## Molecular Mechanics Method

SCIGRESS Mechanics is a module for calculating the optimal structure and other properties of molecules by using molecular mechanics methods. Because molecular mechanics methods determine the pair potentials between the atomic nuclei, which are the particles in these methods, stable conformers of molecules can generally be found with quite good precisions by fast calculation in most cases.

The equations of molecular mechanics use the spring potential energy as represented by a pseudo-elastic force as the bonding force of the electrons. The force field energy of the molecule is represented by a theoretical energy called the steric energy that is found from the energy of the extension, compression, angular deviation, and rotation of bonds.

The potentials that are specific to molecular mechanics are determined by a force field. The bond length, bond angle, dihedral, strain, electrostatic force, van der Waals force, hydrogen bonding, and other properties form parameters of the force field. SCIGRESS uses extensions of the MM2 force field and MM3 force field of Professor Allinger.

The following extensions have been made in SCIGRESS.

- Additional atomic types

- trigonal dipyramids
- square pgramid
- octahedron
- tetrahedron

- Additional bonds

- weak bond
- ionic bond
- hydrogen bond
- coordination bond

- The elements that can be used have been expanded to all of the elements on the periodic table by systematically applying empirical rules.
- Whether or not the parameters that correspond to a π-electron system are applied is automatically determined by searching the structures.

#### Applications of molecular force field methods

- When optimizing the structure of a stable conformer of the ground state of a regular organic molecule
- When searching for a series of stable conformers
- When searching for a path from a given conformer to another conformer
- When estimating the steric interactions between molecules
- When investigating the structures of new substances and organometallic molecules
- When determining the initial structure as a precursor to quantum chemistry calculations

## Dynamics (Molecular Dynamics Method)

SCIGRESS Dynamics is molecular dynamics module that is able to simulate the behavior of molecular models. SCIGRESS Dynamics calculates the potential energy using the same force field as SCIGRESS Mechanics. The kinetic energy is calculated from the atomic velocities in the molecular system that reflects the temperature being simulated.

#### Applications of SCIGRESS Dynamics

SCIGRESS Dynamics creates a trajectory according to the settings.

Dynamics
A trajectory is a collection of structures arranged sequentially in time. Each structure has a potential and a kinetic energy that are calculated according to the temperature.

The results of calculations can be displayed by linking the energy and structure in two windows shown side by side.

Furthermore, the following information can be obtained from this trajectory:

- The various conformations arising from the motion of the molecular model
- The relationship between the structure and energy of the molecular model

## Extended Huckel (Molecular Orbital Method)

SCIGRESS Extended Huckel is an empirical molecular orbital calculation method that solves the Schrodinger equation. All of the elements in the periodic table are supported as calculation targets.

The following items can be calculated using the extended Huckel method.

- Bond order
- Partial charge
- Molecular orbitals
- Orbital energies
- Dipole moments

The extended Huckel parameters and the parameters collected by S. Alvarez are provided as the calculation parameters. The user is also able to create new parameter sets.

## ZINDO (Molecular Orbital Method)

SCIGRESS ZINDO is a semiempirical molecular orbital method program. In order to solve the Schrodinger equation, CNDO/INDO can be used.

The following properties can be calculated using ZINDO.

- Partial charge
- Bond order
- Dipole moments
- Molecular orbital energies
- Ionization potentials
- Optimized structures
- Electron spectra (ultraviolet and visible absorption spectra)
- The molecular absorption spectra in the ultraviolet and visible regions can be calculated and visualized by performing C.I. calculations.

ZINDO incorporates a method for modeling polar solvent effects. This is called the SCRF (Self Consistent Reaction Field) method.

### Limitations of ZINDO

- Because ZINDO only treats valence electrons, it cannot calculate properties that depend on changes in inner shell electrons.
- Note: In general, the molecules have large strains.

However, ZINDO treats small ring-shaped molecules as stable molecules.
- Number of atoms that can be calculated using ZINDO: 200 atoms Basis functions: 700

## MO-G (Molecular Orbital Method)

MO-G is a semiempirical molecular orbital program. MINDO/3, MNDO, MNDO-d, AM1, PM3, and PM5 are included as the Hamiltonians for solving the Schrödinger equation.

The following properties can be calculated using MO-G.

- Partial charge
- Bond order
- Dipole moments
- Molecular orbital energies
- Ionization potentials
- Optimal structures
- Potential energy maps
- Structure of transition states
- Reaction coordinates
- Vibration spectra (IR)

### MO-G main functions

- Linear Scaling SCF calculation using the MOZYME method
- Utility functions for inputting and outputting protein structures
- Structure optimization (EF, BFGS, NLLSQ, and SIGMA methods)
- Transition state calculation
- Energy decomposition
- Solvent effect calculation (COSMO method, TOMASI model)
- Internal reaction coordinate calculation (IRC)
- Dynamic reaction coordinate calculation (DRC)
- Analysis of intersystem crossing structure
- Hyperpolarizability calculation
- Automatic identification of symmetries (up to 8th-order point group representations)
- Infrared spectra calculation
- Ultraviolet/visible spectra calculation
- Normal vibration analysis
- Excited state calculation
- Open shell and radical calculation
- Calculation using periodic boundary conditions
- Parametric Molecular Electrostatic Potential
- Atomic charges using ESP calculation

### Limitations on MO-G

- Because MO-G only treats valence electrons, it cannot calculate properties that depend on changes in inner shell electrons.

Note: MO-G was developed and productized by Fujitsu based on MOPAC2002

## MO-S (Excited State Calculation)

MO-S is able to determine with high precision the ultraviolet and visible spectra of organic molecules. MO-S is also able to calculate the ultraviolet and visible absorption spectra of the ligand molecules in proteins by using QM/MM methods.

Example of calculating absorption spectra by using QM/MM methods

### Elements that can be calculated by MO-S

- AM1, PM3, PM5: H, Li, Be, B, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, K, Ca, Zn, Ga, Ge, As, Se, Br, Rb,Sr, Cd, In, Sn, Sb, Te, I, Cs, Ba, Hg, Tl, Pb, Bi
- INDO/S: H, Li, C, N, O, F, Mg, Si, P, S, Cl, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn †
- CNDO/2: H, Li, Be, B, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, Ge, As, Se, Br
- CNDO/S: H, Li, Be, B, C, N, O, F, Na, Mg, Al, Si, P, S, Cl
- CNDO/S2: H, C, N, O, F, S, Cl, Br
- CNDO/S3: H, C, N, O, F, S, Cl, Br

## CONFLEX3 (Search Stable Conformations Using Molecular Mechanics Methods)

SCIGRESS CONFLEX3 searches the conformation space of flexible molecules and is able to determine the optimal structure of the chemically important comformational isomers without missing any. In previous structural optimization programs (Mechanics, MO-G, etc.), only the locally optimal structure depending on the initial structure input by the user could be found, and it was difficult to identify the most stable structure. Because of this, only a limited amount of information could be obtained about the properties and behavior of flexible molecules. CONFLEX3 is a conformation search program that resolves these problems.

### Features of CONFLEX3

#### 1.Conformation search algorithm

The procedure for searching conformations is as follows:

(1) Select an initial structure from among the previously saved structures and create the corresponding structure

(2) Optimize the structure

(3) Compare to the previously obtained structures and save if it is a new conformation

This procedure is repeated until a termination condition is satisfied.

The biggest feature of CONFLEX3 is the creation of the structure in (1). Superior performance is obtained in particular by using Corner Flap and Edge Flip, which are applicable to ring-shaped sections.

#### 2.Structure creation

Corner Flap

Creates a new starting structure by selecting a single constituent atom from a ring in the initial structure and moving it to the opposite side of the mean plane of the ring.

Edge Flip

Performs a twisting operation by selecting two neighboring atoms from the constituent atoms of a ring in the initial structure and moving these to opposite sides of the mean plane of the ring.

In addition, an indenting operation is performed by moving the two atoms towards the inside of the ring.

Stepwise Rotation

A new starting structure is created by performing a simple rotation operation on a side chain.

#### 3.Reservoir filling algorithm

The above three operations are local searches based on the initial structure. However, CONFLEX3 also selects initial structures from among the found conformational isomers in order from the lowest energy structures. If a conformational isomer with a lower energy is found during this process, that conformation becomes the next initial structure. This makes the search region rapidly move towards lower energies. Next, once the most stable conformation has been found, the search region gradually expands to encompass higher energies. Because this resembles the way in which the surroundings become filled with water as water flows into a reservoir, it is called the “reservoir-filling algorithm”.

#### 4.Structure optimization calculation

The structure optimization in the conformation search calculation is performed by using SCIGRESS Mechanics. This makes it possible to perform calculations that support all elements. Furthermore, structures that have already been found, enantiomers, geometric isomers, saddle-point structures, extremely unstable structures, etc. which frequently occur in the calculations are automatically deleted.

#### 5.Simple input settings

Rings, asymmetric carbon atom configurations (R/S), and double-bond geometries (E/Z) within the target molecule are automatically identified. This allows the user to complete the preparations simply by automatically setting the “search labels” by creating molecules and using the “Generate Conformations” command.

### Examples of CONFLEX3 calculations

#### Step 1: Draw using Workspace

The input files to CONFLEX3 are created using Workspace.

Figure 1. Molecule input screen

#### Step 2: Set the search labels (optional)

Set the search labels if there are bonds that you want to rotate within the target molecule. When the “Geometry Label Wizard” command, which is one of the Workspace functions is selected, the dialog box shown in Figure 2 is displayed allowing you to easily set the labels. In Figure 2, the dihedral angles are set to -179, 61, and 120 degrees. In CONFLEX3 it is possible to search for rotamers that satisfy rotations in steps of 120 degrees. Furthermore, search labels can be displayed on the molecules after they are set as shown in Figure 3.

Figure 2. Generate Conformation dialog box

Figure 3. Displaying search labels

#### Step 3: Set CONFLEX3 parameters and execute

The Procedure Browser has an edit function that makes it easy to configure search conditions by accessing the following dialog box.

Figure 4. CONFLEX3 parameter settings dialog box

#### Step 4: Display the calculation results

The energy and structure of each conformer in the calculation results can be viewed simultaneously.

Figure 5. Calculation results

CONFLEX3 is a program developed by Prof. Gotoh of the Toyohashi University of Technology.

Reference documents:

•J. Am. Chem. Soc., 1989, 111, 8950-8951;

•J. Chem. Soc., Perkin Trans. 2, 1993, 187-198;

(Note 1) CONFLEX is a registered trademark of the Conflex Corporation.

## MD-ME (Molecular Dynamics Method)

This allows a variety of phenomena to be simulated from bulk effects to surfaces and boundaries by constructing crystal structures and aggregations of atoms and molecules using simple operations. Furthermore, graphs of various physical quantities and animations of atomic placement can be displayed. This is also able to handle large-scale high-speed calculations. This provides a wide variety of uses including research and development of various materials and education.

#### Polymer Modeling Function

This is a function for joining monomers to create polymers and dendrimers

Example of the polymers that can be created: a chain-shaped polymer (left) and a dendrimer (right)
#### MD Cell Modeling Function

This is a function for creating polymer aggregates (amorphous and infinite chain), liquid crystal structures, crystal structures (using templates), and randomly placed MD cells

Function for creating MD cells using crystal structure templates

### MD-ME features

Easy crystal model construction function

Equipped with a rich potential parameter library and functions. Suitable for a wide variety of materials research and simulations

### MD-ME modeling functions

#### Crystal structure modeler

Function for constructing various crystal structures by expanding the space group

#### Cutting planes

Function for cutting planes by specifying the Miller indices

#### Dynamics models

Able to use potential models, constrained models, and rigid body models

Figure 1:Cutting plane function: Cut along the (111) plane of a sodium chloride crystal

### MD-ME interaction settings and potentials

MD-ME is equipped with the major potential functions used in molecular dynamics. In addition, it includes a library of 85 different potential parameters.

The dissimilar material interfaces (such as Si/SiO2) can be calculated by applying variable charge potentials where the charge varies depending on the environment. (Can only be used with Si)

[Potential functions]

Interatomic interactions (two-body: 16, three-body: 8, many-body: 14)

Intramolecular interactions (bonds: 4, angular: 7, dihedral: 4, out-of-plane: 5)

### MD-ME calculation parameter settings and molecular dynamics calculations

Simulations can be performed by specifying experimental parameters such as temperature, pressure, heating or cooling, increasing or decreasing pressure, etc.

Simulations can also be executed by applying external fields such as electrostatic and electromagnetic fields.

A function that allows the temperature and pressure to be set in multiple stages, and a function that allows the cell lengths to vary during calculation (used for calculating elastic constants) are also provided.

A variety of systems can be freely simulated under the flexible calculation parameter settings like those above.

[Ensembles]

NEV, NTV, NPH, and NTP ensembles are available

[Stress calculation using variable length MD cells]

This function varies the cell side length during calculation

The stress can be obtained by applying a tensile or compressive strain to the cell, and the elastic constant of the material can then be obtained from the relationship between the stress and strain.

[External field application function]

This function applies a stress, electrostatic field, magnetostatic field, or gravitational field of the designated magnitude and direction

Particles are constrained within a sphere of the designated radius

[Control algorithms]

Temperature: Scaling method, Nose method

Pressure: Parrinello-Rahman method. Increased speed: Link-cell method, bookkeeping method, two-body force tables

[Time integration methods]

Gear method, Hernandez method

[Creating atoms and molecules]

This is a function for creating atoms and molecules while a molecular dynamics calculation is executing

This allows simulation of crystal growth and surface adsorption

(Patented Japanese patent number 3648033)

Calculation results of atomic and molecular creation calculation

### MD-ME results display function

This function displays graphs of the time variations in physical quantities such as temperature, pressure, and internal energy, and displays animations of atomic arrangement.

MD-ME results display function

[Calculation results]

Graph of internal energy, volume, pressure, and temperature (left of screen)

Variations in the various physical quantities obtained by the calculations can be displayed in a graph.

[Animation display (right of screen)]

Calculation results can be displayed as an animation.

[Secondary analysis functions]

These are functions for analyzing the calculation results of the molecular dynamics calculations

- Mean-square displacement
- Two-body correlation function
- Voronoi polyhedra
- Molecular internal coordinates
- Interference function
- Coefficient of viscosity
- Elastic constant
- Velocity auto-correlation function
- Rotation correlation function

Display of analysis results (two-body correlation function)

### MD-ME high-speed parallel calculation

Molecular dynamics calculations are also able to support high-speed large-scale calculations by using the SCIGRESS MD (scale-up option) network-linked molecular dynamics calculation engine.

Creating the initial data, performing various analyses, and displaying the calculation and analysis results can be performed on the SCIGRESS for Materials (required) side and used without having to know about the remote environment.