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Generalized polarizabilities and the molecular charge distribution can describe the response of a molecule in an arbitrary static electric field up to second order. Depending on the expansion functions used to describe the perturbing potential, the generalized polarizability matrix can have rather large dimension (~1000). This matrix is the discretized version of the density response function or electronic susceptibility. Diagonalizing and truncating it can lead to significant (over an order of magnitude) speed‐up in simulations. We have analyzed the convergence behavior of the generalized polarizability using a plane wave basis for the potential. The eigenfunctions of the generalized polarizability matrix are the natural polarization potentials. They are potentially useful to construct efficient polarizability models for molecules. [ABSTRACT FROM AUTHOR]

It is much more difficult to find on the potential energy surface (PES) a transition state (TS) than a local minimum (LM). We propose a new methodology which makes this task much easier. Applying external forces to nuclei in a molecule we can locate on PES not just one particular TS but a number of consecutive transition states. With our approach it is possible to move over PES from one transition state to another without involving any local minima. The latter can be located in a separate step through the reaction path calculations performed for every transition state found before. Preliminary results for the 2‐fluorofuran molecule illustrate the usefulness of the proposed method. [ABSTRACT FROM AUTHOR]

Following the pioneering work of Jurgens-Lutovsky and Almlöf [Chem. Phys. Lett. 178, 451 (1991)], a second-order Møller-Plesset program was developed which allows the use of a large basis set for the pair correlation functions and a more modest one for the self-consistent field (SCF) orbitals. For several test systems, correlation energies closely approximate the results of a large basis set calculation, at substantial savings. The SCF energy of the large basis set calculation can also be estimated using perturbation theory. [ABSTRACT FROM AUTHOR]

Abstract In this work we use our Enforced Geometry Optimization (EGO) method to investigate conformational transitions in the pyranose ring under mechanical stress caused by external forces. We examine possible transitions and/or inversions induced by external forces in the pyranose ring in the chair conformation with two axial glycosidic bonds. The results obtained provide new insight into the mechanism of the conformational transitions which strongly depends on substituents present in a pyranose ring. We also conclude that interpretation of AFM force-extension curves is not necessarily straightforward; not every plateau there corresponds to a conformational transition and not every transition can be clearly seen as a plateau. Graphical abstract Image 1 Highlights • Interpretation of AFM force-extension curves is not necessarily straightforward. • Mechanism of enforced conformational transition depends on pyranose ring substituents. • The Enforced Geometry Optimization approach can be useful for the explanation of the experimental AFM force-extension curves. [ABSTRACT FROM AUTHOR]

Analyzes the magnetic shielding tensor as a continuous function of space point coordinates in atoms and molecules. Application of magnetic shielding surface to better understand nuclear magnetic shieldings; Connection between magnetic shielding at an arbitrary point and nuclear magnetic shielding; Magnetic shielding surface calculations for atoms and small linear molecules.

The 31P shielding tensor for PH3 has been calculated without electron correlation (self-consistent field) and with electron correlation (second-order Mo\llet–Plesset) using the gauge including atomic orbital method. The best results obtained for the absolute isotropic chemical shielding constant (608.09 ppm) and chemical shielding anisotropy (64.54 ppm) compare quite favorably with the experimental values of 600 and 64.5 ppm. The contribution of electron correlation to the absolute shielding value has been found to be significant. The convergence of the calculated shielding tensor with respect to the quality of the basis set employed and the importance of d and f polarization orbitals are discussed. [ABSTRACT FROM AUTHOR]

The recently proposed consistent generalization of the Mo\ller–Plesset perturbation theory to arbitrary reference states is reviewed and compared to previous methods. We have implemented the second order of this theory (GMP2) for systems which can be described by a two-configuration wave function. GMP2 is applied here to bond-breaking potential curves: HF, F2, CH3–H, and twisted ethylene, as well as to the geometry and dipole moment of ozone, to the electron affinity of the cyano radical, to the vertical ionization potentials of ethylene, and to the excited singlet states of formaldehyde. In general, the performance of GMP2 is very good and comparable to the two-configuration based doubles CI method. However, like all methods based on a single reference function, GMP2 is not applicable in nearly degenerate situations. We also discuss the continuity of potential surfaces in Monte Carlo self-consistent-field (MC-SCF) theory. [ABSTRACT FROM AUTHOR]

Second derivatives of the molecular energy with respect to the nuclear coordinates (the nuclear Hessian or force constant matrix) are important for predicting infrared and Raman spectra, for calculating thermodynamic properties, for characterizing stationary states, and for guiding geometry optimization. However, their calculation for larger systems scales with molecular size one power higher than the calculation of the energy and the forces. The step responsible for the steep scaling of the nuclear Hessian is the coupled-perturbed self-consistent field (CP-SCF) iteration. This is omitted in the uncoupled SCF (UC-SCF) approximation. We have found that, though UC-SCF performs rather poorly at the Hartree-Fock and hybrid DFT levels, its performance for "pure" (non-hybrid) DFT is remarkably good. This is valid also for imaginary frequencies that characterize transition states. UC-SCF vibrational frequencies and normal modes are compared with coupled calculations for various exchange-correlation functionals including Hartree-Fock, and with basis sets ranging from simple to large for a variety of organic and some organometallic molecules. Their unexpectedly good performance makes them good candidates for calculating thermodynamic properties and for guiding difficult geometry optimizations, including the determination of transition states. [ABSTRACT FROM AUTHOR]

We present a method to calculate the density response function (DRF), also known as the density response kernel or the polarization propagator in the static limit. Our method uses generalized polarizabilities (GPs) which are second derivatives of the molecular energy with respect to two arbitrary perturbations of the external electrostatic potential. They are generalizations of the common multipole polarizabilities. The latter use solid spherical harmonics as perturbing potentials, while GPs can use any function. We use a sine function expansion of the electrostatic potential. Generalized polarizabilities were originally introduced for a different project, ultrafast quantum/molecular mechanics calculations. By transforming the GPs to a (discretized) direct space representation, we obtain the DRF in the static limit. The method has been implemented for single-determinant (Hartree–Fock and density functional theory) wavefunctions, but can be generalized to more accurate wavefunctions. The number of coupled-perturbed self-consistent field (CP-SCF) calculations in our method is proportional to the molecular volume at a given spatial resolution, i.e., scales linearly with the system size, and is independent of the basis set size. The best previous method has the number of CP-SCF calculations proportional to the product of the number occupied and virtual orbitals, and therefore scaling quadratically with the system size at constant basis set quality. The diagonal elements of the DRF (local polarizabilities) of water and butadiene in the molecular plane are displayed. An example of non-diagonal DRF is presented for butadiene 0.77 Å above the molecular plane, with one point fixed over the midpoint of a C=C bond. We obtain a fairly localized DRF, even in this conjugated system. The values become quite small if the distance of the two local perturbations exceeds a bond length. By using frequency-dependent polarizabilities, one could readily calculate the dynamic DRF. [ABSTRACT FROM AUTHOR]

In this paper, we present a number of novel pure-carbon structures generated from cyclo[18]carbon. Due to the very high reactivity of cyclo[18]carbon, it is possible to link these molecules together to form bigger molecular systems. In our studies, we generated new structures containing 18, 36 and 72 carbon atoms. They are of different shapes including ribbons, sheets and tubes. All these new structures were obtained in virtual reactions driven by external forces. For every reaction, the energy requirement was evaluated exactly when the corresponding transition state was found or it was estimated through our new approach. A small HOMO–LUMO gap in these nanostructures indicates easy excitations and the multiple bonds network indicates their high reactivity. Both of these factors suggest that some potential applications of the new nanostructures are as components of therapeutically active carbon quantum dots, terminal fragments of graphene or carbon nanotubes obtained after fracture or growing in situ in catalytic reactions leading to the formation of carbonaceous materials. [ABSTRACT FROM AUTHOR]

Abstract: A fast and accurate Quantum Mechanics/Molecular Mechanics method is described for thermodynamic simulation of solutes (or active sites in flexible molecules) in polar environments. The solute is described quantum mechanically and is held fixed during averaging over solvent configurations, which are described by Molecular Mechanics. Quantum calculations during simulation are replaced by the evaluation of the response of the solute to the long range electric field of the solvent, using precalculated generalized electric moments and polarizabilities. This results in huge decrease of computational time without affecting the accuracy of the QM/MM results. Implementation in a Monte Carlo program accelerated the simulations of guanine and the phenylalanine dipeptide in TIP3P water by over four orders of magnitude. Polarizability is essential for accuracy. Its inclusion decreases the average signed energy error and its standard deviation from 5.69 to 0.003 and 1.22 to 0.013kcal/mol, respectively, for the dipeptide. Hyperpolarizability contributions are insignificant. [Copyright &y& Elsevier]

We present details of our efficient implementation of full accuracy unrestricted open-shell second-order canonical Møller-Plesset (MP2) energies, both serial and parallel. The algorithm is based on our previous restricted closed-shell MP2 code using the Saebo-Almlöf direct integral transformation. Depending on system details, UMP2 energies take from less than 1.5 to about 3.0 times as long as a closed-shell RMP2 energy on a similar system using the same algorithm. Several examples are given including timings for some large stable radicals with 90+ atoms and over 3600 basis functions. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011 [ABSTRACT FROM AUTHOR]

Following on from our recent enforced geometry optimization (EGO) investigation of isomerization in cis-stilbene ( J Comput Chem, in press) we report the discovery of two interesting new, symmetrical 'fused sandwich' isomers of both cis-stilbene and the related cis-azobenzene. The isomers were obtained by applying external forces to pairs of carbon atoms from each of the benzene rings in cis-stilbene and cis-azobenzene simultaneously, and are all at least 100 kcal mol higher in energy than the starting material. Each new structure was characterized as a minimum by vibrational analysis. Despite their high energy, all of the new isomers appear to be kinetically stable with respect to rearrangement back to cis-stilbene or cis-azobenzene, respectively. [ABSTRACT FROM AUTHOR]

Using our recently proposed quantum chemical model to simulate the effect of external forces acting on a molecule (Wolinski and Baker, Mol Phys 2009, 107, 2403), which we subsequently termed enforced geometry optimization (EGO), we investigate structural isomerism in CH, starting from cis-stilbene. By applying an external force to pairs of carbon atoms, one from each 'half' of the molecule, we have generated 10 different structural isomers. Each was characterized as a minimum by vibrational analysis. Not only can EGO generate potentially new, metastable isomers it can also provide good initial guesses for transition states connecting the starting and final structures, thus giving an estimate of the stability of the new isomers to rearrangement back to the starting material. In addition to the new isomers, we provide a full set of vibrational fundamentals for cis- and trans-stilbene and 4a,4b-dihydrophenanthrene. The agreement with experimental assignments is excellent, with mean average deviations for the stilbenes of 5.0 cm or less. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010 [ABSTRACT FROM AUTHOR]

Recently, we proposed a very simple quantum chemical model to simulate the effect of external forces acting on a single molecule [Mol. Phys. 107, 2403 (2009)]. It is based on optimizing the geometry of a molecule with an external force applied to selected pairs of nuclei. In this study we extend this model by considering interactions of external forces not only with the nuclei but also with their electrons, in particular their core electrons, which can be viewed as 'rigidly' connected to a nucleus. In the proposed revised model an external force acts on an object which consists of the nucleus of an atom and its 1s core electrons. It is shown in this study that such a model predicts the same conformational (structural) changes in a molecule as our simpler model where the external forces interact with the nuclei only. However, the magnitude of the forces required to cause these changes is now lower and within the range of forces used in real AFM experiments. [ABSTRACT FROM AUTHOR]

A very simple quantum chemical model is proposed to simulate the effect of external forces acting on a single molecule. It involves optimising the geometry of a molecule with an external force applied to selected nuclei. This approach is used to investigate conformational transitions of the pyranose ring, which have been the subject of several atomic force microscopy (AFM) experiments, and to generate a number of previously unknown isomers of azobenzene. [ABSTRACT FROM AUTHOR]

This article describes the capabilities and performance of the latest release (version 4.0) of the Parallel Quantum Solutions (PQS) ab initio program package. The program was first released in 1998 and evolved from the TEXAS program package developed by Pulay and coworkers in the late 1970s. PQS was designed from the start to run on Linux-based clusters (which at the time were just becoming popular) with all major functionality being (a) fully parallel; and (b) capable of carrying out calculations on large—by ab initio standards—molecules, our initial aim being at least 100 atoms and 1000 basis functions with only modest memory requirements. With modern hardware and recent algorithmic developments, full accuracy, high-level calculations (DFT, MP2, CI, and Coupled-Cluster) can be performed on systems with up to several thousand basis functions on small (4-32 node) Linux clusters. We have also developed a graphical user interface with a model builder, job input preparation, parallel job submission, and post-job visualization and display. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009 [ABSTRACT FROM AUTHOR]

The dual basis set approach has proven to be very successful for accurately estimating total energies with large basis sets. This study extends the applications of this technique to the calculation of molecular properties, including energy derivatives with respect to nuclear positions and to an external electric field. All energy derivatives have been calculated numerically via finite-differences. Molecular gradients and Hessians as well as dipole moments and polarizabilites have been calculated at the HF and MP2 levels using two alternative versions of the dual basis set method. The accuracy of these approaches is discussed in the context of quality of basis sets used in calculations. It is shown that even quite poor results obtained with the 6-311G basis set are significantly improved in dual basis set calculations with the 6-311G(d,p) and 6-311G(3df,3dp) basis sets. [ABSTRACT FROM AUTHOR]

The recently described Fourier Transform Coulomb (FTC) algorithm for fast and accurate calculation of Density Functional Theory (DFT) gradients (Füsti-Molnar, J Chem Phys 2003, 119, 11080) has been parallelized. We present several calculations showing the speed and accuracy of our new parallel FTC gradient code, comparing its performance with our standard DFT code. For that part of the total derivative Coulomb potential that can be evaluated in plane wave space, the current parallel FTC gradient algorithm is up to 200 times faster in total than our classical all-integral algorithm, depending on the system size and basis set, with essentially no loss in accuracy. Proposed modifications should further improve the overall performance relative to the classical algorithm. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007 [ABSTRACT FROM AUTHOR]

We present an efficient, parallel implementation for the calculation of Hartree-Fock and density functional theory analytical Hessian (force constant, nuclear second derivative) matrices. These are important for the determination of harmonic vibrational frequencies, and to classify stationary points on potential energy surfaces. Our program is designed for modest parallelism (4-16 CPUs) as exemplified by our standard eight-processor QuantumCube™. We can routinely handle systems with up to 100+ atoms and 1000+ basis functions using under 0.5 GB of RAM memory per CPU. Timings are presented for several systems, ranging in size from aspirin (C 9 H 8 O 4 ) to nickel octaethylporphyrin (C 36 H 44 N 4 Ni). [ABSTRACT FROM AUTHOR]

Based on the orbital-invariant atomic orbital formulation of the MP2 (Møller–Plesset second-order perturbation theory) energy and gradient [P. Pulay and S. Saebø, Theor. Chim. Acta 69, 357 (1986)], we have derived and programmed detailed working equations for closed-shell MP2 gradients. The orbital-invariant form avoids the difficulties of other formulations with frozen orbitals, and allows the use of arbitrary occupied orbitals, an important consideration for local correlation theories, although the present program uses canonical molecular orbitals. The atomic orbital formulation offers savings both in storage and computer time. Test calculations on systems containing up to ∼100 atoms and ∼1000 basis functions, performed on a single personal computer, are reported. Parallelization of the code is underway. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Abstract: Using quantum chemistry methods we have evaluated the solvent effects on the 14N NMR chemical shifts in five oxa- and oxadiazoles dissolved in twelve solvents. These solvents differ in their polarity with the dielectric constants varying from 2 to 80. Moreover, three of them have a hydrogen-bond donor character. All possible hydrogen-bonding in the water solution with the oxygen and nitrogen (hydrogen-acceptor) centers in oxazoles (2) and oxadiazoles (3) have been considered in our studies. It has been shown that both the pure solvent and hydrogen-bonding effects are significant and result in 14N magnetic shielding increase. In water solutions the pure solvent effect is larger than the hydrogen-bonding effect. In addition, the solvent effect has been analyzed in terms of its direct and indirect contributions. It should be emphasized that our theoretical results for 14N chemical shifts in oxa- and oxadiazoles remain in a very good agreement with the accurate experimental data. [Copyright &y& Elsevier]

GIAO calculations of the 1H NMR chemical shifts for ethanol at the SCF and DFT levels of theory are presented. The importance of molecular geometry and basis set is discussed. Vibrational correction to the hydroxyl proton chemical shift is also considered in calculations for the monomer of ethanol. The final theoretical results for the monomer obtained at the optimized DFT/B3LYP/6-311G(d,p) geometry with the 6-311G++ (d,p) basis set for NMR are in very good agreement with gas phase experimental data. For the liquid phase ethanol the hydrogen bonding effects are taken into account by performing calculations on various clusters of ethanol. It is shown that inaccuracy due to molecular geometry and basis set in the monomer of ethanol is magnified significantly in calculations for its clusters. In this context the structure of liquid ethanol as predicted recently by quantum cluster equilibrium (QCE) theory is discussed. [ABSTRACT FROM AUTHOR]

It is argued that appropriate methods for timing comparisons with the resolution of identity second-order Møller–Plesset (RI-MP2) technique are local MP2 and dual-basis MP2, not full-accuracy MP2. Like RI-MP2, these methods accelerate MP2 energy evaluation for large molecules and large basis sets, respectively, and generate smooth energy surfaces, at the cost of a small deviation from the canonical results. RI-MP2 is an excellent technique for moderately large molecules and large basis sets. However, its asymptotic scaling with molecular size is much steeper than local MP2, and scaling with basis set size is also worse than dual-basis MP2. We take issue with the claim of Ko¨hn and Ha¨ttig that the precision of the programs should reflect the accuracy provided by the one-electron basis set. Three incorrect MP2 correlation energy values in our previous paper are corrected. [Copyright &y& Elsevier]