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Open Access Publications from the University of California

Scholarly Works (360 results)

  • Article
  • Peer Reviewed
UC Berkeley Previously Published Works (2023)
The technique of surrogate optimisation is to use a simpler function to approximate a complex function that is time-consuming to evaluate. We show that the maximum of a special type of surrogate function (Formula presented.) is at (Formula presented.), and that there is one and only one local maximum both in (Formula presented.) and (Formula presented.). This function (Formula presented.) has been found to be useful in various aspects of electronic structure theory, including proving the Carlson-Keller theorem, and localising orbitals. As one other example, we apply it here to optimise the ground state of molecules using the Generalised Valence Bond wavefunction.
    Cover page: A linear surrogate for optimising functions of an orthogonal matrix with applications in wave function theoryCreative Commons 'BY' version 4.0 license
    • Article
    • Peer Reviewed
    UC Berkeley Previously Published Works (2014)
    A 10-parameter, range-separated hybrid (RSH), generalized gradient approximation (GGA) density functional with nonlocal correlation (VV10) is presented. Instead of truncating the B97-type power series inhomogeneity correction factors (ICF) for the exchange, same-spin correlation, and opposite-spin correlation functionals uniformly, all 16,383 combinations of the linear parameters up to fourth order (m = 4) are considered. These functionals are individually fit to a training set and the resulting parameters are validated on a primary test set in order to identify the 3 optimal ICF expansions. Through this procedure, it is discovered that the functional that performs best on the training and primary test sets has 7 linear parameters, with 3 additional nonlinear parameters from range-separation and nonlocal correlation. The resulting density functional, ωB97X-V, is further assessed on a secondary test set, the parallel-displaced coronene dimer, as well as several geometry datasets. Furthermore, the basis set dependence and integration grid sensitivity of ωB97X-V are analyzed and documented in order to facilitate the use of the functional.
      Cover page: ωB97X-V: A 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy
      • Article
      • Peer Reviewed
      UC Berkeley Previously Published Works (2019)
      The physical origin of blue-shifting hydrogen bonds remains a subject of debate, although many plausible explanations have been proposed. Using a molecular property decomposition analysis based on absolutely localized molecular orbitals, we investigated several representative F3CH···Y (Y = H2O, NH3, Cl-) complexes. We reveal that features of a blue-shifting H-bond already appear on the frozen surface where both polarization and charge transfer (CT) are "turned off", and that the final frequency shift observed depends on the strength of CT. Further decomposition of forces at the frozen level shows that Pauli repulsion is the only component that shortens the C-H bond in the short-range, while both permanent electrostatics and dispersion lengthen the bond. The effects of these forces from the medium to long-range are also discussed. Our analysis provides a complete picture for blue-shifting H-bonds and suggests two necessary conditions for their features to be observed at equilibrium structures: (i) stronger Pauli repulsion than the combination of electrostatic and dispersion forces; (ii) relatively weak CT that is insufficient to compensate for the blue-shifting effect of the frozen interaction.
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      Cover page: Probing Blue-Shifting Hydrogen Bonds with Adiabatic Energy Decomposition Analysis
      • Article
      • Peer Reviewed
      UC Berkeley Previously Published Works (2019)
      We present a comprehensive study of two single-reference approaches to singlet biradicaloids. These two approaches are based on the recently developed regularized orbital-optimized Møller-Plesset method (κ-OOMP2). The first approach is to combine Yamaguchi's approximate projection (AP) scheme and κ-OOMP2 with unrestricted (U) orbitals (κ-UOOMP2). By capturing only essential symmetry breaking, κ-UOOMP2 can serve as a suitable basis for AP. The second approach is κ-OOMP2 with complex, restricted (cR) orbitals (κ-cROOMP2). Although its applicability is more limited due to the comparative rarity of cR solutions, κ-cROOMP2 offers a simple framework for describing singlet biradicaloids with complex polarization while removing artificial spatial symmetry breaking. We compare the scope of these two methods with numerical studies. We show that AP+κ-UOOMP2 and κ-cROOMP2 can perform similarly well in the TS12 set, a dataset that includes 12 data points for triplet-singlet gaps of several atoms and diatomic molecules with a triplet ground state. This was also found to be true for the barrier height of a reaction involving attack on a cysteine ion by a singlet oxygen molecule. However, we also demonstrate that in highly symmetric systems like C30 (D5h), κ-cROOMP2 is more suitable as it conserves spatial symmetry. Finally, we present an organic biradicaloid that does not have a κ-cROOMP2 solution in which case only AP+κ-UOOMP2 is applicable. We recommend κ-cROOMP2 whenever complex polarization is essential and AP+κ-UOOMP2 for biradicaloids without essential complex polarization but with essential spin-polarization.
        Cover page: Two single-reference approaches to singlet biradicaloid problems: Complex, restricted orbitals and approximate spin-projection combined with regularized orbital-optimized Møller-Plesset perturbation theoryCreative Commons 'BY' version 4.0 license
        • Article
        • Peer Reviewed
        UC Berkeley Previously Published Works (2018)
        We present an improved energy decomposition analysis (EDA) scheme for understanding intermolecular interactions in delocalized excited states, especially in excimers. In the EDA procedure, excited states are treated with linear response theory such as configuration interaction singles (CIS) or time-dependent density functional theory (TDDFT), and absolutely localized molecular orbitals (ALMOs) are used to define the intermediate (frozen, excitonic coupling, and polarized) states. The intermolecular interaction energy is thereby separated into frozen, excitonic splitting, polarization, and charge transfer contributions. The excitonic splitting term describes the delocalization effect as two or more degenerate local excitations coupled with each other, which is often an important binding force in excimers. A maximum overlap state-tracking procedure is introduced to connect the initial fragment excitations to the constrained intermediate states and finally to the unconstrained delocalized states of the complex. The EDA scheme is applied to several excimer systems, including the He2* and Ne2* noble gas excimers, the doubly hydrogen-bonded 2-pyridone dimer, and the aromatic benzene and perylene excimers. We are able to gain some useful insights into the role each term is playing in the formation of these excimers, and the resulting method may also be useful for understanding a range of other complexes in excited states.
          Cover page: Energy Decomposition Analysis for Excimers Using Absolutely Localized Molecular Orbitals within Time-Dependent Density Functional Theory and Configuration Interaction with Single Excitations
          • Thesis
          • Peer Reviewed
          UC Berkeley Electronic Theses and Dissertations (2024)

          This dissertation advances the field of density functional theory (DFT) by evaluating the performance of modern density functionals in predicting a variety of chemical properties and by developing new functionals with improved accuracy and transferability. The work begins with the derivation and efficient implementation of the second analytical derivative of the VV10 nonlocal correlation (NLC) functional, enabling the calculation of second-order properties---such as harmonic vibrational frequencies and excitation energies---with VV10-containing functionals without significant computational overhead.

          Building on this foundation, the performance of VV10-containing functionals is benchmarked for harmonic vibrational frequencies. While the VV10 contribution is minimal for small covalent molecules, it proves significant for systems where weak interactions are critical, such as water clusters. Scaling factors are provided to convert harmonic frequencies to fundamental frequencies and zero-point vibrational energies for several modern functionals, facilitating more accurate infrared spectroscopy predictions.

          The study further evaluates over 40 popular and recently developed density functionals for 463 vertical excitation energies using the comprehensive QuestDB benchmark set. The findings confirm that while time-dependent DFT adheres to the principles of Jacob's Ladder, hybrid meta-generalized gradient approximation (meta-GGA) functionals do not consistently outperform hybrid GGAs. Factors influencing the accuracy of excitation energy calculations---including basis set convergence, gauge invariance corrections for meta-GGAs, and the role of VV10 NLC---are thoroughly investigated.

          Addressing the need for improved functional transferability, a new and extensive chemical database named GSCDB138 is developed. This database significantly expands upon existing benchmarks by incorporating underrepresented areas such as transition metals, main-group metal clusters, electric properties, vibrational frequencies, and specialized noncovalent interactions. Most reference data are updated to theoretical best estimates, enhancing the reliability of functional assessments.

          Leveraging the expanded database, a new range-separated hybrid meta-GGA functional is developed using a mixed-integer optimization algorithm. This approach explores an immense functional space while enforcing multiple physical constraints to maximize accuracy without overfitting. The resulting functional exhibits exceptional performance across a wide array of chemical systems, surpassing existing functionals like $\omega$B97M-V in both accuracy and transferability.

          In summary, this work provides significant contributions to computational chemistry by offering comprehensive benchmarks and advanced functionals that collectively enhance the predictive power of DFT for diverse chemical applications.

            Cover page: Benchmarking and Development of Modern Density Functional Theory
            • Article
            • Peer Reviewed
            UC Berkeley Previously Published Works (2015)
            An energy decomposition analysis (EDA) of intermolecular interactions is proposed for second-order Møller-Plesset perturbation theory (MP2) based on absolutely localized molecular orbitals (ALMOs), as an extension to a previous ALMO-based EDA for self-consistent field methods. It decomposes the canonical MP2 binding energy by dividing the double excitations that contribute to the MP2 wave function into classes based on how the excitations involve different molecules. The MP2 contribution to the binding energy is decomposed into four components: frozen interaction, polarization, charge transfer, and dispersion. Charge transfer is defined by excitations that change the number of electrons on a molecule, dispersion by intermolecular excitations that do not transfer charge, and polarization and frozen interactions by intra-molecular excitations. The final two are separated by evaluations of the frozen, isolated wave functions in the presence of the other molecules, with adjustments for orbital response. Unlike previous EDAs for electron correlation methods, this one includes components for the electrostatics, which is vital as adjustment to the electrostatic behavior of the system is in some cases the dominant effect of the treatment of electron correlation. The proposed EDA is then applied to a variety of different systems to demonstrate that all proposed components behave correctly. This includes systems with one molecule and an external electric perturbation to test the separation between polarization and frozen interactions and various bimolecular systems in the equilibrium range and beyond to test the rest of the EDA. We find that it performs well on these tests. We then apply the EDA to a halogen bonded system to investigate the nature of the halogen bond.
              Cover page: An energy decomposition analysis for second-order Møller–Plesset perturbation theory based on absolutely localized molecular orbitals
              • Article
              • Peer Reviewed
              UC Berkeley Previously Published Works (2022)
              While bonding molecular orbitals exhibit constructive interference relative to atomic orbitals, antibonding orbitals show destructive interference. When full localization of occupied orbitals into bonds is possible, bonding and antibonding orbitals exist in 1:1 correspondence with each other. Antibonding orbitals play an important role in chemistry because they are frontier orbitals that determine orbital interactions, as well as much of the response of the bonding orbital to perturbations. In this work, we present an efficient method to construct antibonding orbitals by finding the orbital that yields the maximum opposite spin pair correlation amplitude in second order perturbation theory (AB2) and compare it with other techniques with increasing basis set size. We conclude the AB2 antibonding orbitals are a more robust alternative to the Sano orbitals as initial guesses for valence bond calculations due to having a useful basis set limit. The AB2 orbitals are also useful for efficiently constructing an active space, and they work as good initial guesses for valence excited states. In addition, when combined with the localized occupied orbitals, and relocalized, the result is a set of molecule-adapted minimal basis functions that is built without any reference to atomic orbitals of the free atom. As examples, they are applied to the population analysis of halogenated methane derivatives, H-Be-Cl, and SF6, where they show some advantages relative to good alternative methods.
                Cover page: Non-iterative method for constructing valence antibonding molecular orbitals and a molecule-adapted minimum basisCreative Commons 'BY' version 4.0 license
                • Article
                • Peer Reviewed
                UC Berkeley Previously Published Works (2016)
                  Cover page: Note: The performance of new density functionals for a recent blind test of non-covalent interactions
                  • Article
                  • Peer Reviewed
                  UC Berkeley Previously Published Works (2018)
                  Double hybrid (DH) density functionals are amongst the most accurate density functional approximations developed so far, largely due to the incorporation of correlation effects from unoccupied orbitals via second order perturbation theory (PT2). The xDH family of DH functionals calculate energy directly from orbitals optimized by a lower level approach like B3LYP, without self-consistent optimization. XYG3 and XYGJ-OS are two widely used xDH functionals that are known to be quite accurate at equilibrium geometries. Here, we show that the XYG3 and XYGJ-OS functionals can be ill behaved for stretched bonds well beyond the Coulson-Fischer point, predicting unphysical dipole moments and humps in potential energy curves for some simple systems like the hydrogen fluoride molecule. Numerical experiments and analysis show that these failures are not due to PT2. Instead, a large mismatch at stretched bond-lengths between the reference B3LYP orbitals and the optimized orbitals associated with the non-PT2 part of XYG3 leads to an unphysically large non-Hellman-Feynman contribution to first order properties like forces and electron densities.
                    Cover page: Communication: xDH double hybrid functionals can be qualitatively incorrect for non-equilibrium geometries: Dipole moment inversion and barriers to radical-radical association using XYG3 and XYGJ-OS
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