The Conformational module consists of a series of algorithms designed to study the conformational space of medium-sized organic molecules.

## Questions about Conformations and Energy Profiles

How do I know I have the global minimum?
The only way to be sure you have the global minimum is to do a systematic search with a very large/dense grid. For example, increase the rotation count for sp3-sp3 carbon bond rotors from the default of 3 to 10. This is known to be very inefficient, and chances are that if you have a non-trivial molecule you may not have the patience required for this calculation to complete.

Our experience with medium (drug-size) organic molecules is that the Monte-Carlo algorithm, in general, does a good job of finding the global minimum. See "How do I know my MC result is good?", and "Is the global minimum the best minima?"

Is the systematic algorithm reproducible?

Yes, if you start from the same conformation. In simple molecules the systematic algorithm is almost always inclusive of all (important) minima. As molecules become more complicated the default grid size, while likely correct in finding all classes of minima, may skip some minima. For example, the single "gauche plus-gauche minus" [-120,+120] conformation of olefins might bifurcate into multiple minima as steric bulk increases. It is likely that one of the two new minima would be found using the standard systematic approach. But 'which one' would depend on the initial conformation.

To ensure you find all minima, it is useful to increase the default rotor values. Doing so will increase computational time; an alternate approach would be to use to the Monte-Carlo algorithm.

Another example of the initial conformer affecting systematic results can be found by inspecting an 8 member carbon chain: "C1-C2-C3-C4-C5-C6-C7-C8". For illustrative purposes consider the central "C4-C5" bond as we rotate it 360 degrees; from -180 to 180 degrees. If one starts in the all "trans" conformation, we find that as we rotate the "C4-C5" bond the final conformation of 360 degrees is identical to the initial at 0 degrees. However, if the initial conformation had a number of kinks in it, we might discover that at the 120 degree mark, the C1 and C8 ran into each other. To relieve this steric problem the other dihedral angles, will relax, likely changing by more than 100 degrees and falling into new energy wells. As we continue the coordinate driving of the central C4-C5 angle to trans (180), we might find that the final conformation is not the same as the initial conformation because these other dihedrals have changed.

Is the global minimum the truth?

The global minimum is often the most interesting, and at the very least, is often representative of an equilibrium conformer found at room temperature. However, what conformation is 'best' depends on what you are looking for. There are often many other variables that conformational analysis ignores, including the effect of solvent and the quality of the energy reported at the given theory level.

How should I use QM methods with Conformation Analysis?

Because QM methods take more time than molecular mechanics (by orders of magnitude), it is usually a mistake to try conformational algorithms with QM methods. Typically, one uses the MMFF mechanics force field to generate a list of low energy conformers. This list is then resubmitted at the desired QM level as either an "equilibrium geometry" or "single point energy" calculation. The original MMFF conformers may change geometry slightly and their relative energies will likely differ.

For small systems (1 or 2 degrees of freedom) it is sometimes possible to use conformational analysis to scan conformer space with a QM method. However, the time required, (as well as the possibility of bad initial conformers with steric problems causing the breaking and forming of bonds), require that users apply caution when applying QM methods to conformational analysis.

A further warning about "bad" initial conformers: It is highly likely that in doing a full conformer search one may start in an unfavorable position. For example, a gauche+/gauche+ conformer in propylene. At the beginning of the minimization two hydrogens may be within 0.25 Angstroms of each other. With molecular mechanics this "bad" starting position is easily handled, but with quantum chemical methods "chemistry" will occur; resulting in the breaking and reforming of bonds. You will likely not end up with the molecule you started with. Given that this is probably not what is intended, and that it will take a very long time to rearrange all atoms into a "new" molecule, you will be lucky if the job runs out of 'geometry cycles' before taking up too much computer time. The best approach is to "know" that you are starting at a good conformer. This is another reason why it is a good idea to start with MMFF conformers.

This said, beginning in Spartan'18, Wavefunction has introduced multi-step recipes taking advantage of the strengths of both MM and QM models to provide accurate Boltzmann distributions. Further, when utilized in conjunction with the NMR Spectrum task, these also provide a Boltzmann averaged NMR spectrum,. See the Dealing With Conformatoinally Flexible Molecules topic: Menu -> Activities -> Topics, from within Spartan.

How do I tell if the Monte Carlo results are correct?
The only way to know for sure is to compare results with a complete, systematic calculation. (see How do I know I have the global minimum?.) You can build your confidence in the Monte Carlo results by restarting the search from different initial conformations. If multiple starting points yield the same "global minimum" you should have confidence that the algorithm is spanning the conformational space fairly well.

What are the details of the algorithm?
• The conformation module has two modes: Each of these algorithms consist of moving or rotating one or more of the molecule's bonds, followed by a minimization. Each of these topics are covered, in turn, followed by a short discussion of how to customize the algorithm and keywords:

• SYSTEMATIC uses a systematic method to explore the majority of conformations of a molecule. For acyclics, the algorithm rotates each bond by a specified angle (usually 120 degrees) and searches for minima. This typically spans the conformational space effectively enough to find all conformations of small molecules. For cyclics, a similar rotation (the Osawa rotation) is used to sequentially bend rings within the molecule. However, the conformations of rings are not necessarily well defined, and this may not result in a complete search. For large molecules, this method is time consuming, as the number of conformers searched grows exponentially. For this reason, SYSTEMATIC should only be used for small, preferably acyclic, molecules.

• MONTE CARLO uses a "simulated annealing" method to generate conformations of a molecule. This procedure randomly rotates bonds and bends rings until a preferential (minimum energy) geometry is attained. Initially, the molecule is considered to be a high-temperature system; this means that it has significant energy and is flexible enough to move from a low to high energy conformation. This is important because often the global minimum may be very different from the initial conformation. As more conformers are explored, the temperature of the system decreases, making the molecule less inclined to move out of low energy conformations, thus looking "more closely" at other minima in the nearby vicinity.

The algorithm is a standard simulated annealing algorithm with a temperature ramp of
T = T(final) + K*(1-I/Imax)3
Some modifications have been made to avoid dead-ends; if the system appears "stuck", the current conformer will be replaced with a randomly picked (but previously calculated) conformation. The new conformation is weighted via the usual (normalized) Boltzmann criteria.

• Moves:
The basic moves are the same for both Systematic and Monte Carlo algorithms:
1. Basic torsion rotation:
The basic move in conformational searching. This may have undesired long range effects, such as greatly straining (or breaking) rings. (this move is avoided in rings.)
2. Osawa wag:
2 correlated rotations that keep ring closure. If 4 atoms (A,B,C,D) are connected in series, the atom C, and everything connected to it is to rotated around the B--D axis. (If required, rearrangement of large flexible groups attached to atoms B and D will performed internally.) The 'Osawa wag' is the default move for atoms in a ring.
3. 6-member flip:
For 6 member rings, if 2 (and only 2) opposite atoms are selected they are flipped in pairs. This move switches from one chair conformation to the other, making it unlikely that one will find a twist-boat conformation (typically much higher in energy). If one wants to catch the twist-boat conformations, select more (than the default--2) atoms in six member rings (and increase the WINDOW variable). The FINDBOATS keyword does this automatically by choosing 3 of the 6 atoms to flip in a non-correlated way.
4. Non-Planar flip:
Some (non-planar nitrogen) atoms with 3 bonds are also "flipped". This can occur via a wag of one of the arms (for non-cages) or an atom inversion. These moves are indicated as an "Atom-Fold-Count" of 100. This "Non-Planar flip" is sometimes combined with the Osawa wag and is displayed as an Atom-Fold-Count of 103.

• Minimization algorithm:
When using a molecular mechanics method a multi-step minimization algorithm is used:
1. A rigid rotation (or set of rotations) is applied the current molecule. (see moves)
2. A minimization is applied given the set torsion constraints.
3. The constraints are relaxed.
4. A second minimization is applied.
5. The constraints are removed.
6. A fast minimization is done to get a rough geometry.
7. If the energy is too high or the geometry has diverged from the goal geometry by more than 90 degrees the job is considered to have failed.
8. A final minimization is done to remove all residual forces on the molecule.
If a semi-empirical or quantum mechanical conformation is requested, steps 1 and 2 listed above are completed, followed by a minimization at the requested quantum mechanics level.

How can I modify the algorithm?
Within the 'Set Torsions' mode, you can choose the bonds and ring atoms involved in the conformational search. This is done by double-clicking on either the desired bond or atom. When a bond or atom is selected for rotation, a type-in box will appear. This box is used to enter the number of increments in the rotation. For example, if the value of 3 is entered, rotations of 0, 120 and 240 degrees will be applied. If you do not specify bonds or ring atoms, Spartan will use heuristics to decide which elements are relevant in attaining new conformers. Unless you have some chemical insight as to the relevant rotatable members, Spartan's default selections will typically provide good results. Additionally, several keywords will modify calculation details.

What do the fold numbers mean in the Set-Torsions mode?

On bonds, the fold number is simply the number of gross conformers. So for '3' there are assume 3 states, each 360/3=120 degrees apart. Thus each move is +- 120 degrees. A fold number of 2 would mean two conformers, each +- 360/2=180 degrees.

On atoms the fold number contains more specific information. An atom fold number of 3 means an "Osawa wag" is preformed. (A 4 implies a coupled Osawa wag in a cyclohexane like ring.) In the case where the number contains 3 digits, the ones-digit is either 3 or 0 for Osawa wag or no wag, respectively. The hundred's digit, if present indicates that an inversion will be tried. This may occur on asymmetric, non-planar, trivalent nitrogens.

Use the keyword PRINTLEV=2 when the job is run to see more information on what precisely is being flipped and/or rotated.

Interpreting the output file:

Description of the columns:
• column 1: Iteration
• column 2: Energy of current conformer
• column 3: Current MC temperature
• column 4: Local success rate. Averaged over the last few iterations.
if (*) appears the current conformation was accepted by the MC search algorithm as the basis for the next conformation.
• "New Best: The current lowest energy
• "Duplicate: Minima has been previously found
• "Chirality: Minimization failed, chirality has changed
• "No Minima: Torsions have deviated too much from goal
• "Strained": Highly strained (unphysical) conformation
• column 6: Conformation label. Only available when using the PRINTLEV=2 (or greater) keyword.
Labels each conformation by breaking each torsion into 12 classes each spanning 30 degrees:
```
c                  Cis  c   : -15 ..   0 ..  15
0.0   c+                 c+  :  15 ..  30 ..  45    c- ~  -30
-30  |  30   g+       Gauche g+  :  45 ..  60 ..  75    g- ~  -60
-60    \|/    60                p+  :  75 ..  90 .. 105    p- ~  -90
-90 -----*----- 90  p+           l+  : 105 .. 120 .. 135    l- ~ -120
-120   /|\   120                t+  : 135 .. 150 .. 165    t- ~ -150
-150 | 150   l+        Trans t   : 165 .. 180 ..-165
180   t+
t
```

Why does the output say it is removing molecules from the list and how is it deciding what to remove?

Any conformer that has an energy greater than WINDOW (10.0 kcal/mol) of the lowest energy conformer is thrown away. If there are more than MAXCONFS (100) conformers with acceptable energies the program will discard conformers with the goal of keeping as diverse a group as possible, while, at the same time as keeping the lowest energy conformers.

How many cycles will my molecule take? or
Will my molecule use the Systematic or Monte Carlo method?

The number of cycles a molecule will take depends on the type and number of rotatable bonds. Each rotatable bond has a fold number. (This fold number can be modified in the 'Set Torsions' mode.) For example sp3-sp3 bonds have a default fold number of 3 because these bonds usually have 3 minima 120 degrees apart. For systematic methods the number cycles is the product of all the fold numbers. For Monte Carlo methods the default number of cycles is the square of the sum of all folds. (This equation is a purely empirical formula; experience has shown it to be adequate.) One can limit this value to an upper limit using the "Maximum Conformers Examined" field in the setup panel, and increase the value above the default using the McConfs= keyword.

The program will choose between the Systematic or Monte Carlo method by choosing the one with the fewest default conformer tries (unless the SEARCHMETHOD keyword is used to override the default).

Keywords: