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In this work we shall develop a quantitative approach for extracting predictions on the primordial gravitational waves energy spectrum for $f(R)$ gravity. We shall consider two distinct models which yield different phenomenology, one pure…

The molecular dipole moment and magnetic hyperfine structure constant demand an accurate wavefunction far from the nucleus and in near nuclear region, respectively. We, therefore, employ the so-called Z-vector method in the domain of…

The excitation energies and ionization potentials of the atoms in the first transition series are notoriously difficult to compute accurately. Errors in calculated excitation energies can range from 1--4 eV at the Hartree-Fock level, and…

Extended Lagrangian Born-Oppenheimer molecular dynamics [Phys. Rev. Lett., ${\bf 100}$, 123004 (2008)] is formulated for general Hohenberg-Kohn density functional theory and compared to the extended Lagrangian framework of first principles…

The classic second-order average vector field (AVF) method can exactly preserve the energy for Hamiltonian ordinary differential equations and partial differential equations. However, the AVF method inevitably leads to fully-implicit…

We introduce a novel approach for a fully quantum description of coupled electron-ion systems from first principles. It combines the variational quantum Monte Carlo (QMC) solution of the electronic part with the path integral (PI) formalism…

Nonlinear system identificationhas proven to be effective in obtaining accurate models from data for complex real-world systems. In particular, recent encoder-based methods with artificial neural network state-space (ANN-SS) models have…

In visual cognition, illusions help elucidate certain intriguing latent perceptual functions of the human vision system, and their proper mathematical modeling and computational simulation are therefore deeply beneficial to both biological…

The calculation of caloric properties such as heat capacity, Joule-Thomson coefficients and the speed of sound by classical force-field-based molecular simulation methodology has received scant attention in the literature, particularly for…

A first principles quantum formalism to describe the non-adiabatic dynamics of electrons and nuclei based on a second quantization representation (SQR) of the electronic motion combined with the usual representation of the nuclear…

We extract the dynamics implicit in an algebraic fitted model Hamiltonian for the deuterium chromophore's vibrational motion in the molecule CDBrClF. The original model has 4 degrees of freedom, three positions and one representing…

Simulating response properties of molecules is crucial for interpreting experimental spectroscopies and accelerating materials design. However, it remains a long-standing computational challenge for electronic structure methods on classical…

Mixed Quantum Classical (MQC)-IVR is a recently introduced semiclassical framework that allows for selective quantization of the modes of a complex system. In the quantum limit, MQC reproduces the semiclassical Double Herman-Kluk IVR…

The recent progress of linear-scaling or O(N) methods in the density functional theory (DFT) is remarkable. We expect that first-principles molecular dynamics (FPMD) simulations based on DFT can now treat more realistic and complex systems…

In many recent applications when new materials and technologies are developed it is important to describe and simulate new nonlinear and nonlocal diffusion transport processes. A general class of such models deals with nonlocal fractional…

First-principles phonon calculations have been widely performed for studying vibrational properties of condensed matter, where the dynamical matrix is commonly constructed via supercell force-constant calculations or the linear response…

Quantum Monte Carlo (QMC) methods such as Variational Monte Carlo, Diffusion Monte Carlo or Path Integral Monte Carlo are the most accurate and general methods for computing total electronic energies. We will review methods we have…

Devising a computational tool that assesses the thermodynamic stability of materials is among the most important steps required to build a ``virtual laboratory'', where materials could be designed from first-principles without relying on…

We present a new formulation for the mean-field propagation part of the relativistic quantum molecular dynamics, simulating an $N$-body system of interacting Gaussian wave packets via Lorentz scalar and vector potentials. Covariant…

Results of quasi-classical molecular dynamics simulations of the quantum electron gas are reported. Quantum effects corresponding to the Pauli and the Heisenberg principle are modeled by an effective momentum-dependent Hamiltonian. The…