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Introduction to ADF ADF (Amsterdam Density Functional) is a Fortran program for calculations of atoms and molecules (in gas phase or solution). The underlying theory is the Kohn-Sham approach to Density-Functional Theory (DFT). This implies a one-electron picture of the many-electron systems but yields in principle the exact electron density (and related properties) and the total energy. ADF can be used for the study of such diverse fields as molecular spectroscopy, organic and inorganic chemistry, crystallography and pharmacochemistry. In this exercise, you will use it to study the thermodynamic properties of simple reactions. As a powerful DFT calculation package, ADF has diverse functionalities, of which the following will be used in your assignments: Geometry optimization: find the optimized geometry for the desired molecule Transition state calculation: find the transition state or activation barrier between reactants and products and observe the corresponding structure transition Frequency and thermodynamic properties: verify that the global optimized structure has zero imaginary frequency and transition structure has exact one imaginary frequency; provide thermal properties, entropy, internal energy and constant volume heat capacity, of the molecule Input File Structure In order to run ADF, an input file structured by keywords is a must. A keyword is a string of characters that does not contain a delimiter (blank, comma or equal sign). Keywords are not case sensitive. Input is read until either the end-of-file condition (eof) becomes true, or until a record END INPUT is encountered, whichever comes first. In the sample input files for all three types of calculations, geometry optimization, transition state search and frequency calculations, the structured blocks begin with the keyword followed by its the arguments. Blocks are closed by a record containing (only) the word END. Please use the space instead of tab for delimiter. Tab will cause errors. The input file starts with a TITLE keyword, which is followed by the specification of the calculation that user can define for his convenience, like the name of the molecule and the corresponding type of calculation. Remember to keep all the TITLE information in one line. The following block begins with UNIT keyword, which specifies the units used for the molecule geometry, saying angstrom for bond length and degrees for bond angle. The usage of keyword RESTRICTED or UNRESTRICTED depends on the molecule to be calculated. If the molecule is in singlet state, closed shell molecule (no unpaired electron for the molecule), RESTRICTED keyword is used. Otherwise, for all the open shell molecules (systems with unpaired electrons), the UNRESTICTED keyword is used. For your assignments, please be cautious with the unpaired electrons for your systems and then select the correct keyword. The block beginning with ATOMS Z-MATRIX/CARTESIAN contains the internal or Cartesian coordinates of the atoms in the system. In the assignment, you are more concerned with this part since it changes with different systems to be calculated. In this block, one atom is specified in a line with geometric specification regarding to the previous atoms. For example, the ATOMS Z-MATRIX BLOCK for ammonia (NH3) is: Atoms Z-matrix 1 N 0 0 0 0.0 0.0 0.0 f=N/1 2 H 1 0 0 r2 0.0 0.0 f=H/1 3 H 1 2 0 r3 a3 0.0 f=H/2 4 H 1 2 3 r4 a4 t4 f=H/3 End here the columns in italic denote atom’s positions with respect to the origin atom, the first atom (1 N). The columns in bold specify the geometry parameters, bond length, bond angle and dihedral angle, according to the position parameters in the italic columns. For example, the second line “2 H 1 0 0 r2 0.0 0.0 f=H/1” specifies the first H atom (2 H) is bonded with the first atom (1 N), denoted by 1 0 0 in the italic column, with bond length of r2. Since so far there are just two atoms, there are no bond angle and dihedral angle denotations in the bold columns. In the third line of Z-matrix, 3 H 1 2 0 r3 a3 0.0 f=H/2, the second H atom (3H) is bonded with the first N atom (1 N) and has a bond angle with the first N and H atoms, denoted by 1 2 0 in the italic columns, with bond length and bond angle of r3 and a3 in the bold columns respectively. In order to determine the geometric position of the third H atom, the dihedral angle, t4, is introduced for the third H atom in the fourth line of Z-matrix in addition to the bond length and angle parameters. It is the dihedral angle between plane of 4(H) 1(N) 2(H) and plane of 1(N) 2(H) 3(H). The next block is the GEOVAR block. It contains the geometry parameters of the atoms specified in the ATOMS Z-MATRIX block. The BASIS block specifies the fragments used in the calculations, in which different basis sets are specified. In your assignments, the double-zeta basis sets with polarization functions will be used. The GEOMETRY block determines the types of calculation and sets up their corresponding environment variables. For geometry optimization calculation, use: Geometry Optim Internal All End For transition state search calculations, use: Geometry Optim Internal All Transitionstate End For frequency calculations, use: Geometry Optim Internal All Frequency End The first line of this block, Optim Internal All, means the optimization is performed on all atoms of the Z-matrix. The transition state search calculation is performed with keyword of transitionstate in this block. For frequency calculations, keyword of Frequency is specified in this block. The block of XC (exchange-and-correlation functional) specifies the Functional used in the calculations. It consists of an LDA and a GGA part. LDA stands for the Local Density Approximation, which implies that the XC functional in each point in space depends only on the (spin) density at the same point. GGA stands for Generalized Gradient Approximation and is an addition to the LDA part, by including terms that depend on derivatives of the density. Below is the list of options for XC: For the exchange part the options are: Becke : the gradient correction proposed in 1988 by Becke [3]. PW86x : the correction advocated in 1986 by Perdew-Wang [4]. PW91x : the exchange correction proposed in 1991 by Perdew-Wang [5]. For the correlation part the options are: Perdew : the correlation term presented in 1986 by Perdew [6]. PW91c : the correlation correction of Perdew-Wang (1991), see [5]. LYP : the Lee-Yang-Parr 1988 correlation correction, [7-9] Some GGA options define the exchange and correlation parts in one stroke. These are: PW91 : this is equivalent to pw91x + pw91c together. Blyp : this is equivalent to Becke (exchange) + LYP (correlation). LB94 : this refers to the XC functional of Van Leeuwen and Baerends [10]. There are no separate entries for the Exchange and Correlation parts respectively of LB94. In your assignment, you will try two functionals from the list above, Becke and Perdew for LDA and PW91 for GGA, and discuss how they affect the energy and geometry calculations of the system. The next block begins with CHARGE and just has one line. The first part of CHARGE is related to the charges of the system and the second part is concerned with the multiplicities of the system: i.e. the number of unpaired electrons. For example, the multiplicity for H atom is 1 but 0 for H2 since electrons in H2 are paired. In your assignment, please be cautious with the multiplicity of your systems since every molecule can have several states, singlet or doublet or triplet or …, and only one of them is the ground state. Reference: 1. ADF examples: http://www.scm.com/Doc/Doc2002/Examples.pdf 2. ADF User Manual: http://www.scm.com/Doc/Doc2002/ADFUsersGuide.pdf 3. Becke, A.D., Physical Review A, 1988. 38: p. 3098. 4. Perdew, J.P. and Y. Wang, Accurate and simple density functional for the electronic exchange energy: generalized gradient approximation. Physical Review B, 1986. 33(12): p. 8800. 5. Perdew, J.P., et al., Physical Review B, 1992. 46: p. 6671. 6. Perdew, J.P., Density-functional approximation for the correlation energy of the inhomogeneous elctron gas. Physical Review B, 1986. 33(12): p. 8822. 7. Lee, C., W. Yang, and R.G. Parr, Development of the Colle-Salvetti correlation-energy formula into a funcitonal of the electron density. Physical Review B, 1988. 37(2): p. 785. 8. Johnson, B.G., P.M.W. Gill, and J.A. Pople, The performance of a family of density funcional mehtods. Journal of Chemical Physics, 1993. 98(7): p. 5612. 9. Russo, T.V., R.L. Martin, and P.J. Hay, Density Functional calculations on first-row transition metals. Journal of Chemical Physics, 1994. 101(9): p. 7729. 10. van Leeuwen, R. and E.J. Baerends, Exchange-correlation potential with correct asymptotic behaviour. Physical Review A, 1994. 49(4): p. 2421-2431. Interpretation of the Output File Once your geometry optimization and transition structure search jobs are done, output files with the name you specified are generated. The output files contain much more information than what you need in your assignments. Below is the part of the information on the convergence of the calculation and the optimized geometry parameters calculated. In addition to the optimized geometry, the total bonding energy is also very important and listed in several units, such as hartree, ev, kcal/mol and kj/mol. In your assignments, please use kcal/mol for convenience. In order to get the desired information quickly, please use the search function in editors like pico, vi or emacs and search for the keyword like “Final Geometry” and “Total Bonding Energy” to locate the optimized geometry and energy for ground state structure and transition state structure. As for the output file from the frequency calculation, it has the same name with the input file but with the file extension of out. The part of information that includes the calculated frequencies is shown below: List of All Frequencies: Intensities =========== Frequency Dipole Strength Absorption Intensity (degeneracy not counted) cm-1 1e-40 esu2 cm2 km/mole ---------- ---------- ---------- -1165.478453 764.071305 -223.211317 298.194636 1213.123186 90.674005 459.284720 1414.641735 162.857039 589.037030 505.329568 74.609715 705.055800 676.149880 119.493570 1210.179005 46.629461 14.144516 1801.529386 570.845596 257.773386 3421.622715 13.308611 11.414133 3740.869138 560.651872 525.707124 Assignment 1: Thermo-chemistry Study of Simple Reaction Calculate the enthalpy for the following reaction: 2H2 + O2 2H2O 1. Calculate the reaction enthalpy for the reactants and products using the LDA by Becke and Perdew functional and the GGA by PW91 functional. Calculate the enthalpy for the whole reaction. The sample input file of Geometry Optimization calculation is provided in your account under directory of ADFAssignment and contains the minimum. Compare your results with the experimental data and assess the accuracy of your calculations and effects of different functionals. 2. Compare the optimized structures of reactants and products from your calculation with those from the experimental data. 3. Play around the molecular visualization tool, ViewerLite, and draw the optimized structures for reactants and products from your preferred tool. Hints: The functional specification for LDA by Becke and Perdew in the input file is: XC LDA VWN Gradients PostSCF BECKE PERDEW End The functional specification for GGA by PW91 in the input file is: XC GGA PW91 End The experimental data for molecule structures and formation enthalpy can be obtained from NIST database: http://srdata.nist.gov/cccbdb/ Be careful with the multiplicity of O2 molecule when calculating its ground state. The different states and find the ground one. Assignment 2: Transition Structure Calculation of the Hydrogen Shift Reaction 1. Calculate the reaction enthalpy for Formaldehyde transforming into trans form of Hydroxycarbene with LDA by Becke and Perdew. Verify the optimized geometries of reactant and product with frequency calculations and tabulate their corresponding frequencies: use the optimized geometry from your geometry optimization result as the input geometry parameters for frequency calculation. The optimized geometry is verified by showing zero imaginary (negative) frequency in your frequency calculation result: H2CO HCOH 2. Calculate the transition structure of the Hydrogen shift from the Carbon terminal of Formaldehyde (H2CO) to the Oxygen terminal of hydroxycarbene (HCOH). Verify that your transition structure with frequency calculation by showing there is exact one imaginary frequency in your frequency calculation result. The guessed geometry of transition structure looks like: O O H H O C C C H H H H Formaldehyde H-Shift TS Hydroxycarbene 3. Plot the potential energy surface (PES) of this reaction by three points you calculated, the enthalpies of reactants, transition state and products. The PES shows activation barrier (saddle point) for the reaction from reactant to product. Explain the height of the PES.