Density Functional Theory (DFT): Theory & Simulation

density functional theory uses electron density, not wave functions, offering lower computational cost and high accuracy, guided by the hohenberg theorem and a universal functional.

Show how electron density identifies electron count and nuclei positions, enabling a Hamiltonian from density to solve Schrodinger equation, and emphasize search for a direct energy density relationship in DFT.

Demonstrates that the ground state energy is uniquely determined by the ground state electron density, introducing the first Hohenberg and Kohn theorem and the external potential in DFT.

The second Hohenberg-Kohn theorem treats the ground-state density as variational, linking density to the wave function; trial densities bound the true density and allow energy minimization via linear variation.

Examine density functional theory foundations, including the Hohenberg–Kohn theorems, variational optimization, Thomas–Fermi and Kohn–Sham functionals, highlighting kinetic and Coulomb interactions.

Examine how the Thomas-Fermi model's electron-electron repulsion creates error, and how the exchange-like function h cancels spurious interactions in one-electron systems, highlighting the challenge for multi-electron density functional applications.

Explore Slater's exchange approximation for Hartree-Fock and its use in density functional theory, including the x-alpha method with an adjustable alpha parameter.

Examine the Kohn-Sham model, decomposing total energy into kinetic and potential parts. Show the non-interacting reference system with Kohn-Sham orbitals and classical versus non-classical electron interactions via exchange-correlation.

Explain how exchange correlation functionals include all contributions to the energy not included in other terms, cancel self-interaction errors, and account for Pauli repulsion, correlation energy, and kinetic energy corrections.

Explore how the exchange correlation functional underpins density functional theory. Acknowledge the Hohenberg Cohn theorems and the density-energy relationship, and that the exact form is unknown.

Explore solving for Kohn–Sham orbitals via variational basis expansion, optimizing density to minimize energy while accounting for kinetic energy, electron–nucleus potential, electron–electron repulsion, and exchange–correlation.

Compare the Kohn-Sham and Hartree-Fock operators, noting identical kinetic energy, electron-nucleus attraction, and electron-electron repulsion terms, with HF lacking correlation and KS adding exchange-correlation via a self-consistent field approach.

Solve kohn-sham orbitals via self-consistent field iterations, using the fock-like kohn-sham operator, the density matrix p_mu nu, and the overlap matrix to obtain orbital energies.

Compare Hartree-Fock and DFT by focusing on the exact density-based energy functional. Learn how approximate exchange-correlation functionals in Kohn-Sham DFT capture exchange, correlation, and kinetic energy corrections.

explains empirical and non-empirical exchange-correlation functionals in density functional theory, comparing parameter fitting to experiment with constraint-based, first-principles approaches, and noting B3 as an empirical hybrid example.

Explore the local density approximation (LDA) for density functional theory, based on a uniform electron gas model, and learn spin variants and functionals like VW and PZ-81.

Learn how generalized gradient approximation improves on LDA by including density gradients, with non-empirical and empirical functionals like BP86 and PBE, and limitations for dispersion and hydrogen bonding.

Explore meta-GGA as an an advanced exchange correlation functional in DFT, adding kinetic energy density to the density and its gradient, increasing accuracy at higher cost, with TPS as an example.

Explore hybrid exchange–correlation functionals that blend Hartree-Fock exchange with DFT, examining B3LYP and related functionals, their parameterization, accuracy, and limitations for dispersion and solids.

Learn to work with Gaussian and Gaussview in computational chemistry, designed for experimentalists, address problems with patience, report errors via email with screenshots or output files.

Explore Gaussian, Vasp, Castep, Quantum Espresso, and Q-chem for quantum calculations; visualize with VMD, Gaussview, PyMol, and Chemcraft; learn force field, ab initio, semi-empirical, density functional theory, and molecular dynamics.

Learn how to obtain and install Gaussian and GaussView for DFT practice, including university access, downloading, extracting with passwords, entering serial numbers, and validating installation.

Learn to customize GaussView display: adjust background, window size, hydrogen visibility, labels, bonds, stereochemistry, symbols, axis, and ball-and-stick vs wireframe, including ONIOM layer tips.

learn how to download and use multi Dwfn 3.8 for windows, extract with seven zip, and access examples, license, and quickstart.

Download and install vmd (visual molecular dynamics) on Windows 64-bit, register for an account, accept license terms, then run vmd from the installer or program files, vmd.exe.

Apply density functional theory to benzene by setting up Gaussian calculations for optimization plus frequency, energy, and NMR, and explore options like Berny optimization, intrinsic reaction coordinates, and stability checks.

Learn how to choose a dft functional in gaussview, switch from hartree-fock to methods like bp86 or b3, and apply diffuse and polarization functions for non-hydrogen and hydrogen atoms.

Configure link0 commands to set memory limits in mw, allocate shared processors, and manage checkpoint and read/write files for long dft calculations.

Learn when to use quadratically convergent SCF as a last resort in optimization, where SCF equals qk is chosen if other methods fail, though simple molecules may not need it.

Learn how to handle symmetry during DFT optimization by choosing to ignore symmetry, and save structures in Cartesian or z matrix formats while enabling polarizability calculations.

Choose a solvation model (IFP, CM, SMD, CPCM, PCM) for benzene in toluene or acetone, guided by Gaussian solvent lists; verify toluene is present and set SRF to CPC model.

Explore the variety of dft methods and the keywords used in gaussian and similar software. Learn how to use hybrid and pure functional keywords correctly, including PPE and B3 variants.

Read atom connectivity in a Gaussian input file by interpreting the root line's geom connectivity and bond values, such as 1.5 for partial double bonds and 1.0 for single bonds.

Learn how to locate and interpret DFT computational methods in a paper, including B3LYP, 6-31G* basis, Gaussian 03, with frequency analysis to identify minima or transition states and barriers.

Open a frequency calculation in Gaussview and review the results summary from the log file for a toluene solvation (B3, CPC), noting zero imaginary frequencies, energy, dipole moment, and polarizability.

Open the log file to view optimized structure and intermediate geometries; confirm the Gaussian job completed in three optimization steps and learn to read intermediate geometries and retain settings.

Explore GaussView’s vibrational analysis by linking infrared and Raman activities to specific modes, view displacement vectors, scale frequencies, and export spectra for experiment comparison.

Explore charge distribution in GaussView for density functional theory using Mulliken charges, with atom-specific numbers, colors, and dipole moment visualization.

Open the Gaussian log file in WordPad to view input and moments, then compare convergence criteria: maximum force, RMSE force, maximum displacement, and mass displacement to thresholds to assess optimization.

Track energy changes at each optimization step, noting FCF done and the energy of successive structures, and observe dipole, quadrupole, optical moments, and Hartree-Fock energy.

Trace the completion of a Gaussian optimization and a frequency calculation, revealing 30 vibrational frequencies, reduced mass, and force constants for a 12-atom system with IR and Raman activities.

Explain how zero point and thermal corrections to energy, enthalpy, and Gibbs free energy adjust the optimization energy to yield corrected values, and note frequency calculations take longer than optimization.

Learn to draw structures in Gaussview, the drawing interface for Gaussian calculations, create input files, and visualize results, using the drawing window, toolbar icons, and atom options.

Draw pentane in Gaussview by choosing carbon tetrahedral for sp3 carbons, replacing hydrogens with carbons, and saving the file as a Gaussian input in Cartesian coordinates.

Explore drawing a square planar nickel complex in a DFT simulation workflow, placing chlorine ligands on nickel and toggling hydrogen defaults across windows to form nickel tetrachloride.

Learn to draw binaphthyl with ethyl and nitro substituents in GaussView, adjust dihedral angles, and validate atom distances for accurate computational chemistry input.

Explore constructing amino acid chains by selecting alanine fragments as central, n-terminal, and c-terminal, then add acetyl or methyl groups and nucleosides to illustrate peptide structures.

Represent molecular orbitals as a linear combination of basis functions to build the density, while choosing basis sets that balance accuracy with the computationally demanding two-electron integrals.

Atom centered Slater type orbitals model the hydrogen 1s cusp and exponential decay (alpha controls decay), but three- and four-center integrals cannot be evaluated analytically, so gaussian orbitals are used.

Explore Gaussian type basis functions as a convenient alternative to Slater type orbitals, detailing normalization, r squared dependence, and how alpha values influence decay beyond r=1, around two angstrom.

Use contracted Gaussian functions to approximate Slater orbitals in density functional theory, combining primitive Gaussians with contraction coefficients to form basis functions and enable analytic three- and four-center integrals.

Learn how contracted Gaussian and Slater basis functions model nodal and angular behavior in atomic orbitals using spherical or Cartesian harmonics.

Describe how a basis set uses contracted gaussian functions centered on atoms, with one basis function per occupied orbital, such as sto 3g for cost–accuracy balance.

Single zeta basis sets describe each atomic orbital with a single contracted Gaussian, such as Sto-NG, and Sto 3G is not suitable for quantitative calculations.

Understand multiple zeta basis sets where each orbital uses more than one contracted Gaussian function; double and triple zeta provide better near-nucleus and away-from-nucleus behavior, increasing accuracy but computational cost.

Learn split valence basis sets (Pople's type) in density functional theory, assigning multiple zeta to valence while core gets single zeta to balance accuracy and cost.

Polarization functions in basis sets are needed to provide higher angular momentum, enabling d and p orbitals to describe SN2 transition states and hydrogen-involved bonds.

Explain how polarization functions are added in 6-311G(d,p) and GDP basis sets, including core and valence orbitals for oxygen, with contracted and primitive Gaussian counts and star notation.

Explore diffuse functions in basis sets, where electron density spreads far from nuclei, and learn how plus notations denote diffuse functions on atoms, with examples from water and anions.

Choose a basis set by testing calculations or consulting literature, with polarization functions needed for publication-quality results. Include diffuse functions for long-range interactions, excited states, or anions.

Apply plane wave basis sets for periodic systems, a natural description under periodic boundary conditions, defined by a kinetic-energy cutoff, with wave functions identical and continuous across cells.

Learn how effective core potentials ignore core electrons to reduce basis functions and cost, while capturing core and nuclear effects for accurate valence calculations with common ECP basis sets.

Demonstrates applying a mixed basis set with gen in a PtCl4 calculation, fixes Gaussian errors, and defines chlorine and platinum pseudopotential basis sets with dummy lines and SCF tweaks.

Learn to import a basis set from Basis Set Exchange for Gaussian calculations by selecting platinum, copying the basis and ECP, and updating the Gaussian input file accordingly.

Explore how to import a cc-pvdz basis set from the basis set exchange into a Gaussian input file, adjust the lines for platinum, and verify energy changes.

Learn to obtain vibrational frequency scaling factors from the NIST CBDB table. Choose a method and basis set from the table and apply 0.9642 scaling factor.

Learn how to perform NMR calculations with DFT on an optimized benzene structure, selecting NMR options and Jiao or CSG methods while skipping spin-spin coupling and using toluene as solvent.

Analyze NMR spectra by selecting nuclei, understanding shielding in ppm with reference choices, compare proton and carbon shifts to literature, and convert DFT methods to WP04 or WC04 via IOP.

Apply DFT-calculated NMR chemical shifts using scaling factors from the chemical shift repository, with proton and carbon-13 tables across solvents or gas phase and various methods.

This lecture explains performing a TD-DFT UV-Vis calculation for benzene, selecting time-dependent methods, configuring singlet and triplet excitations, and solving for 20 excited states to analyze the UV spectrum.

Perform fluorescence calculations with time-dependent DFT by optimizing the excited state and selecting the root from UV results. Set up Gaussian 09 with opt+frequency, singlet state, and acetonitrile solvent model.

Learn to analyze fluorescence output from a DFT calculation, examine long runtimes, address excited-state convergence issues, and track Stokes shifts from optimization steps.

Explore how dispersion corrections are applied in density functional theory, comparing d2, d3, and d4 approaches, and learn to enable empirical dispersion keywords like gd2 or gd3 in Gaussian.

Examine basis set superposition error in fragment interactions and apply counterpoise correction to obtain accurate interaction energy. Learn how overlapping basis functions from fragments a and b drive BSSE.

Explore basis set superposition error (bsse) corrections via counterpoise in dft, using Gaussian 09, M052X and 6-31+G(d,p); optimize, verify minima, and sample orientations on C2 surface.

Set up counterpoise corrections by defining two fragments in the Gaussian input, assign correct charges and multiplicities, ensure fragment labeling and numbering, and validate via Gaussview before running.

Explore density functional theory (DFT) to extract raw and BSSE-corrected interaction energies. Learn how BSSE corrections improve the accuracy of interaction energy calculations in DFT.

Drag a file into multi dwfn to start analysis, view molecular structure and orbitals, and access properties, topology, line, plane, and region plots plus orbital localization and bond order analyses.

Generate a wfn file for multiwfn by running a Gaussian job as energy, ignoring symmetry, setting out=wfn and density=all, and saving as complex w two in the target folder.

Learn to perform energy decomposition analysis (EDA) between two fragments of a C20 fullerene nanobelt, extracting electrostatic, repulsion, and dispersion contributions from Gaussian outputs.

Perform non-covalent interaction index (NCI) analysis using Multiwfn and VMD, selecting RDG analysis with medium quality, generating output text and cube files, then transfer them to the VMD folder.

Open VMD, load visualization state, and render a 3d non-covalent interaction plot to show van der waals interactions between a belt and an amino acid, saving a high-quality image.

Generate a 2d rdg graph by preparing output.txt in Excel, delete columns A, B, and C, confirm two columns remain, then copy Output.txt to Jeonju plot bin directory.

Open the command prompt as administrator, copy the output file path, navigate to c:\program files\plot\bin, and run gnuplot with the corresponding map script to generate the 2d plot.

Learn to create and export a 2D NCI plot from RDG mapper files using image editing software like GIMP, including file rotation and saving as TIFF, JPG, or PDF.

Evaluate NCI results by comparing 2D and 3D plots to distinguish hydrogen bonding from van der waals interactions and steric clashes using sin lambda two rho and rdg.

Learn to perform Quantum Theory of Atoms in Molecules analysis with Multiwfn and VMD to assess non-bonding interactions between fragments, identify bond paths and critical points, and visualize labeled CPS.

Analyze bond critical points (BCP) from QTAIM outputs in Excel, extract BCP data including electron density and energy densities, and optionally export to Python for further processing.

Plot QTAIM 3 with VMD by loading aim.vmd and mole.pdb, revealing 88 atoms and bond critical points, and exporting high-quality images suitable for research papers and theses.

Interpret bcp analysis results to classify bonds by electron density, Laplacian, energy density, and interaction energy, distinguishing covalent, polar covalent, hydrogen, and van der waals interactions.