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• Path search by artificial force induced reaction (AFIR) method

The artificial force can be added to the adiabatic PES in combination with any calculation. For example, an input of MIN which minimizes the AFIR function with a force term between HCHO and CH2=CHOH is shown below:

# MIN/B3LYP/6-31G

0 1
C         -1.953694358578          0.051428373301         -0.462381672082
O         -2.874202130646         -0.064517892271          0.347537662192
H         -1.221862356669         -0.754329860961         -0.638252756531
H         -1.808350872749          0.967674780659         -1.058303513918
C          2.077685115129          0.114719409486          0.023518638131
C          1.393292368474          1.261286104642          0.077854069069
O          1.551552360906         -1.171195222175          0.015398868257
H          3.158480450285          0.062149788186         -0.021818187026
H          0.307941770709          1.295821650032          0.122961746594
H          1.915355307819          2.209783744408          0.078372933902
H          0.573817135316         -1.165646996063          0.055445560334
Options
Fragm.1 = 1-4
Fragm.2 = 5-11
1 2
GAMMA = 100
END

To use AFIR, the Add Interaction … END keyword is added below the Options keyword. There are four lines between the Add Interaction and END keywords: (1) Fragm.1 = 1-4 specifies that atoms 1–4 belong to fragment #1 (HCHO), (2) Fragm.2 = 5-11 specifies that atoms 5–11 belong to fragment #2 (CH2=CHOH), (3) the artificial force is applied between the fragments #1 and #2, and (4) the model collision energy parameter γ is set to 100 kJ/mol. The optimized structure shown at the bottom of the .log file corresponds to a local minimum on the AFIR function.

Optimized structure, SYMMETRY = C1
C         -0.755458695792          0.419573483412         -0.421140869672
O         -1.218478519298         -0.499534023418          0.607634540941
H         -0.774075899055         -0.066727415931         -1.408015724635
H         -1.491738802616          1.226412173065         -0.437999970679
C          1.692619087121         -0.093029628466         -0.083976438974
C          0.605570737615          0.955298639453         -0.133424277007
O          1.478089935819         -1.314778944352         -0.111088656653
H          2.728456322249          0.282771302345         -0.008827236896
H          0.615490723310          1.474247182313          0.839269178899
H          0.901096128657          1.716001745333         -0.873298465662
H         -0.661556228016         -1.293060634515          0.571201269260
ENERGY    = -268.197646700370 (-268.268054516706 :    0.000000000000)

Two energy values are shown below the optimized structure: the value outside the parentheses corresponds to the value of the AFIR function, and the value in the parentheses corresponds to the actual energy value. In xxx_EQ_list.log, etc., both the value of the AFIR function and the actual energy value are shown outside and inside the parentheses, respectively.

In the.log file of MIN, local minima and maxima along the AFIR path (minimization path of the AFIR function) are printed as approximate EQ and TS structures as follows:

---Approximate TS geometry (between 57 and 58)
C         -0.882909544032          0.318335687547         -0.593137961787
O         -1.161127290399         -0.686431033912          0.224060001703
H         -0.660763323346          0.079056002942         -1.643739246799
H         -1.483639961888          1.233034773491         -0.499943773341
C          1.545854836199         -0.057849159008         -0.015425352456
C          0.737323209524          1.091291004270          0.026041601698
O          1.194755408350         -1.141118517131          0.644213280918
H          2.353492556407         -0.181115294754         -0.736890824595
H          0.307442518637          1.362191774576          0.987745613770
H          1.071578582372          1.946559104144         -0.555905834466
H          0.098007798162         -1.156780462923          0.703315844279
ENERGY    = -268.212011242219

These structures are used for further optimization of actual EQs and TSs. In the.log file of MIN, an energy profile along the AFIR path is also shown as:

---Profile of AFIR path
Itr.       Length (ang)          Energy (real)            Energy (fit)
0     0.000000000000       -268.221465734157       -268.221502023247
1     0.048760252608       -268.221228511893       -268.221215215837
2     0.198687036326       -268.220686226849       -268.220618023765
3     0.365307330446       -268.220129678938       -268.220132045216
4     0.560022409577       -268.219402561154       -268.219457908551
5     0.764750721702       -268.218424313939       -268.218503628106
6     0.979499001985       -268.217366161069       -268.217340374536
7     1.195236853787       -268.216400058009       -268.216244522704
8     1.428223673065       -268.215665111327       -268.215413141407
9     1.630368131719       -268.214391873746       -268.215091547541
10     1.839573663534       -268.215398038799       -268.215106173282
∼∼∼
100     9.403272361682       -268.268054241282       -268.268050152375
101     9.404269477377       -268.268054516706       -268.268051047344

In each line, the first integer is the iteration number, the second value is the path length (in Å), and the third one is the potential energy value, and the forth one is a fitted (smoothened) potential energy profile. If the third (or forth) column is plotted against the first (or second) one, an energy profile along the AFIR path can be visualized. It should be noted that the profile is not very smooth because of crude integration (with a large step size adopted in default) of the AFIR path for efficiency.

##### Special usages:

An input to apply the force among three components (γ = c/3 is applied to the three fragment pairs):

Fragm.1 = i-j
Fragm.2 = k-l
Fragm.3 = m-n
1 2
1 3
2 3
GAMMA = c
END

An input to apply the force among four components (γ = c/4 is applied to the four fragment pairs):

Fragm.1 = i-j
Fragm.2 = k-l
Fragm.3 = m-n
Fragm.4 = o-p
1 2
2 3
3 4
1 4
GAMMA = c
END

An input to apply the negative force between Fragm.2 and Fragm.3 (γ = c/3 is applied between 1 and 2, γ = c/3 is added between 1 and 3, and γ = −1×c/3 is added between 2 and 3):

Fragm.1 = i-j
Fragm.2 = k
Fragm.3 = l
1 2
1 3
2 3 -
GAMMA = c
END

An input to apply a specific force γ = c between Fragm.1 and Fragm.2 (γ = d/2 to the remaining two pairs):

Fragm.1 = i-j
Fragm.2 = k-l
Fragm.3 = m-n
1 2 c
1 3
2 3
GAMMA = d
END

In MIN, MC-AFIR, and the AFIR path calculation step of SC-AFIR, γ initially set to a small value d is gradually increased to a final value c when the following input is given:

Fragm.1 = i-j
Fragm.2 = k-l
1 2
GAMMA = c set d
END

##### Available external software
• Gaussian 03/09/16
• Molpro
• GAMESS
• Turbomole
• SIESTA