Chemistry 4560/5560 Molecular Modeling Fall 2014 · Chemistry 4560/5560 Molecular Modeling Fall 2014 2 d. Give specific examples of stationary points and briefly explain why they

Chemistry 4560/5560 Molecular Modeling Fall 2014

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Final Exam Name:……………………………………….

User’s guide: 1. Read questions carefully and make sure you understand them before answering (if not, ask). 2. Answer only the question that is asked, not a different question. 3. Unless directed otherwise (e.g. offered a short answer such as Yes/No) answer in a complete, grammatically meaningful English sentences. 4. Formulate your answers clearly and precisely. 5. Write legibly. Example: Q: What is Huckel theory? A: Huckel theory is an empirical molecular orbital method designed for electronic structure calculations for conjugated hydrocarbons.

1. Potential Energy Surface (PES).

a. Potential energy surface (PES) is one of the central concepts in molecular modeling. Define

PES:

b. Can PES be experimentally measured? (Yes/No)

c. What are the so called ‘stationary points’ on the PES surface?


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d. Give specific examples of stationary points and briefly explain why they are important:

e. For a model molecule (e.g. in Gaussian), conceptually describe how a stationary point on the

PES is found:


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f. Stationary points can be characterized by calculation of vibrational frequencies. For the

examples of the stationary points on the PES you gave above, explain how.

g. Does it make sense to calculate (harmonic) vibrational frequencies at other than stationary points

of the PES? Explain you answer.


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2. In the following, you will describe in general terms (no specific keywords etc. needed) the

sequence of steps and types of calculations that you need to obtain a desired molecular

property.

For example:

Q: NMR chemical shift of molecule X with respect to TMS

A: 1. Optimization of X

2. Calculation of NMR shieldings for X

3. Optimization of TMS

4. Calculation of NMR shieldings for TMS

5. Subtraction of TMS shieldings from those of the molecule X yields the desired chemical

shifts.

For following reaction

CH3Cl + OH ⇌ CH3OH + Cl

a. The reaction enthalpy at 450K and 10 atm pressure.


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b. The equilibrium constant at the same T and p:


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c. The forward rate of the reaction at the same T and p


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d. The isotopic effect of deuteration of CH3Cl (i.e. CH3Cl becomes CD3Cl where D stands for

deuterium) on the rate of the reaction. Isotopic effects means how the reaction rate changes upon

the isotopic substitution.


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3. When using various computational levels, it is important to pay attention to their

availability. This is an excerpt from the Gaussian manual:

AVAILABILITY

Analytic energies and gradients for CCD and CCSD, numerical gradients for CCSD(T), and numerical

frequencies for all methods. The restricted open-shell (RO) method is available for CCSD and CCSD(T)

energy calculations.

Explain the meaning and practical implications of the availability of

a. Analytic gradients:

b. Analytic frequencies:


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c. Numerical gradients:

d. Numerical frequencies:


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5. The Hartree-Fock (HF) theory forms the basis of the entire computational chemistry (as

well as computational physics). Yet, as you know, HF theory provides neither correct, nor

even very accurate solution to the molecular electronic structure problem (= molecular

Schrodinger equation).

a. Why, then, is HF theory so important?

b. Despite its central importance, however HF level is rarely used in computational chemistry.

What is the major drawback of HF that demands use of different (higher-level) methods?


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c. Even though HF equations significantly simplify the multi-electron problem, they still cannot

be solved in the closed form. Rather, they require a procedure known as the Self-Consistent Field

(SCF). Describe how this procedure works:


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d. There are several incarnations of HF methodology in practical use. In particular, we distinguish

between the so-called ab initio HF and semi-empirical HF methods. Describe the difference

between them.


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f. Furthermore, HF can be restricted (RHF) or unrestricted (UHF). For what kinds of problems are

RHF calculations appropriate, and for what problems UHF ones are used? Explain briefly and

illustrate the RHF and UHF electron configuration with a sketch.


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6. Basis sets

a. Molecular orbitals (MO) are generally described as a linear combination of atomic orbitals

(MO-LCAO). The AO’s are in turn expressed in terms of (atomic) basis functions. The Slater-type

orbital (STO) is considered to correct form of the atomic basis function. Why?

b. What is the difference, if any, between the Slater-type orbital (STO) and Slater determinant?


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c. STOs are virtually never used in actual basis sets. What types of functions are used instead and

why?

d. This is a piece of the Gaussian calculation output:

There are 297 symmetry adapted basis functions of A symmetry.

Integral buffers will be 131072 words long.

Raffenetti 2 integral format.

Two-electron integral symmetry is turned on.

297 basis functions, 516 primitive gaussians, 322 cartesian basis functions

86 alpha electrons 86 beta electrons

What is the difference between:

i) a basis function (297 of them) and a primitive Gaussian (516 of them) ?


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ii) a basis function (297 of them) and a Cartesian basis function (322 of them)?

e. Explain what effective core potential (ECP) is and for what types of calculations it is

advantageous (or necessary) to use ECPs:


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7. Post HF methods: configuration interaction (CI), Moller-Plesset perturbation theory

(MPn) and coupled cluster (CC) theory.

a. What is the objective of the configuration interaction (CI) methods?

b. Describe briefly how the CI method works:


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c. Why is CID (configuration interaction doubles) the lowest possible level of CI?

d. Truncated CI (such as CID) is seldom used in practice. What is the main reason?

e. On the other hand, coupled clusters (CC) are a very popular and useful (though quite demanding)

computational method. How does CC solve the main deficiency of the CI methods?


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f. Moller-Plesset methods, such as MP2, are also very frequently used in practical calculations.

What is the main limitation of MP methods?

g. What is meant by non-dynamical electron correlation (as opposed to dynamical electron

correlation) and what types of methods are designed to specifically deal with it?


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8. Density functional theory (DFT).

a. Density functional methods account for the vast majority of quantum-chemical calculations done

today and over the last two or so decades. Why are DFT methods so popular?

b. As you answered above somewhere, HF equations are solved by a SCF procedure. The DFT is

formulated in a similar manner – the so-called Kohn-Sham (KS) equations. Are the KS equations

also solved by the SCF procedure? (Yes/No)

c. What is the difference between HF orbitals and Kohn-Sham (KS) orbitals?


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d. Further contrasting DFT with HF methods (in general, conceptual terms regarding the overall

theory, rather than e.g. specific practical results) what are two main disadvantgates of the DFT?

e. List five basic classes of DFT functionals:


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9. Molecular mechanics.

a. Molecular mechanics (MM) methods are based on an empirical energy function, called a MM

force field (FF). Unlike for quantum calculations, it is necessary to specify not only an atom type

(i.e., H, C, etc.) but also how and to what other atoms it is bonded for the MM FF to work. Briefly

describe why that is:

b. To be useful, a MM FF must be transferable. What is meant by FF transferability and why is it

important?


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c. In general, is it possible to study chemical reactions where covalent bonds are broken and formed

by MM? Explain.

d. Molecular dynamics (MD) simulations are the most frequently used approach for calculation of

equilibrium macroscopic properties of condensed phases, solutions of macromolecules etc. Why

is MD simulation, i.e. a run over a period of time necessary for obtaining such properties, rather

than e.g. a single calculation?


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10. Population analyses, implicit solvent, excited states etc.

a. Are atomic partial charges uniquely defined? (Yes/No)

c. Explain the concept of the reaction field (RF) and how a self-consistent reaction field (SCRF)

calculation works:

b. The main contributions to the solvation (free) energy are: electrostatics, cavitation and

dispersion. Which ones do polarized continuum solvent models (PCM) generally account for and

which ones do they neglect?


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d. Give two main reasons why it is generally incorrect to write an excited state wavefunction as a

single (Slater) determinant:

e. Why is CIS a method for excited state calculation, while CID for a ground state one?

f. Is time-dependent DFT (TD-DFT) used for calculations of any time-dependent properties?

Explain.

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Chemistry 4560/5560 Molecular Modeling Fall 2014 · Chemistry 4560/5560 Molecular Modeling Fall 2014 2 d. Give specific examples of stationary points and briefly explain why they