Gaussian - quantum chemistry - look inside molecular

Here I want to demonstrate another program software to glance inside the molecule. As before I said that thinking about Reverse Engineering of exe files and computer tools which are so popular now. The hackers and crackers are becoming as geniuses closing the elite of modern society.  I just remember one theme we studied in the University - Computational Chemistry. This branch is not popular in Russia, but it remind me reverse engineering of molecular.

Progress in the development of computer technology and software has made quantum chemistry methods is one of the most important tools of chemical and physicochemical studies. Computer modeling of structure and properties of the material not only complements the experimental information but help of computer simulation to study the transition states of chemical reactions and mechanisms, intermediates, non-existent substance which is impossible on the basis of existing experimental methods.

Molecular mechanics uses classical mechanics to model molecular systems. The potential energy of all systems in molecular mechanics is calculated using force fields. Molecular mechanics can be used to study molecule systems ranging in size and complexity from small to large biological systems or material assemblies with many thousands to millions of atoms.

All-atomistic molecular mechanics methods have the following properties:

- Each atom is simulated as one particle

- Each particle is assigned a radius (typically the van der Waals radius), polarizability, and a constant net charge (generally derived from quantum calculations and/or experiment)

- Bonded interactions are treated as springs with an equilibrium distance equal to the experimental or calculated bond length.

In the context of molecular modeling, a force field (a special case of energy functions or interatomic potentials; not to be confused with force field in classical physics) refers to the functional form and parameter sets used to calculate the potential energy of a system of atoms or coarse-grained particles in molecular mechanics and molecular dynamics simulations. The parameters of the energy functions may be derived from experiments in physics or chemistry, calculations in quantum mechanics, or both.

All-atom force fields provide parameters for every type of atom in a system, including hydrogen, while united-atom interatomic potentials treat the hydrogen and carbon atoms in each methyl group (terminal methyl) and each methylene bridge as one interaction center. Coarse-grained potentials, which are often used in long-time simulations of macromolecules such as proteins, nucleic acids, and multi-component complexes, provide even cruder representations for higher computing efficiency.

Look at the background

Both molecular and quantum mechanics methods rely on the Born-Oppenheimer approximation. In quantum mechanics, the Schrödinger equation (1) gives the wave functions and energies of a molecule.

HY = EY                                                                                                                           (1)

  where

H is the molecular Hamiltonian,

Y is the wave function,

E is the energy.

The molecular Hamiltonian is composed of these operators:

- the kinetic energy of the nuclei (N) and electrons (E),

- nuclear-nuclear (NN) and electron-electron repulsion (EE),

- and the attraction between nuclei and electrons (NE)

(equation 1).

H(kinetic energy)_N + (kinetic energy)_E = + (repulsion)_NN + (repulsion)_EE + (attraction)_NE        (2)

Nuclei have many times more mass than electrons. During a very small period of time when the movement of heavy nuclei is negligible, electrons are moving so fast that their distribution is smooth. This leads to the approximation that the electron distribution is dependent only on the fixed positions of nuclei and not on their velocities. This approximation allows two simplifications of the molecular Hamiltonian. The nuclear kinetic energy term drops out of the molecular Hamiltonian. The nuclear kinetic energy term drops out (equation 3).

H = (kinetic energy)_E + (repulsion)_NN + (repulsion)_EE + (attraction)_NE                                   (3)

Since the nuclear-nuclear repulsion is constant for a fixed configuration of atoms, this term also drops out. The Hamiltonian is now purely electronic. 

H_electronic = (kinetic energy)_E + (repulsion)_EE + (attraction)_NE                                    (4)

After solving the electronic Schrödinger equation (equation 4), to calculate a potential energy surface, you must add back nuclear-nuclear repulsions (equation 5).

H_electronicY_electronic = E_electronicY_electronic

V_PES = E_electronic + (repulsion)_NN  
         

I want to demostrate the example of molecular calculation using the Gaussian complex.

it is not the last version of Gaussian.

We try again investigate H₂O using Gaussian. Create the molecule of water. 

Then I want to make the Geometry optimiztion of molecular and find the thermodynamic characteristic. 

I want to demostrate the example of molecular calculation using the Gaussian complex.

it is not the last version of Gaussian.

We try again investigate H₂O using Gaussian

rfg calculation in computational physics and chemistry, the Hartree–Fock (HF) method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system in a stationary state.

 6-31g  - gaussian basis -long distance interaction

---------------------------

 # opt=calcfc freq rhf/6-31g

 ---------------------------

 1/10=4,18=20,38=1/1,3;

 2/9=110,17=6,18=5,40=1/2;

 3/5=1,6=6,11=1,16=1,25=1,30=1/1,2,3;

 4/7=1/1;

 5/5=2,38=5/2;

 8/6=4,10=90,11=11,27=262144000/1;

 11/6=1,8=1,9=11,15=111,16=1/1,2,10;

 10/6=1,7=6/2;

 6/7=2,8=2,9=2,10=2,28=1/1;

 7/10=1,18=20,25=1/1,2,3,16;

 1/10=4,18=20/3(1);

 99//99;

 2/9=110/2;

 3/5=1,6=6,11=1,16=1,25=1,30=1/1,2,3;

 4/5=5,7=1,16=3/1;

 5/5=2,38=5/2;

 7//1,2,3,16;

 1/18=20/3(-5);

 2/9=110/2;

 6/7=2,8=2,9=2,10=2,19=2,28=1/1;

 99/9=1/99;

 -------------------

 Title Card Required

 -------------------

 Symbolic Z-matrix:

 Charge =  0 Multiplicity = 1

 8                    -0.138     0.279     0.

 1                    -0.235     1.262    -0.096

 1                     0.324     0.233     0.903

Distance matrix (angstroms):

                    1          2          3

     1  O    0.000000

     2  H    0.961377   0.000000

     3  H    0.960254   1.579499   0.000000

 Stoichiometry    H2O

 Framework group  CS[SG(H2O)]

 Deg. of freedom     3

 Full point group                 CS      NOp   2

 Largest Abelian subgroup         CS      NOp   2

 Largest concise Abelian subgroup C1      NOp   1

                         Standard orientation:                        

 ---------------------------------------------------------------------

 Center     Atomic     Atomic              Coordinates (Angstroms)

 Number     Number      Type              X           Y           Z

 ---------------------------------------------------------------------

    1          8             0        0.000000    0.109446    0.000000

    2          1             0        0.789749   -0.438771    0.000000

    3          1             0       -0.789749   -0.436800    0.000000

 ---------------------------------------------------------------------

 Rotational constants (GHZ):    942.7706306    401.9972633    281.8264885

 Standard basis: 6-31G (6D, 7F)

 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

 Berny optimization.

 Initialization pass.

We get the important result:

------------------------------------------------------------

 #N Geom=AllCheck Guess=Read SCRF=Check GenChk RHF/6-31G Freq

 ------------------------------------------------------------

rfg calculation in computational physics and chemistry, the Hartree–Fock (HF) method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system in a stationary state.

 6-31g  - gaussian basis -long distance interaction

-------------------

 - Thermochemistry -

 -------------------

 Temperature   298.150 Kelvin.  Pressure   1.00000 Atm.

 Atom  1 has atomic number  8 and mass  15.99491

 Atom  2 has atomic number  1 and mass   1.00783

 Atom  3 has atomic number  1 and mass   1.00783

 Molecular mass:    18.01056 amu.

 Principal axes and moments of inertia in atomic units:

                           1         2         3

     EIGENVALUES --     1.82416   4.43665   6.26081

           X            1.00000  -0.00008   0.00000

           Y            0.00008   1.00000   0.00000

           Z            0.00000   0.00000   1.00000

 This molecule is an asymmetric top.

 Rotational symmetry number  1.

 Rotational temperatures (Kelvin)     47.48138    19.52236    13.83428

 Rotational constants (GHZ):         989.35259   406.78037   288.25995

 Zero-point vibrational energy      59047.5 (Joules/Mol)

                                   14.11269 (Kcal/Mol)

 Vibrational temperatures:   2499.23  5739.32  5965.00

          (Kelvin)

 Zero-point correction=                           0.022490 (Hartree/Particle)

 Thermal correction to Energy=                    0.025324

 Thermal correction to Enthalpy=                  0.026269

 Thermal correction to Gibbs Free Energy=         0.004262

 Sum of electronic and zero-point Energies=            -75.962869

 Sum of electronic and thermal Energies=               -75.960035

 Sum of electronic and thermal Enthalpies=             -75.959091

 Sum of electronic and thermal Free Energies=          -75.981097

                     E (Thermal)             CV                S

                      KCal/Mol        Cal/Mol-Kelvin    Cal/Mol-Kelvin

 Total                   15.891              5.994             46.316

 Electronic               0.000              0.000              0.000

 Translational            0.889              2.981             34.608

 Rotational               0.889              2.981             11.703

 Vibrational             14.114              0.032              0.004

                       Q            Log10(Q)             Ln(Q)

 Total Bot       0.109498D-01         -1.960594         -4.514434

 Total V=0       0.242140D+09          8.384067         19.305027

 Vib (Bot)       0.452313D-10        -10.344561        -23.819232

 Vib (V=0)       0.100023D+01          0.000099          0.000229

 Electronic      0.100000D+01          0.000000          0.000000

 Translational   0.300432D+07          6.477746         14.915562

 Rotational      0.805789D+02          1.906221          4.389236

-------------------------------------------------------------------

 Center     Atomic                   Forces (Hartrees/Bohr)

 Number     Number              X              Y              Z

 -------------------------------------------------------------------

    1          8           0.000009806   -0.000040911    0.000015326

    2          1          -0.000018361    0.000062849   -0.000030020

    3          1           0.000008555   -0.000021938    0.000014694

 -------------------------------------------------------------------

 Cartesian Forces:  Max     0.000062849 RMS     0.000029746

Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering

 activities (A**4/AMU), depolarization ratios for plane and unpolarized

 incident light, reduced masses (AMU), force constants (mDyne/A),

 and normal coordinates:

                     1                      2                      3

                    A'                     A'                     A'

 Frequencies --  1737.0520              3989.0283              4145.8886

 Red. masses --     1.0915                 1.0371                 1.0887

 Frc consts  --     1.9405                 9.7227                11.0257

 IR Inten    --   123.0293                 2.9558                54.2706

 Raman Activ --    10.6284                90.1160                40.0927

 Depolar (P) --     0.3960                 0.2177                 0.7500

 Depolar (U) --     0.5674                 0.3576                 0.8571

 Atom AN      X      Y      Z        X      Y      Z        X      Y      Z

   1   8     0.00   0.07   0.00     0.00   0.04   0.00     0.07   0.00   0.00

   2   1    -0.38  -0.59   0.00     0.61  -0.35   0.00    -0.58   0.40   0.00

   3   1     0.38  -0.59   0.00    -0.61  -0.35   0.00    -0.58  -0.40   0.00

Lets remember here:

Enthalpy - measure ordering system. Enthalpy Listeni/ˈɛnθəlpi/ (Symbol: H) is a measurement of energy in a thermodynamic system. It is the thermodynamic quantity equivalent to the total heat content of a system. It is equal to the internal energy of the system plus the product of pressure and volume.

Gibbs Free Energy - The Gibbs energy (also referred to as G) is also the thermodynamic potential that is minimized when a system reaches chemical equilibrium at constant pressure and temperature. Its derivative with respect to the reaction coordinate of the system vanishes at the equilibrium point. As such, a reduction in G is a necessary condition for the spontaneity of processes at constant pressure and temperature.

Entropy - chaos measure. Thermodynamic entropy - thermodynamic function that characterizes the measure of irreversible energy dissipation in it.

This is my small investigation in molecular structured field.  

Gauissian mostly deal with Molecular Mechanics

Little about the theory 

Molecular Mechanics

Molecular mechanical force fields use the equations of classical mechanics to describe the potential energy surfaces and physical properties of molecules. A molecule is described as a collection of atoms that interact with each other by simple analytical functions. This description is called a force field. One component of a force field is the energy arising from compression and stretching a bond.

We try to find the potential energy. The potential energy of a molecular system in a force field is the

sum of individual components of the potential, such as bond,  angle, and van der Waals potentials (equation 8). The energies of the individual bonding components (bonds, angles, and dihedrals) are functions of the deviation of a molecule from a hypothetical compound that has bonded interactions at minimum values.

E_Total = term₁ + term₂ + ¼+ term_n                                                          (8)

The absolute energy of a molecule in molecular mechanics has no intrinsic physical meaning; E_Total values are useful only for comparisons between molecules. Energies from single point calculations are related to the enthalpies of the molecules. However, they are not enthalpies because thermal motion and temperature dependent contributions are absent from the energy terms (equation 8).

Unlike quantum mechanics, molecular mechanics does not treat electrons explicitly. Molecular mechanics calculations cannot describe bond formation, bond breaking, or systems in which electronic delocalization or molecular orbital interactions play a major role in determining geometry or properties. This discussion focuses on the individual components of a typical molecular mechanics force field. It illustrates the mathematical functions used, why those functions are chosen, and the circumstances under which the functions become poor approximations.

- Parametrised forces between atoms or groups

-  No description of electronic structure

- Cheap => large systems and/or long dynamics simulations

-  Not good for change in bond structure

- Often problems associating atom types

- Force fields optimised for certainclass of molecule

Force Fields:

UFF

AMBER

CHARMM

OPLS

Dreiding

Semiempirical Methods 

Fastest electronic structure method! Electronic structure with severe approximations and parametrised integrals  Originally optimised for small organic molecules  Only PM6/7 (not in Gaussian) parametrised for all elements.

Methods:

AM1 PM3 PM6 PM7

Often good for initial optimisation. For many purposes a good Force Field is better. Consider QM/MM.

Density Functional Theory 

All ground state properties can be determined as a functional of the electron density (Hohenberg-Kohn Theorem)  This functional is not known. Many model functionals in use.  Current functionals do not describe static correlation (London dispersion), although some are parametrised to experimental results. Empirical corrections for forces available.

Post-HF Methods

-MP2 

- Similar to DFT in total accuracy

- Describes all kinds of correlation- energy 

- Scales n⁵ with basis functions.

CCSD(T) 

- Best feasible black-box method- for small molecules 

- Scaling n⁷

Many more Methods: MP3, MP4 QCISD, BD CCSDT(Q)

MP2 may be necessary in case of dispersion dominated interactions )p-p(e.g.)

QM/MM

Treat “interesting” region with higher accuracy Anything not part of the reaction treated on lower level (typically MM) Boundary atoms saturated with H atoms Careful where you cut! Gaussian keyword: ONIOM(HF/6- 31G(d):AM1:UFF) Up to 3 layers

This is about Guaissian Basis we use in our analysisi 

Geometry Optimisation

• Find (local) minimum (equilibrium structure) or saddle point (transition state) on potential energy surface

• No guarantee to find “correct” minimum or TS

• TS considerably more difficult

• Most methods are quasi-Newton with updated Hessian

-  Need good initial guess of curvature

– Frequency calculation at lower level

– Optimisation at lower level (ReadFC)

– In extreme cases, calculate Hessian in every step Opt=CalcFC in Gaussian

 

Transition State Optimisation

- Transition state:

1st order saddle point on potential energy surface

- Method:

follow Eigenvector of negative Eigenvalue uphill.  All other directions downhill

         

UV/Visible Spectroscopy

Electronically excited states - vertical excitation

energies

- HOMO-LUMO gap (Koopman’s Theorem)

Bad; virtual HF/DFT orbital energies unreliable,

no orbital relaxation

- ZINDO

semiempirical, limited selection of atoms;

fast, qualitatively OK

- CIS

HF based; rather inaccurate (but better than Koopman)

- TD-DFT

DFT equivalent of CIS (but founded in different theory);

better than CIS

- CIS(D)

CIS with approximate doubles

based on MP2; accurate but expensive

Thermochemistry

Frequency calculation gives zero-point correction to Energy, Enthalpy and Gibbs Free Energy

Properties calculated at 298.15K (default) or user-specified temperature

Thermodynamic reaction properties can be determined in a “model chemistry” (CBS-QB3,

G2, …)

The idea of the example in my blog to show the different sense and goals of reverse engineering. The all discoveries in science as we know can be used for god and evil. Now with so fast development of IT science we forget about our presents in nature, we stop notice the beautiful diversity around us but concentrated on own us and our desires and desires to become high that nature. The professions hacker and cracker become modern society elite making us blind behind our real goal. For us the new and new gadget developed to make us robots to kills the human soul inside us.

Look around we all seek to be famous with any way, just get click like and removing us staying human.