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Lab 1, Module 1. Chem126/226, Winter 2012. 35 points. This lab in one of only 2 labs that runs for a week and a half, instead of just a week. We will learn about the several standard ab initio electronic structure methods, their accuracy, speed, and limitations. We will learn how to use those methods to find the most stable structure of a molecule, identify other (local) minima on the potential energy surface (PES), find transition states between different minima, and calculate free energy barriers to chemical reactions. Read or remind yourself about:Schrodinger equation, Harmonic oscillator, normal modes of vibration, variational principle. HartreeFock, electron correlation, basis sets, foundation of DFT, how different DFT methods differ, and what is approximate about them. Part I (15 points). Exploring different ab initio techniques for geometry optimization and predicting IR spectra of molecules We will start from probing the accuracy of different ab initio methods. We will use a simple molecule of methanol for this exercise:
I.1. Simple geometry optimization and vibrational frequencies calculation Please build the zmatrix for methanol, either by hand, or using MOLDEN, or just vi, if you prefer. Make the input for Gaussian 09, for geometry optimization of the methanol molecule at the HartreeFock level with the 321G basis set (HF/321G). Optimize the geometry, read the final geometry and molecular orbitals from this job and perform the vibrational frequencies calculation. Confirm that the found structure is a minimum on the PES of methanol. Compare the obtained frequencies with the experimental IR spectrum of methanol. Make the assignment of features in the experimental spectrum (what normal modes of vibration correspond to what features in the spectra?). You can visualize normal modes using MOLDEN. Why is that that only some of the normal modes are seen in the IR spectrum?
Source:webbook.nist.gov
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Are you satisfied with your agreement between theory and experiment? What do you think is missing in our approach that would let us reproduce the spectrum better? I.2. Exploring basis sets Part of the reason the result abstained in I.1 is soso is that the basis set, 321G, is really small. Why is that that bigger basis sets are better? Let us now increase the basis set size, and see what happens to the total energy of the methanol molecule, and to the agreement of the theoretical and experimental IR spectrum. Repeat geometry optimization for methanol, using HF/631G*, and HF/6311++G**. What happens to the total energy of the optimized molecule, as the basis set grows? Is the trend reasonable, based on the variational principle? I.3. Exploring electron correlation and its effect on the quality of the results Another reason our HF results are lacking some chemical accuracy is the lack of electron correlation. Correlated electronic structure methods based on the HF reference function include, for example, MPn and CCSD(T), which allow to improve the HF solution, provided it is not too bad to begin with. Let us pick the 631G* basis set, as a compromise between accuracy and computation time. Please reoptimize the geometry of methanol using MP2/631G*, MP3/6 31G*, and CCSD(T)/631G* (do not perform frequencies calculations, as it would take too long). Observe how the increase in the amount of accounted electron correlation leads to the increase in computational expenses. Observe how the total energy of the molecule changes between the methods. Please compare the quality of these computational methods. A principally different group of methods is based on the Density Functional Theory (DFT), where the total energy, as well as all other properties of chemical systems are dependent on the overall electron density (i.e. one number), instead of coordinates of all electrons. Let us explore DFT. Please reoptimize the geometry of methanol with B3LYP/631G* and TPSSh/631G*. How does the speed of calculations compare to those done with HF, MP2, and CCSD(T)? Note that, because DFT is a “handmade” method, the total energy may be lower than the experimental value. Extra Credit (5 points):you find the experimental value for the total energy of the Can methanol molecule? How do our results compare to it? Using the optimized geometries of methanol at corresponding levels of theory, recalculate the vibrational spectra at MP2/631G* and TPSSh/631G*. How do the results compare to the experimental IR spectrum? Would you agree that, at least for organic molecules, DFT is an excellent compromise between the computational cost and accuracy? Please be aware though that this is not always the case! We will consider cases where DFT fails later in the course. But for closeshell organic molecules, we are usually safe to use DFT. Part II (15 points). Potential Energy Surfaces For a molecule consisting of N atoms, the PES has the dimensionality of (3N6). Often, these PESs have exceptionally complex structures, with many low energy local minima, and it can be nontrivial to find the true global minimum. The global minimum is the most chemically significant isomer, because it is he one that can be obtained in the experiment and characterized, using spectroscopy, Xray christalography, and other techniques. Sometimes, metastable minima can be captured too. Two of the most famous examples of chemical systems that are stable in
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their notglobal minimum forms are benzene and diamond. II.1. Local and global minima We will start from a reaction of tautomerization between the amino and iminoforms of cytosine. Tautomarization in general can be either acidcatalyzed, or basecatalyzed. It is an important reaction in biology, where, for example, DNA base pairing relies on tautomerization and proper tautomeric forms of the bases.
Notice that only one of tautomers can form the CG WatsonCrick base pair:
Our first goal here is to identify which isomer is lower in energy. Notice that there are many other isomers on the PES of C4N3OH5, besides the two forms shown above. However, from our organic chemistry intuition, we expect cytosine to have one of the forms shown above. Prepare the zmatrixes for the two isomers, optimize their geometries at the B3LYP/631G* level, and calculate vibrational frequencies. Notice that the molecule must reside at least at the first vibrational level, and not at the bottom of the well on the PES. Hence, the ZPEcorrection total energy is: Etotal=EB3LYP/631G*+ZPEEtotal arethe energies to be used to compare the two isomers. Find the ZPE values in your output files for frequency calculations, and calculate the energy difference between the two isomers, in kcal/mol (conversion factor from Hartree to kcal/mol is 607.506). One of the isomers is the global minimum on the PES of cytosine. Which one? II.2. Transition states Now we want to find the transition state (TS) on the PES between the two tautomeric forms of cytosine. By definition, TS is a first order saddle point on the PES, with the only imaginary frequency corresponding to the normal mode that coincides with the reaction coordinate. For the uncatalyzed reaction, the transition state can be guessed to have the transferring proton being halfway between the donor and the acceptor, and the bond lengths being halfway
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to be between the reactants and the products. One may try to find the TS by hand, by guessing its initial structure, preparing a zmatrix for it, and optimizing to the saddle point as follows: # B3LYP/631G* opt=(ts,noeigentest,zmatrix) Alternatively, there are automated techniques implemented in Gaussian http://www.gaussian.com/g_whitepap/qst2.htm), called QST2 and QST3. We will use QST2 here. We have uploaded the instructions for using QST2/3 to VOH, as Handout_TS.pdf, for your convenience. Notice that QST2 and QST3 may fail, in which case the “by hand” approach is unavoidable. You may struggle for a while, trying to find the way that works. Ask for help, we are here for you.Important:when using QST2 or QST3, atoms in your molecules would have to be in the same order. In particular, the transferring H has to be defined with respect to the same 3 atoms in all cases. Find TS by either method. For the found TS, examine the calculated vibrational frequencies, visualize them in MOLDEN, and confirm that there is only one imaginary frequency of the right nature. Using the calculated (optimized) total energy and ZPE of the TS, alculate the energy barriers on the PES for the reaction of tautomerization (forward and backward). Remember to use the ZPEcorrected energy values for the reactant, products, and TS. II.3. Reaction thermodynamic parameters Calculate theG of the reaction of isomertization (the difference in free energy between the reactants and the products), using the thermodynamic quantities obtained in frequencies calculations, according to the following formula: G=Etotal+Ethermal+nRTTSWhereEthermalthe change in the thermal energy between the reactants and the products is (consists of vibrational, rotational, and translational energies),nthe change in the total is number of chemical species in the course of reaction (it equals zero in our case),T isthe temperature (by default it is 298 K, in Gaussian calculations), andS isthe change in entropy. The quantities are available in your Gaussian output files. Using the energy, entropy, and other calculated quantities for the found reactant, TS, and product, calculate the activation free energy ‡ barrier to the reaction of tautomerization,G. Part IV (5 points). Check up questions(please answer concisely; each answer should be no longer than just a couple of sentences)1.What is the principle difference between HF and HFbased methods, and DFT? 2.Is DFT exact? What is approximate about DFT methods that we use? 3.Why is that that MP2 works best when the HOMOLUMO gap of a molecule is large? Hint:look up the expression for the correction to the total energy calculated at MP2 level. 4.What are the major assumptions of the classical transition state theory? 5.Vibrational frequencies calculated in this lab are harmonic, i.e. the Harmonic oscillator approximation was used. When is this approximation valid? Would it be valid for a weakly bound molecule, with a relatively flat PES, like a HeHe dimer?
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