Monte carlo method for the automated and highly efficient calculation of kinetic data of chemical reactions

A computer-implemented method of calculating transition states of a chemical reaction, comprising the steps of:

• A Generating a starting geometry by
• A1 providing the three-dimensional representation of at least one molecule at ground state energy,
• A2 selecting at least one bond of the at least one molecule and selecting a length of the bond, where the selected length does not correspond to the length of the bond at ground state energy of the molecule, such that a starting geometry for the chemical reaction is obtained,
• A3 representing the starting geometry in three dimensions in Cartesian and/or internal coordinates, and
• B Ascertaining an optimized starting geometry
• B1 defining a function space encompassing the at least one bond from step A2 and the atoms joined by this bond,
• B2 optimizing the geometry of the function space selected in step B1 by means of a quantum-chemical method and with the boundary condition that the length of the at least one bond selected in step A2 is kept constant, such that an optimized starting geometry is obtained,
• B3 ascertaining the gradient norm B3 for the optimized starting geometry, where the gradient norm is obtained via the first derivative of a function E=f(x) of the quantum-chemical method and, with E=total energy of the optimized starting geometry and x=nuclear coordinates of the molecule in the optimized starting geometry, and
• B4.1 when the gradient norm B3 ∇ is 0≤∇≤0.03 Eh a0−1, classifying the optimized starting geometry as a precursor to the transition state of the chemical reaction and continuing the method with step D1, or
• B4.2 when the gradient norm B3 ∇ is >0.03 Eh a0−1, ascertaining the precursor to the transition state of the chemical reaction proceeding from the optimized starting geometry by a method comprising the following steps:
• C Ascertaining the precursor to the transition state of the chemical reaction by
• C1 varying the optimized starting geometry using a Monte Carlo algorithm,
• C1.1 wherein at least one atom from the function space selected in step B1 is selected at random,
• C1.2 wherein a vector for a deflection of the atom chosen in step C1 is selected at random, weighting the randomly chosen magnitude of the vector by the gradient norm B3,
• C1.3 wherein the atom selected in step C1.1 is deflected from the position of the atom in the optimized starting geometry using the vector from step C1.2, so as to obtain a precursor to a transition state of the chemical reaction,
• C2 optimizing the geometry of the precursor to the transition state by means of the quantum-chemical method and with the boundary condition that the at least one bond from step A2 has the length that was ascertained in step C3,
• C3 ascertaining the gradient norm C3 for the precursor to the transition state from step C2, where the gradient norm is obtained via the first derivative of the function E=f(x) of the quantum-chemical method and, with E=total energy of the precursor to the transition state and x=nuclear coordinates of the molecule in the precursor to the transition state, and
• C4.1 when the gradient norm C3 ∇ is 0≤∇≤0.03 Eh a0−1, continuing the method with step D1, or
• C4.2 when the gradient norm C3∇>0.03 Eh a0−1, repeating steps C1 to C3 until a gradient norm C3 ∇ of 0≤∇≤0.03 Eh a0−1 is obtained, wherein
• (a) if steps C1 to C3 have been performed once, the geometry of the precursor to the transition state is varied in step C1 when the value of its gradient norm C3 is lower than the value of the gradient norm B3 of the optimized starting geometry, or
• (b) if steps C1 to C3 have been performed more than once, the geometry of the optimized starting geometry or that precursor to the transition state from the preceding repetitions that has the lowest value for the gradient norm C3 or B3 compared to all the gradient norms C3 and B3 previously obtained is varied in step C1,
• D Ascertaining the transition state by
• D1 varying the precursor from step C4.1 or the precursor from step B4.1 by performing the following steps for one atom within the function space defined in B1:
• D1.1 selecting an atom from the function space selected in step B1,
• D1.2 selecting a vector for a deflection of the atom chosen in step D1.1,
• D1.3 deflecting the atom selected in step D1.1 using the vector from step D1.2 from its position in the precursor, wherein the position is deflected once by the positive value of the magnitude of the vector and once by the negative value of the magnitude of the vector, such that two deflected precursors are obtained when steps D1.1 to D1.3 are conducted,
• D2 optimizing the geometry of the two deflected precursors from step D1 by means of the quantum-chemical method under the constraint that the bond distances obtained in D1 are kept constant, such that two optimized precursors (i) and (ii) are obtained,
• D3 calculating the energy of the two optimized precursors (i) and (ii) from step D2 by means of the quantum-chemical method,
• D4 comparing the energy values of the two optimized precursors with the value of the gradient norm C3 or B3 of the precursor that was used in step D1,
• D4.1. if the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are each smaller than the energy value C3 or B3 of the precursor that was used in step D1, classifying the precursor that was used in step D1 as the transition state,
• D4.2. if the energy value of the optimized precursor (i) or the energy value of the optimized precursor (ii) is not smaller than the energy value C3 or B3 of the precursor that was used in step D1, repeating the method from step C1.