Practical approaches of Quantum Chemistry [part 3] : Ab initio Quantum Chemistry

Anant　Babu Marahatta
Ph.D. student in chemistry
Tohoku University
Japan

(This article is intended to introduce an ab initio technique of Quantum chemistry)

(Interested fellows are suggested to read Part 1 & part 2 of this article before proceeding it. And if necessary, you are reminded to consult the article “Computational Chemistry” archived herewith.)

Basically, the Computational quantum chemistry methods range from highly accurate to very approximate techniques. Ab initio [lat.word-at the beginning] techniques are based entirely on the solution of the Schrödinger equations unlike the empirical or semi-empirical techniques [will be clarified on part 4] which employ experimental results.

More specifically, most ab initio calculations are based on the Born–Oppenheimer approximation, which greatly simplifies the Schrödinger equation by freezing the nuclei in place during the calculation. Such methods converge to the exact solution of the underlying Schrödinger equations by reducing the number of approximations. So the computational cost is the very serious matter. They often take enormous amounts of computer time, memory, and disk space.

For example, the Hartree–Fock (HF) method, a very reasonable ab initio model of quantum chemistry, which does not include full treatment of the effects of electron correlation (the energy contributions arising from electrons interacting with one another) scales as N 4 (where N is the number of basis functions used to create the molecular orbitals) – i.e. a calculation twice as big takes 16 times as long to complete. Density Functional Theory (DFT), which computes electron correlation via general functional of the electron density, scale in a similar manner to HF. However, it is more expensive than equivalent HF calculation due to the introduction of the concept of electron density interactions. Similarly, Moller-Plesset (MPn) Perturbation theories scale as: MP2- N5, MP4 - N6 etc. MP2 model is one of the least expensive ways to improve the HF model and was the first correlation method applied to chemistry. The geometries optimized by it are usually quite accurate.

The following animation illustrates an action of the ab initio technique of Quantum chemistry which explains the double proton transfer in Watson-Crick AT (A=Adenine, T =Thymine) base-pair model of DNA.


Usually, considering the Born–Oppenheimer approximation in order to simplify the Schrödinger equations is okay in ground electronic state which assumes independent motions of electrons and nuclei [but it is not really true]. In practice, however, it is impossible to eliminate all the difficulties arise. Thus, to minimize the errors produced, the empirical or semi-empirical calculations help the quantum/computational chemists by keeping the calculations in track.

……………to be continued………….

The general concept of the empirical or semi-empirical techniques will be posted on part 4.

Reference:
http://www.scidacreview.org/0902/html/qsiman.html

Practical approaches of Quantum chemistry [part 2]

Anant　Babu Marahatta
Ph.D. student in chemistry
Tohoku University
Japan

(Interested fellows are suggested to read the first part [Part 1] of this article before proceeding it).

In order to assist solving Schrödinger equations of the multi electron systems [referred as n body problems], Several Computers / Supercomputers with different mathematical software packages have been developed by applying the results of the theoretical chemistry [refer to an article “Computational chemistry” archived herewith].

By using the solution of the Schrödinger equations, these calculating packages generate information such as properties of molecules and simulate the experimental results. For instance, we can calculate:

• electronic structure determinations [(i.e. the expected positions of the constituent atoms)]
• dipoles and higher multipole moments
• absolute and relative (interaction) energies
• geometry optimizations [the lowest energy and the most stable form]
• frequency calculations [ vibrational and other spectroscopic quantities]

• migrating mechanisms of the active groups
• Dynamics of the molecular rotor, gyroscope, brake, motor etc.
• transition structures
• protein calculations

Here is the video of chaperonin [example of protein] transition from open to closed conformation *.
• reaction mechanisms
• cross sections for collision with other particles
• electron and charge distributions
• potential energy surfaces (PES) **

• rate constants for chemical re actions (kinetics)
• Thermodynamic calculations- heat of reactions, energy of activation etc.
• NMR Calculations etc.

The Computational quantum chemistry methods which range from highly accurate to very approximate techniques will be clarified on part 3.

References:

*Booth et al., 2008 - www.nature.com
**Johnson et al., Chemical & Engineering News (vol.80, No. 2, 2002)

Valentine conversations between HCl and NaOH

(Dedicated to all the valentine couples)

Anant Babu Marahatta
Ph.D. student in Chemistry
Tohoku university
Japan

It is well known that both HCl and NaOH is strong acid and strong base respectively. During their conversations, they themselves confuse each other and request to the phenolphthalein (hph) for checking the neutralization. Here are their detail conversations:

HCl- Hi, how are you today?

NaOH- Hello!! I am ok, what about you? It’s so cold, isn’t it?

HCl- Yeah, you are right. It’s snowing too. The nature also supports the valentine couple like us.

NaOH- I agree. By the way, what’s your plan today? May I know?

HCl- Sure!! I am planning to react with strong base like you in the presence of hph even though we will be completely neutralized /destroyed at the end point.

NaOH- Showing chemical reaction is not a big deal but among us we have to be careful while acting as a titrant and titrand. I mean, who must be kept into the burette?

HCl- Yeah, that’s the good point. But it’s universally accepted that you must be pipetted out and kept into the receiver [conical flask] and I must be poured drop wise from the burette till the pink color of hph created by your OH ion disappeared.You must be shaked uniformly for the vigorous reaction.

NaOH- What do you think about me? I am not like NH4OH. I am as strong as you. One mole [Avogadro’s number] of you can be easily neutralized by one mole of me. Then why should I be kept into the receiver?

HCl- In terms of strength, I agree with your point. But you know, “Acid is acid”. We have to follow the scientific evidences otherwise there will be problematic during complete neutralization processing. And we must use hph properly so that it helps us to detect complete neutralization. It only gives the pink color dropped upon you which can be traced during reaction.

NaOH- Ok, I agree. But if I was made in China, the hph would not be the perfect indicator and I must have been kept into the burette. Any way, it’s out of our discussion.

HCl- In such case, methyl orange could be the best indicator but it is a rare case, however, valid to somebody else. Any way, we are at the end of our discussion now. Good luck!!

-------------Happy Valentine day!!!!-------------

Practical approaches of Quantum chemistry [part 1]

Anant Babu Marahatta
Ph.D. student in chemistry
Tohoku University
Japan


Even the high school/senior high school students are acquainted with the “Bohr model” which says electrons are "particles" that revolve around the nucleus in orbits and are quantized so that they can show absorption and emission phenomena.

It is a primitive model of the hydrogen atom though it is verified later after the introduction of the quantum mechanical concept.This model strongly supports the existence of the “Covalent Bond Theory [CBT]” and the “Valence Shell Electron Pair Repulsion theory [VSEPR]” of bonding between the atoms.

The “Quantum model” on the other hand, says that electrons are not particles, but have wavelike characteristics just like photons and their wave length can be explained by the “de Broglie's equation”. In order to calculate the various properties of the electrons, Quantum model developed a famous equation by considering the “de Broglie concept” which is named as a Schrödinger’s equations and appeared as a stepping stone of the Quantum chemistry / Physics. I am sure that most of the chemistry undergrad./ grad. students are encountered with these two forms of Schrödinger equations:
Ĥ ψ = E ψ & Ĥ ψ = iħ (δ/ δt)ψ (time independent and time dependent respectively). These equations model the atoms and molecules with mathematics.

It is well-known for the physical chemists that the quantum n-body problem [many electrons atoms or molecules, beyond Helium] cannot be solved analytically. However, the case for Hydrogen molecular ion [H2+ = 1 electron system] is relatively easy and the results normally agree with the information obtained by the chemical experiments. By considering such agreements, the necessity of the Quantum chemistry arises in order to verify and explore the chemistry of the micro particles which act as a foundation of the matter. The following movie has highlighted about the “Quantum chemistry in action” which explains the equilibrium process between ionized water and hydroxyl radical [OH.] plus hydronium ion [H3O+].



The detailed applications and the general way of simplifying Schrödinger equations will be posted on the days to come. Interested fellows are suggested to visit the site time to time.
---------------------To be continued-----------------------

Computational chemistry

Anant Babu Marahatta
Ph.D. student in chemistry
Tohoku University
Japan

Perspectives:
In the real world, “A Digital Laboratory could eventually mean that most chemical experiments are conducted inside the silicon chips instead of the glassware of laboratories. Turn off that Bunsen burner; it will not be wanted in ten years.” This intension of the “1998 Chemistry Nobel Prize Awardees” directed the computational procedures for conducting cutting-edge research. In the present condition, computational procedures have become a “superstar”.

Overview: Computational chemistry is a branch of chemistry that uses principles of computer science to assist in solving chemical problems. It is simply the application of chemical, mathematical and computing skills to the solution of interesting chemical problems.
It uses computers to generate information such as properties of molecules, simulated experimental results, displays almost all the information with the chemical visualization package developed by considering the results of the theoretical chemistry.

Computational chemistry has become a useful way to investigate materials that are too difficult to find or too expensive to purchase. It also helps chemists to make predictions before running the actual experiments so that they can be better prepared for making observations.
Similarly, it can predict unobserved chemical phenomena of the macro molecules like amino acids, protein, DNA, enzymes etc. in the visual form. The following animation has explained about the preliminary processes of molecule modeling, electron density tracing and some prerequisites of the computational chemistry.
To calculate the structures and properties of molecules and solids computationally, several computer software have been developed. Some of the common software includes,
• Gaussian xx, Gaussian 09 currently [Gauss. Inc. USA]
• GAMESS [Gordon research group, Iwa state Univ.]
• MolPro, 2010.1 currently [H.-J. Werner and P. J. Knowles]
• DFTB+ [Bremen Center for Computational Materials Science]
• MOPAC [Stewart Computational Chemistry ]
• Spartan [Spartan Chemical Company, Inc.]
• Sybyl [Tripos, a Certara company]
• SIESTA[Spanish Initiative for Electronic Simulations with Thousands of Atoms]
The employed computational methods rely on the software installed and can cover both static and dynamic situations. In all cases, the computational time and other resources (such as memory and disk space) increase rapidly with the size of the system being studied. That system can be a single molecule, a group of molecules, or a solid. In order to perform the calculation in an efficient way with extremely low computational cost, proper selection of the computational method is mandatory.