Ground- and excited-state properties of DNA base molecules from plane-wave calculations using ultrasoft pseudopotentials

We present equilibrium geometries, vibrational modes, dipole moments, ionization energies, electron affinities, and optical absorption spectra of the DNA base molecules adenine, thymine, guanine, and cytosine calculated from first principles. The comparison of our results with experimental data and results obtained by using quantum chemistry methods show that in specific cases gradient-corrected density-functional theory (DFT-GGA) calculations using ultrasoft pseudopotentials and a plane-wave basis may be a numerically efficient and accurate alternative to methods employing localized orbitals for the expansion of the electron wave functions.     

Direct calculation of long time correlation functions using an optical potential

We present an ℒ︁² method aimed at directly computing autocorrelation functions 〈Φ₀|Φ_t〉 for systems displaying long time recurrences. By making use of a Lanczos scheme, as previously proposed by Wyatt [Chem. Phys. Lett. 121, 301 (1985)], the method avoids explicit time propagation of the wavefunction. The problem associated with spurious recurrences, due to the finite size of the ℒ︁²-box, is solved in terms of an optical potential located in the asymptotic region. The resulting complex representation of the Hamiltonian operator is handled by a complex symmetric Lanczos scheme, which retains the same basic advantages as its real version. The method is illustrated on the ozone photodissociation process which displays a very detailed recurrence structure over a long time period. It is shown that such a direct calculation of the correlation function is about one order of magnitude faster than an actual wavepacket propagation. The accuracy of the method is assessed by comparison to calculations performed without any optical potential but using a very large box size along the dissociation coordinate. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 317–328, 1998     

Si(001)-(2×2×1):H表面O2吸附的密度泛函理论研究

A novel model was developed to theoretically evaluate the O2 adsorption on H-terminated Si(001)-(2*2*1) surface. The periodic boundary condition, the ultrasoft pseudopotentials technique based on density functional theory (DFT) with generalized gradient approximation (GGA) functional were applied in our ab initio calculations. By analyzing bonding energy on site, the favourable adsorption site was determined. The calculations also predicted that the adsorption products should be Si=O and H2O. This theoretical study supported the reaction mechanism provided by Kovalev et al. The results were also a base for further investigation of some more complex systems such as the oxidation on porous silicon surface.     

Accuracy and efficiency of atomic basis set methods versus plane wave calculations with ultrasoft pseudopotentials for DNA base molecules

Recent results from Preuss et al. (J Comput Chem 2004, 25, 112) on DNA base molecules, obtained by plane wave density functional calculations using ultrasoft pseudopotentials, are compared with calculations using Gaussian basis sets. Bond lengths and angles agree closely, but dihedral angles and vibrational frequencies show significant differences. The Gaussian basis calculations are at least an order of magnitude more efficient than the plane wave/ultrasoft pseudopotential calculations at a similar level of accuracy; the advantage is even larger if the Fourier Transform Coulomb method is used. To obtain definite benchmark values, the geometries of the four DNA bases were optimized at the MP2 level with large basis sets, up to cc-pVQZ and aug-cc-pVTZ.     

Phenanthrenequinone adsorbed on Si(001): geometries, electronic properties, and optical response

As a prototypical case of a pi-conjugated organic overlayer on a semiconductor surface the adsorption of phenanthrenequinone (C14O2H8) on the Si(001) surface is studied by means of first principles calculations, using gradient-corrected density functional theory together with ultrasoft pseudopotentials and the projector augmented wave method. A thermodynamic phase diagram gives adsorption geometries depending on experimental conditions, the microscopically most favorable bonding configuration representing a "[4+2]-cycloaddition product". The surface electronic structure depends strongly on the respective adsorption configuration. Calculations of the surface optical signature show its sensitivity to molecular adsorption and are in agreement with experimental results. A detailed analysis illustrates that the bonding to the surface has to be taken into account accurately to unveil the molecule's contribution to the surface optical response.     

Ultrasoft pseudopotentials for lanthanide solvation complexes: core or valence character of the 4f electrons

The 4f electrons of lanthanides, because of their strong localization in the region around the nucleus, are traditionally included in a pseudopotential core. This approximation is scrutinized by optimizing the structures and calculating the interaction energies of Gd(3+)(H(2)O) and Gd(3+)(NH(3)) microsolvation complexes within plane wave Perdew-Burke-Ernzerhof calculations using ultrasoft pseudopotentials where the 4f electrons are included either in the core or in the valence space. Upon comparison to quantum chemical MP2 and CCSD(T) reference calculations it is found that the explicit treatment of the 4f electrons in the valence shell yields quite accurate results including the required small spin polarization due to ligand charge transfer with only modest computational overhead.     

Truncation of small matrix elements based on the Euclidean norm for blocked data structures

Methods for the removal of small symmetric matrix elements based on the Euclidean norm of the error matrix are presented in this article. In large scale Hartree-Fock and Kohn-Sham calculations it is important to be able to enforce matrix sparsity while keeping errors under control. Truncation based on some unitary-invariant norm allows for control of errors in the occupied subspace as described in (Rubensson et al. J Math Phys 49, 032103). The Euclidean norm is unitary-invariant and does not grow intrinsically with system size and is thus suitable for error control in large scale calculations. The presented truncation schemes repetitively use the Lanczos method to compute the Euclidean norms of the error matrix candidates. Ritz value convergence patterns are utilized to reduce the total number of Lanczos iterations.     

Full S matrix calculation via a single real-symmetric Lanczos recursion: the Lanczos artificial boundary inhomogeneity method

We present an efficient and robust method for the calculation of all S matrix elements (elastic, inelastic, and reactive) over an arbitrary energy range from a single real-symmetric Lanczos recursion. Our new method transforms the fundamental equations associated with Light's artificial boundary inhomogeneity approach from the primary representation (original grid or basis representation of the Hamiltonian or its function) into a single tridiagonal Lanczos representation, thereby affording an iterative version of the original algorithm with greatly superior scaling properties. The method has important advantages over existing iterative quantum dynamical scattering methods: (a) the numerically intensive matrix propagation proceeds with real symmetric algebra, which is inherently more stable than its complex symmetric counterpart; (b) no complex absorbing potential or real damping operator is required, saving much of the exterior grid space which is commonly needed to support these operators and also removing the associated parameter dependence. Test calculations are presented for the collinear H+H(2) reaction, revealing excellent performance characteristics.     

Static and dynamic density functional investigation of hydrated beryllium dications

Using density functional theory with Becke's gradient correction for the exchange part and Vanderbilt's ultrasoft pseudopotentials, we investigated [Be(H₂O)_n]²⁺ clusters for n = 1 and 3. A new scheme implemented with the Car-Parrinello method is used, upon which no periodic boundary conditions are imposed so that isolated and possibly charged molecules can also be treated dynamically in a plane-wave basis. Harmonic vibrational frequencies are obtained via a fit of the molecular dynamics trajectory in terms of harmonic oscillators, for which we use a fragmentation scheme to analyze complex spectra. Based on this combination of techniques, we find good agreement with data from SCF calculations and correlated methods. © 1996 John Wiley & Sons, Inc.     

First-principle molecular dynamics with ultrasoft pseudopotentials: parallel implementation and application to extended bioinorganic systems

We present a plane-wave ultrasoft pseudopotential implementation of first-principle molecular dynamics, which is well suited to model large molecular systems containing transition metal centers. We describe an efficient strategy for parallelization that includes special features to deal with the augmented charge in the contest of Vanderbilt's ultrasoft pseudopotentials. We also discuss a simple approach to model molecular systems with a net charge and/or large dipole/quadrupole moments. We present test applications to manganese and iron porphyrins representative of a large class of biologically relevant metalorganic systems. Our results show that accurate density-functional theory calculations on systems with several hundred atoms are feasible with access to moderate computational resources.     

Cyanoacetylene adsorption on amorphous and crystalline water ice films: investigation through matrix isolation and quantum study.

The structure and energy properties of the 1:1 complexes formed between cyanoacetylene and H2O (D2O) are investigated using FT-IR matrix isolation spectroscopy and ab initio calculations at the MP2/ 6-31G(d,p) level. Cyanoacetylene adsorption and desorption on amorphous ice film are monitored by FT-IR using the temperature-programmed desorption method. In an argon matrix, two types of 1:1 complexes are observed. The first one corresponds to the NH structure, which involves a hydrogen bond with the terminal nitrogen of cyanoacetylene. The second corresponds to the HO form, which involves a hydrogen bond from the cyanoacetylene to the oxygen of water. This last complex is the more stable (DeltaE = -8.1 kJ/mol.). As obtained in argon matrixes, two kinds of adsorption site are observed between HC3N and ice. The first one, stable between 25 and 45 K is characterized by a nu(OH) shift similar to the one observed in matrix for the NH complex. The second, stable at higher temperatures (between 45 and 110 K), corresponds to an interaction with the dangling oxygen site of ice and is similar to the HO complex observed in matrix. From theoretical calculations (DFT method combined with a plane wave basis set and ultrasoft pseudopotentials), it is shown that, for this adsorption site, the HC3N moiety is flattened on the ice surface and stabilized by a long-distance interaction ( approximately 3 A) between one dangling OH and the pi system of the C triple bond C triple bond. The HC3N desorption occurs between 110 and 140 K, and the associated desorption energy is 39 kJ/mol. This value is in good agreement with the first principle calculation based on density functional theory and ultrasoft pseudopotentials (34 kJ/mol). These calculations confirm the electrostatic nature of the interaction forces. A small amount of cyanoacetylene is incorporated into the bulk and desorbs at the onset of the ice crystallization near 145 K. In these two kinds of experiments, HC3N acts as both an electrophilic and a nucleophilic molecule.     

Ultrasoft X-ray emission and the electronic structure of the acetaldehyde molecule

The electronic structure of the acetaldehyde molecule was studied by the ultrasoft X-ray emission method with the use of quantum-chemical calculations. The OK _?? and CK _?? spectra of the compound in the gas phase were obtained. Quantum-chemical calculations were performed at the RHF/6-311++G** level. The calculation results were used to construct theoretical X-ray spectra. The experimental spectra are interpreted.     

Ab initio study of optical properties of rhodamine 6G molecular dimers

Equilibrium atomic geometries of rhodamine 6G (R6G) dye molecule dimers are studied using density-functional theory. Electron-energy structure and optical properties of R6G H and J dimers are calculated using the generalized gradient approximation method with ab initio pseudopotentials. Our theory predicts substantial redshifts or blueshifts of the optical absorption spectra of R6G dye molecules after aggregation in J or H dimers, respectively. Predicted optical properties of R6G dimers are interpreted in terms of interatomic and intermolecular interactions. Results of the calculations are discussed in comparison with experimental data.     

Energy-consistent pseudopotentials for quantum Monte Carlo calculations

The authors present scalar-relativistic energy-consistent Hartree-Fock pseudopotentials for the main-group elements. The pseudopotentials do not exhibit a singularity at the nucleus and are therefore suitable for quantum Monte Carlo (QMC) calculations. They demonstrate their transferability through extensive benchmark calculations of atomic excitation spectra as well as molecular properties. In particular, they compute the vibrational frequencies and binding energies of 26 first- and second-row diatomic molecules using post-Hartree-Fock methods, finding excellent agreement with the corresponding all-electron values. They also show their pseudopotentials give superior accuracy than other existing pseudopotentials constructed specifically for QMC. Finally, valence basis sets of different sizes (VnZ with n=D,T,Q,5 for first and second rows, and n=D,T for third to fifth rows) optimized for our pseudopotentials are also presented.     

Calculating vibrational energies and wave functions of vinylidene using a contracted basis with a locally reorthogonalized coupled two-term Lanczos eigensolver

We use a contracted basis+Lanczos eigensolver approach to compute vinylidene-like vibrational states of the acetylene-vinylidene system. To overcome problems caused by loss of orthogonality of the Lanczos vectors we reorthogonalize Lanczos vector and use a coupled two-term approach. The calculations are done in CC-HH diatom-diatom Jacobi coordinates which make it easy to compute states one irreducible representation at a time. The most costly parts of the calculation are parallelized and scale well. We estimate that the vinylidene energies we compute are converged to approximately 1 cm(-1).     

Ab initio calculation of temperature effects in the optical response of open-shell sodium clusters

Many properties of atomic clusters have been found to be size dependent, e.g., the optical response. There are, however, factors other than size that can also play an important role in determining the properties of nanoscale systems. Temperature, in particular, has been shown to have a strong effect on the optical response of open-shell sodium clusters. We incorporate the temperature effect on the optical absorption spectra by combining pseudopotentials, Langevin molecular dynamics, and time-dependent density functional theory. We have done calculations for several open-shell sodium clusters, Na(4) (+), Na(7) (+), and Na(11) (+), for which experimental data are available for comparison. We find that the positions of the lower energy peaks of the calculated spectra correspond very well to the peaks in the experimental spectra, although the local density approximation tends to overestimate the gap of the smaller clusters by up to 0.2 eV and underestimate the gap of the largest cluster by 0.4 eV. We fit the width of the peaks in the lower-temperature calculations to the corresponding experimental result to obtain the instrumental linewidth. We then use this same width for the high-temperature calculations and find very good agreement with experiment. Finally, we analyze the transitions that contribute to the observed peaks in the absorption spectra and we plot the effective valence charge density for specific transitions for each cluster. We find that for the two smaller clusters the absorption spectra are dominated by transitions from the occupied levels to a few (three for Na(4) (+) and five for Na(7) (+)) empty levels, although the contribution from transitions to other empty levels can still be significant. In contrast, the absorption spectra for Na(11) (+) come from a greater mixture of transitions as evidenced in the analysis as well as in the plot of the effective valence charge density.     

Gradient-based direct normal-mode analysis

A formulation of a direct, iterative method for obtaining the lowest eigenvalues and eigenvectors of a Hessian matrix is presented. Similar to the iterative schemes in electronic structure configuration interaction calculations (methods due to Lanczos, Davidson, and others), the mass-weighted Hessian matrix K is not constructed explicitly; instead, its operation on a basis vector (a direction in the 3N Cartesian configuration space of the atoms) is computed based on the principles of dynamical equations of motion. By noting that the time derivative of the gradient vector in the harmonic force field is related to the particles' momenta via dg/dt = Kp, a Hessian-vector product can be computed on the fly by finite differentiation of the gradient along the direction specified by the p vector. Thus, only two evaluations of the gradient are required per Davidson-like iteration per root, which leads to a linear scaling behavior of the computational effort with the number of atoms (provided that the evaluation of the gradient scales linearly). Preliminary results are presented for a 27,000-atom 4He nanodroplet.     

Pseudopotential and electron propagator methods for the calculation of the photoelectron spectra of anionic silicon clusters: predictions on Si10-

Photoelectron spectra of anionic clusters of silicon require reliable theoretical calculations for their assignment and interpretation. Electron propagator calculations in the outer valence Green's-function approximation with two well-characterized, all-electron basis sets on vertical electron detachment energies (VEDEs) of anions are compared to similar calculations that employ Stuttgart pseudopotentials. Tests on Si(n) (-) clusters with n=3-7 exhibit an encouraging agreement between the all-electron and pseudopotentials results and between electron propagator predictions and experiments and values obtained from coupled-cluster calculations. To illustrate the capabilities of the new approach based on a Si pseudopotential and electron propagator methods, VEDE calculations on Si(10) (-) are presented.     

Using nonproduct quadrature grids to solve the vibrational Schrödinger equation in 12D

In this paper we propose a new quadrature scheme for computing vibrational spectra and apply it, using a Lanczos algorithm, to CH(3)CN. All 12 coordinates are treated explicitly. We need only 157'419'523 quadrature points. It would not be possible to use a product Gauss grid because 33 853 318 889 472 product Gauss points would be required. The nonproduct quadrature we use is based on ideas of Smolyak, but they are extended so that they can be applied when one retains basis functions θ(n(1))(r(1))···θ(n(D))(r(D)) that satisfy the condition α(1)n(1) + ··· + α(D)n(D) ≤ b, where the α(k) are integers. We demonstrate that it is possible to exploit the structure of the grid to efficiently evaluate the matrix-vector products required to use the Lanczos algorithm.