0 N 1.202180 1 113.155540 1 0.000000 0 2 1 0 C 1.966090 1 119.158120 1 -0.225080 1 3 2 1 N 1.204290 1 117.797000 1 0.208860 1 4 3 2 C 1.232120 1 113.400400 1 0.138660 1 1 2 3 H 1.072690 1 84.948440 1 -179.892470 1 2 1 6 H 1.074200 1 90.932120 1 -179.793900 1 4 3 2 H 1.105800 1 130.401600 1 -179.962710 1 6 1 2 0 0.000000 0 0.000000 0 0.000000 0 0 0 0 $$ weight - transition vector weights
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 $$ t.v. - transition vector coordinates
-0.6491 0.0895 0.1390 -0.6234 -0.0818 0.0000 0.1023 0.1930 0.0000 0.0964
-0.0773 0.0000 0.0162 0.1837 -0.0000 0.0124 0.1666 -0.0000 0.0193 -0.1753 0.0000 $$ end of extra data
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The geometry provided to PATH is the transition state geometry. |
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This is the extra input section marker for the weights on the transition vector. Note, that this marker can be shortened to “$$ weig”. Details of these markers are found in the section called “Extra Input Data”. |
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These are the weights of the transition vector components, and are supplied because the keyword WEIGHT was specified. PATH works in internal coordinates, so there must be one weight for each internal coordinate (in this case 21) and must appear in the same order that they appear in the input geometry. This case is primarily for demonstration, so all of the weights have been set to 1.0000, which is identical to defaults used if WEIGHT is not present. One can increase or decrease these weights to enhance or deemphasize a given component of the transition vector. |
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This is the extra input section marker for the components of the transition vector. Note, that this marker can be shortened to “$$ t.v.”. Details of these markers are found in the section called “Extra Input Data”. |
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This is the oriented transition vector (T.V.) in internal coordinates as requested by the T.V. keyword. This information may be obtained from an LTRD calculation. Using this input file but removing keywords “IRC”, “T.V.”, and “WEIGHT” and adding “LTRD” and “PRINT=2” will generate an eigenvector needed for T.V. The resulting keyword line would look like: am1 uhf singlet t=1h gradients ltrd print=2 The eigenvectors can be found in the output file as follows.
AND FIRST EIGENVECTORS:
1 -0.6491 0.0895 0.1390 -0.6234 -0.0818 0.0000 0.1023 0.1930 0.0000
0.0964 -0.0773 0.0000 0.0162 0.1837 -0.0000 0.0124 0.1666 -0.0000
0.0193 -0.1753 0.0000
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Timestamp: 2011-08-31-12-49-09-000000141C-win64
User Info: John Millam, Nahum,
SUMMARY OF AM1 CALCULATION
Aug-31-2011
AMPAC Version 10.0.1
Presented by:
Semichem, Inc.
www.semichem.com
FORMULA: C3H3N3
Triple Wammy (C3H3N3 -> 3HCN)
PATH - Read in TV and Weight
SCF FIELD WAS ACHIEVED
FINAL HEAT OF FORMATION = 167.958424 kcal
= 702.906006 kJ
ELECTRONIC ENERGY = -3333.260540 eV
CORE-CORE REPULSION = 2292.974752 eV
TOTAL ENERGY = -1040.285787 eV
GRADIENT NORM = 70.375439
RMS GRADIENT NORM = 15.357180
FOR REACTION COORDINATE = 0.000000 angstroms or radians
IONIZATION POTENTIAL = 9.029155 eV
HOMO-LUMO GAP = 8.718548 eV
DIPOLE = 2.114237 debyes
MOLECULAR WEIGHT = 81.076800
MOLECULAR POINT GROUP = Cs 0.100000
(SZ) = 0.000000
(S**2) = 0.000000
NO. OF ALPHA ELECTRONS = 15
NO. OF BETA ELECTRONS = 15
TOTAL NUMBER OF ORBITALS = 27
COMPUTATION TIME = 3.23 SECONDS
FINAL GEOMETRY OBTAINED CHARGE
AM1 UHF SINGLET PATH T=AUTO T.V. WEIGHT GRADIENTS
Triple Wammy (C3H3N3 -> 3HCN)
PATH - Read in TV and Weight
N 0.000000 0 0.000000 0 0.000000 0 0 0 0 -0.2979
C 2.167880 1 0.000000 0 0.000000 0 1 0 0 -0.0297
N 1.202180 1 113.155540 1 0.000000 0 2 1 0 -0.2147
C 1.966090 1 119.158120 1 -0.225080 1 3 2 1 0.0331
N 1.204290 1 117.797000 1 0.208860 1 4 3 2 -0.1132
C 1.232120 1 113.400400 1 0.138660 1 1 2 3 -0.0673
H 1.072690 1 84.948440 1 -179.892470 1 2 1 6 0.2602
H 1.074200 1 90.932120 1 -179.793900 1 4 3 2 0.2632
H 1.105800 1 130.401600 1 -179.962710 1 6 1 2 0.1662
0 0.000000 0 0.000000 0 0.000000 0 0 0 0
========
Timestamp: 2011-08-31-12-49-09-000000141C-win64
User Info: John Millam, Nahum,
SUMMARY OF AM1 CALCULATION
Aug-31-2011
AMPAC Version 10.0.1
Presented by:
Semichem, Inc.
www.semichem.com
FORMULA: C3H3N3
Triple Wammy (C3H3N3 -> 3HCN)
PATH - Read in TV and Weight
SCF FIELD WAS ACHIEVED
FINAL HEAT OF FORMATION = 58.008859 kcal
= 242.767074 kJ
ELECTRONIC ENERGY = -3510.280310 eV
CORE-CORE REPULSION = 2465.226751 eV
TOTAL ENERGY = -1045.053558 eV
GRADIENT NORM = 0.447407
RMS GRADIENT NORM = 0.097632
UNSTABLE MODE(S) = 9 ( ESTIMATE )
FOR REACTION COORDINATE = 1.550959 angstroms or radians
IONIZATION POTENTIAL = 11.317693 eV
HOMO-LUMO GAP = 10.764985 eV
DIPOLE = 0.002177 debyes
MOLECULAR WEIGHT = 81.076800
MOLECULAR POINT GROUP = D3h 0.100000
(SZ) = 0.000000
(S**2) = 0.000000
NO. OF ALPHA ELECTRONS = 15
NO. OF BETA ELECTRONS = 15
TOTAL NUMBER OF ORBITALS = 27
COMPUTATION TIME = 3.65 SECONDS
FINAL GEOMETRY OBTAINED CHARGE
AM1 UHF SINGLET PATH T=AUTO T.V. WEIGHT GRADIENTS
Triple Wammy (C3H3N3 -> 3HCN)
PATH - Read in TV and Weight
N 0.000000 0 0.000000 0 0.000000 0 0 0 0 -0.1905
C 1.364273 1 0.000000 0 0.000000 0 1 0 0 -0.0096
N 1.363786 1 125.763994 1 0.000000 0 2 1 0 -0.1901
C 1.364340 1 114.225219 1 -0.082786 1 3 2 1 -0.0095
N 1.363745 1 125.758251 1 0.064912 1 4 3 2 -0.1904
C 1.363858 1 114.267735 1 0.051211 1 1 2 3 -0.0094
H 1.110061 1 116.976906 1 -179.972523 1 2 1 6 0.1998
H 1.110056 1 117.024346 1 -179.927893 1 4 3 2 0.1998
H 1.110002 1 117.228854 1 -179.991983 1 6 1 2 0.1999
0 0.000000 0 0.000000 0 0.000000 0 0 0 0
Timestamp: 2011-08-31-12-49-09-000000141C-win64
User Info: John Millam, Nahum,
*******************************************************************************
AM1 CALCULATION RESULTS
*******************************************************************************
* AMPAC Version 10.0.1
* Presented by:
*
* Semichem, Inc.
* www.semichem.com
*
* AM1 - THE AM1 HAMILTONIAN TO BE USED
* UHF - UNRESTRICTED HARTREE-FOCK CALCULATION
* PATH - FOLLOW THE STEEPEST DESCENT PATH
* T.V. - TRANSITION VECTOR TO BE PROVIDED FOR PATH
* WEIGHT - WEIGHT TO BE PROVIDED FOR PATH
* T=AUTO - AUTOMATIC DETERMINATION OF ALLOWED TIME
* GRADIENTS- ALL GRADIENTS TO BE PRINTED
* SINGLET - IS THE REQUIRED SPIN MULTIPLICITY
*******************************************************************************
AM1 UHF SINGLET PATH T=AUTO T.V. WEIGHT GRADIENTS
Triple Wammy (C3H3N3 -> 3HCN)
PATH - Read in TV and Weight
ATOM CHEMICAL BOND LENGTH BOND ANGLE TWIST ANGLE
NUMBER SYMBOL (ANGSTROMS) (DEGREES) (DEGREES)
(I) NA:I NB:NA:I NC:NB:NA:I NA NB NC
1 N
2 C 2.16788 * 1
3 N 1.20218 * 113.15554 * 2 1
4 C 1.96609 * 119.15812 * -0.22508 * 3 2 1
5 N 1.20429 * 117.79700 * 0.20886 * 4 3 2
6 C 1.23212 * 113.40040 * 0.13866 * 1 2 3
7 H 1.07269 * 84.94844 * -179.89247 * 2 1 6
8 H 1.07420 * 90.93212 * -179.79390 * 4 3 2
9 H 1.10580 * 130.40160 * -179.96271 * 6 1 2
MOLECULAR POINT GROUP SYMMETRY CRITERIA
Cs 0.10000000
SINGLET STATE CALCULATION
UHF CALCULATION, NO. OF ALPHA ELECTRONS = 15
NO. OF BETA ELECTRONS = 15
** REFERENCES TO PARAMETERS **
H (AM1): M.J.S. DEWAR ET AL, J. AM. CHEM. SOC. 107 3902-3909 (1985).
C (AM1): M.J.S. DEWAR ET AL, J. AM. CHEM. SOC. 107 3902-3909 (1985).
N (AM1): M.J.S. DEWAR ET AL, J. AM. CHEM. SOC. 107 3902-3909 (1985).
CARTESIAN COORDINATES
ATOM X Y Z
1 N 0.00000000 0.00000000 0.00000000
2 C 2.16788000 0.00000000 0.00000000
3 N 2.64061152 1.10533328 0.00000000
4 C 1.43867741 2.66123135 -0.00674480
5 N 0.25228034 2.45440685 -0.00682707
6 C -0.48934175 1.13077710 -0.00273657
7 H 2.07342731 -1.06852337 0.00058055
8 H 2.27797559 3.33166458 -0.00861251
9 H -1.54681662 1.45410433 -0.00297099
STANDARD DEVIATION ON ENERGY (KCAL) 0.00000055521
STANDARD DEVIATION ON GRADIENT (KCAL/A,RD,RD) 0.00010723 0.00019916 0.00012867
REACTION PATH...VERSION 1.3 (NOVEMBER 2006)
MIN/MAX STEPS : 0.00150 0.02100 WITH REQUIRED ACCURACY :0.000600
MAX ITERATIONS= 710 PRINTOUT LEVEL = 0
CONV. THRESHOLD ON RMS-G = 1.0D-01
STANDARD DEVIATION ON GRADIENT 1.1D-04 2.0D-04 1.3D-04
STARTING POINT ENERGY= 1.6796D+02, RMS-G = 1.536D+01
WEIGHTS 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
1.000 1.000 1.000
ORIENTED T.V. -0.6491 0.0895 0.1390 -0.6234 -0.0818 0.0000 0.1023 0.1930
0.0000 0.0964 -0.0773 0.0000 0.0162 0.1837 0.0000 0.0124 0.1666 0.0000
0.0193 -0.1753 0.0000
CRUDE MOVE ALONG THE TRANSITION VECTOR:
LENGTH= 0.0000 E= 1.6796D+02 RMS-G= 15.3572 (TV,G) COSINE= 0.21 +- 0.000
LENGTH= 0.0040 E= 1.6802D+02 RMS-G= 15.4013 (TV,G) COSINE= 0.20 +- 0.000
LENGTH= 0.0080 E= 1.6807D+02 RMS-G= 15.4492 (TV,G) COSINE= 0.18 +- 0.000
LENGTH= 0.0120 E= 1.6812D+02 RMS-G= 15.5012 (TV,G) COSINE= 0.17 +- 0.000
LENGTH= 0.0160 E= 1.6817D+02 RMS-G= 15.5575 (TV,G) COSINE= 0.15 +- 0.000
LENGTH= 0.0240 E= 1.6825D+02 RMS-G= 15.6846 (TV,G) COSINE= 0.12 +- 0.000
LENGTH= 0.0320 E= 1.6831D+02 RMS-G= 15.8332 (TV,G) COSINE= 0.09 +- 0.000
LENGTH= 0.0400 E= 1.6836D+02 RMS-G= 16.0062 (TV,G) COSINE= 0.06 +- 0.000
LENGTH= 0.0480 E= 1.6838D+02 RMS-G= 16.2063 (TV,G) COSINE= 0.03 +- 0.000
LENGTH= 0.0640 E= 1.6839D+02 RMS-G= 16.7001 (TV,G) COSINE= -0.03 +- 0.000
START EULER-CAUCHY PREDICTOR-CORRECTOR AT ITERATION 9
WITH ENERGY= 1.68386949D+02 RMS-G= 1.6700D+01 AND LENGTH= 0.064000
START EXPONENTIAL PREDICTOR-CORRECTOR AT ITERATION 10
WITH ENERGY= 1.68179392D+02 RMS-G= 1.3856D+01 AND LENGTH= 0.067007
WHAO ... CONVERGENCE ACHIEVED.
AM1 UHF SINGLET PATH T=AUTO T.V. WEIGHT GRADIENTS
Triple Wammy (C3H3N3 -> 3HCN)
PATH - Read in TV and Weight
GEOMETRY OPTIMIZED : GRADIENT NORM MINIMIZED
SCF FIELD WAS ACHIEVED
AM1 CALCULATION
VERSION 10.0.1
Aug-31-2011
FINAL HEAT OF FORMATION = 58.008859 kcal
= 242.767074 kJ
ELECTRONIC ENERGY = -3510.280310 eV
CORE-CORE REPULSION = 2465.226751 eV
TOTAL ENERGY = -1045.053558 eV
GRADIENT NORM = 0.447407
RMS GRADIENT NORM = 0.097632
UNSTABLE MODE(S) = 9 ( ESTIMATE )
IONIZATION POTENTIAL = 11.317693 eV
HOMO-LUMO GAP = 10.764985 eV
MOLECULAR WEIGHT = 81.076800
MOLECULAR POINT GROUP = D3h 0.100000
NO. OF ALPHA ELECTRONS = 15
NO. OF BETA ELECTRONS = 15
TOTAL NUMBER OF ORBITALS = 27
SCF CALCULATIONS = 300
COMPUTATION TIME = 3.14 SECONDS
FINAL GEOMETRY AND DERIVATIVES
PARAMETER ATOM TYPE VALUE GRADIENT
1 2 C BOND 1.364273 0.028500 kcal/angstrom
2 3 N BOND 1.363786 -0.031337 kcal/angstrom
3 3 N ANGLE 125.763994 0.063907 kcal/radian
4 4 C BOND 1.364340 0.031506 kcal/angstrom
5 4 C ANGLE 114.225219 -0.095162 kcal/radian
6 4 C DIHEDRAL -0.082786 -0.023272 kcal/radian
7 5 N BOND 1.363745 -0.039451 kcal/angstrom
8 5 N ANGLE 125.758251 0.061598 kcal/radian
9 5 N DIHEDRAL 0.064912 0.032019 kcal/radian
10 6 C BOND 1.363858 -0.023039 kcal/angstrom
11 6 C ANGLE 114.267735 -0.005527 kcal/radian
12 6 C DIHEDRAL 0.051211 0.028513 kcal/radian
13 7 H BOND 1.110061 -0.003083 kcal/angstrom
14 7 H ANGLE 116.976906 -0.311282 kcal/radian
15 7 H DIHEDRAL -179.972523 0.010611 kcal/radian
16 8 H BOND 1.110056 -0.000543 kcal/angstrom
17 8 H ANGLE 117.024346 -0.216646 kcal/radian
18 8 H DIHEDRAL -179.927893 0.029676 kcal/radian
19 9 H BOND 1.110002 -0.004528 kcal/angstrom
20 9 H ANGLE 117.228854 0.176265 kcal/radian
21 9 H DIHEDRAL -179.991983 0.005369 kcal/radian
ATOM CHEMICAL BOND LENGTH BOND ANGLE TWIST ANGLE
NUMBER SYMBOL (ANGSTROMS) (DEGREES) (DEGREES)
(I) NA:I NB:NA:I NC:NB:NA:I NA NB NC
1 N
2 C 1.36427 * 1
3 N 1.36379 * 125.76399 * 2 1
4 C 1.36434 * 114.22522 * -0.08279 * 3 2 1
5 N 1.36374 * 125.75825 * 0.06491 * 4 3 2
6 C 1.36386 * 114.26774 * 0.05121 * 1 2 3
7 H 1.11006 * 116.97691 * -179.97252 * 2 1 6
8 H 1.11006 * 117.02435 * -179.92789 * 4 3 2
9 H 1.11000 * 117.22885 * -179.99198 * 6 1 2
MOLECULAR POINT GROUP SYMMETRY CRITERIA
D3h 0.10000000
ALPHA EIGENVALUES
-41.18022 -34.37982 -34.37738 -25.89474 -25.89191 -19.19792
-18.79665 -15.88636 -15.87217 -14.75668 -14.75454 -11.89809
-11.89759 -11.32023 -11.31769 -0.55271 -0.55174 2.23917
2.58923 2.61747 2.61834 3.70217 3.70292 4.59012
4.99307 4.99501 6.66416
BETA EIGENVALUES
-41.18022 -34.37982 -34.37738 -25.89474 -25.89191 -19.19792
-18.79665 -15.88636 -15.87217 -14.75668 -14.75454 -11.89809
-11.89759 -11.32023 -11.31769 -0.55271 -0.55174 2.23917
2.58923 2.61747 2.61834 3.70217 3.70292 4.59012
4.99307 4.99501 6.66416
NET ATOMIC CHARGES AND DIPOLE CONTRIBUTIONS
ATOM CHARGE ATOM ELECTRON DENSITY
1 N -0.1905 5.1905
2 C -0.0096 4.0096
3 N -0.1901 5.1901
4 C -0.0095 4.0095
5 N -0.1904 5.1904
6 C -0.0094 4.0094
7 H 0.1998 0.8002
8 H 0.1998 0.8002
9 H 0.1999 0.8001
DIPOLE (DEBYE) X Y Z TOTAL
POINT-CHG. -0.001 0.000 -0.001 0.002
HYBRID -0.001 0.000 0.000 0.001
SUM -0.002 0.000 -0.001 0.002
CARTESIAN COORDINATES
ATOM X Y Z
1 N 0.00000000 0.00000000 0.00000000
2 C 1.36427295 0.00000000 0.00000000
3 N 2.16133479 1.10661861 0.00000000
4 C 1.47894320 2.28804284 -0.00179772
5 N 0.12205404 2.42461443 -0.00225014
6 C -0.56054692 1.24333966 -0.00111129
7 H 1.86783132 -0.98927441 0.00040978
8 H 2.08295288 3.21938322 -0.00312051
9 H -1.66906643 1.30068053 -0.00102444
ATOMIC ORBITAL ELECTRON POPULATIONS
1.74495 1.07522 1.21016 1.16012 1.28368 0.89505
0.99095 0.83991 1.74503 1.30564 0.97931 1.16009
1.28369 0.90939 0.97656 0.83991 1.74488 1.04664
1.23877 1.16012 1.28371 1.02434 0.86150 0.83985
0.80022 0.80019 0.80012
(SZ) = 0.000000
(S**2) = 0.000000
ATOMIC ORBITAL SPIN POPULATIONS
0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
0.00000 0.00000 0.00000
ELAPSED WALL CLOCK TIME : 1.15 SECONDS
FULL COMPUTATION TIME : 3.65 SECONDS
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The information listed here describes the algorithms and criteria that will be used in the calculation. |
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These are the normalized weighting factors for the components of the T.V. Changing the phase of the T.V. can be accomplished by changing the signs of the T.V. components, not by specifying negative scaling factors. |
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This is the T.V. in internal coordinates. There are 21 items, corresponding to the 21 optimizable geometric parameters, both in number and order, in the molecule. The user should be certain that these correspond to the values entered. |
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The geometry represents the final geometry along the PATH. Since the T.V. was oriented toward the reactant, this is the optimized geometry for triazine. |
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Copyright © 1992-2013 Semichem, Inc. All rights reserved. |
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| Chapter 27. Finding a Specific Transition State (CHN) |  |
Chapter 29. Intrinsic Reaction Coordinate (IRC) Calculation |