Volume 126, Issue 22, 14 June 2007
Index of content:
- Theoretical Methods and Algorithms
126(2007); http://dx.doi.org/10.1063/1.2745299View Description Hide Description
The existing tau-selection strategy, which was designed for explicit tau leaping, is here modified to apply to implicit tau leaping, allowing for longer steps when the system is stiff. Further, an adaptive strategy that identifies stiffness and automatically chooses between the explicit and the (new) implicit tau-selection methods to achieve better efficiency is proposed. Numerical testing demonstrates the advantages of the adaptive method for stiff systems.
126(2007); http://dx.doi.org/10.1063/1.2737444View Description Hide Description
In this paper the authors develop a method to accurately calculate localized vibrational modes for partially optimized molecular structures or for structures containing link atoms. The method avoids artificially introduced imaginary frequencies and keeps track of the invariance under global translations and rotations. Only a subblock of the Hessian matrix has to be constructed and diagonalized, leading to a serious reduction of the computational time for the frequency analysis. The mobile block Hessian approach (MBH) proposed in this work can be regarded as an extension of the partial Hessian vibrational analysis approach proposed by Head [Int. J. Quantum Chem.65, 827 (1997)]. Instead of giving the nonoptimized region of the system an infinite mass, it is allowed to move as a rigid body with respect to the optimized region of the system. The MBH approach is then extended to the case where several parts of the molecule can move as independent multiple rigid blocks in combination with single atoms. The merits of both models are extensively tested on ethanol and di--octyl-ether.
126(2007); http://dx.doi.org/10.1063/1.2737454View Description Hide Description
We introduce a new formula for the acceleration weight factor in the hyperdynamics simulation method, the use of which correctly provides an exact simulation of the true dynamics of a system. This new form of hyperdynamics is valid and applicable where the transition state theory(TST) is applicable and also where the TST is not applicable. To illustrate this new formulation, we perform hyperdynamics simulations for four systems ranging from one degree of freedom to 591 degrees of freedom: (1) We first analyze free diffusion having one degree of freedom. This system does not have a transition state. The TST and the original form of hyperdynamics are not applicable. Using the new form of hyperdynamics, we compute mean square displacement for a range of time. The results obtained agree perfectly with the analytical formula. (2) Then we examine the classical Kramers escape rate problem. The rate computed is in perfect agreement with the Kramers formula over a broad range of temperature. (3) We also study another classical problem: Computing the rate of effusion out of a cubic box through a tiny hole. This problem does not involve an energy barrier. Thus, the original form of hyperdynamics excludes the possibility of using a nonzero bias and is inappropriate. However, with the new weight factor formula, our new form of hyperdynamics can be easily implemented and it produces the exact results. (4) To illustrate applicability to systems of many degrees of freedom, we analyze diffusion of an atom adsorbed on the surface of an fcc crystal. The system is modeled by an atom on top of a slab of six atomic layers. Each layer has 49 atoms. With the bottom two layers of atoms fixed, this system has 591 degrees of freedom. With very modest computing effort, we are able to characterize its diffusion pathways in the exchange-with-the-substrate and hop-over-the-bridge mechanisms.
126(2007); http://dx.doi.org/10.1063/1.2746026View Description Hide Description
The block-localized wave function (BLW) method is a variant of ab initio valence bond method but retains the efficiency of molecular orbital methods. It can derive the wave function for a diabatic (resonance) state self-consistently and is available at the Hartree-Fock (HF) and density functional theory(DFT) levels. In this work we present a two-state model based on the BLW method. Although numerous empirical and semiempirical two-state models, such as the Marcus-Hush two-state model, have been proposed to describe a chemical reaction process, the advantage of this BLW-based two-state model is that no empirical parameter is required. Important quantities such as the electronic coupling energy, structural weights of two diabatic states, and excitation energy can be uniquely derived from the energies of two diabatic states and the adiabatic state at the same HF or DFT level. Two simple examples of formamide and thioformamide in the gas phase and aqueous solution were presented and discussed. The solvation of formamide and thioformamide was studied with the combined ab initio quantum mechanical and molecular mechanical Monte Carlo simulations, together with the BLW-DFT calculations and analyses. Due to the favorable solute-solvent electrostatic interaction, the contribution of the ionic resonance structure to the ground state of formamide and thioformamide significantly increases, and for thioformamide the ionic form is even more stable than the covalent form. Thus, thioformamide in aqueous solution is essentially ionic rather than covalent. Although our two-state model in general underestimates the electronic excitation energies, it can predict relative solvatochromic shifts well. For instance, the intense transition for formamide upon solvation undergoes a redshift of , compared with the experimental data .
On the performance of local, semilocal, and nonlocal exchange-correlation functionals on transition metal molecules126(2007); http://dx.doi.org/10.1063/1.2739539View Description Hide Description
The lowest singlet-triplet transition of AgI has been used to study systematically the performance of local [local density approximation (LDA)], semilocal [generalized gradient approximation (GGA)], and nonlocal (semiempiric hybrid and meta)-type exchange-correlation functionals on a transition metal molecule where dynamic electronic correlation effects are essential. Previous benchmark ab initio calculations showed that the triplet ground state possesses a shallow well in the Franck-Condon region before becoming repulsive at longer internuclear distance [A. Ramírez-Solís, J. Chem. Phys.118, 104 (2003)]. Several density functional theory(DFT) descriptions are compared with the benchmark complete active space self-consistent- coupled pair functional results, using the same relativistic effective core potentials and optimized Gaussian basis sets. A rather unreliable performance of exchange-correlation functionals was found when ascending the various rungs in DFT Jacob’s ladder for this complex molecule. While some of the simpler (LDA and GGA) functionals correctly predict the presence of a short-distance maximum for the state, more sophisticated hybrid and meta-functionals lead to totally repulsive or oscillating curves for the ground triplet state. A thorough discussion addressing the local versus nonlocal character of the exchange and correlation effects on the triplet potential curve is presented. The author concludes that any new efforts directed at producing more accurate exchange-correlation functionals must take into account the more complex electronic structure arising in transition metal molecules, whether these efforts follow the dominant pragmatic semiempiric trend or the more philosophically correct nonempiric pathway to develop better exchange-correlation functionals; only then will the Kohn-Sham version of DFT make the necessary improvements to correctly describe the electronic structure of complex transition metal systems.
Efficient multiparticle sampling in Monte Carlo simulations on fluids: Application to polarizable models126(2007); http://dx.doi.org/10.1063/1.2745293View Description Hide Description
A novel Monte Carlo simulation scheme based on biased simultaneous displacements of all particles of the system has been developed. The method is particularly suited for systems with nonadditive interactions and its efficiency is demonstrated by its implementation for the polarizable Stockmayer fluid. Performance of the method is compared with both the standard one-particle move method and an unbiased multiparticle scheme by computing the mean squared displacements, rotation relaxation, and the speed of equilibration (translational order parameter). It is shown that the proposed biased method is about a factor of 10 faster, for the system considered, when compared with the other schemes.
126(2007); http://dx.doi.org/10.1063/1.2736697View Description Hide Description
By using perturbations in the molecular external potential, the authors deduce the Fukui function from the change in Kohn-Sham orbital energies, avoiding the troublesome differentiation of the density with respect to electron number. Though this paper focuses on the Fukui function, the same general technique can be used to compute the functional derivative of any observable with respect to the external potential. In this paper, the method is used to compute the Fukui function for the beryllium atom and the formaldehyde molecule. The follow-up paper (part II) addresses the problem of computing condensed reactivity indicators.
Computing Fukui functions without differentiating with respect to electron number. II. Calculation of condensed molecular Fukui functions126(2007); http://dx.doi.org/10.1063/1.2736698View Description Hide Description
The Fukui function is a frequently used DFT concept in the description of a system’s regioselective preferences to undergo electrophilic, nucleophilic, or radical attacks. Until now, this function has usually been evaluated using finite difference approximations. The first paper in this series proposed a method for obtaining the Fukui function by a direct calculation of the functional derivative of the chemical potential with respect to the external potential. This paper extends the method to condensed Fukui functions and applies it to an extensive testing set of molecules. Results are promising, which demonstrates the usefulness of the new formalism.
126(2007); http://dx.doi.org/10.1063/1.2741252View Description Hide Description
The binomial -leaping method of simulating the stochastic time evolution in a reaction system uses a binomial random number to approximate the number of reaction events. Theory implies that this method can avoid negative molecular numbers in stochastic simulations when a larger time step is used. Presented here is a modified binomial leap method for improving the accuracy and application range of the binomial leap method. The maximum existing population is first defined in this approach in order to determine a better bound of the number reactions. To derive a general leap procedure in chemically reacting systems, in this method a new sampling procedure based on the species is also designed for the maximum bound of consumed molecules of a reactant species in reaction channel. Numerical results indicate that the modified binomial leap method can be applied to a wider application range of chemically reacting systems with much better accuracy than the existing binomial leap method.
126(2007); http://dx.doi.org/10.1063/1.2743972View Description Hide Description
All-electron variational and diffusionquantum Monte Carlo calculations of the ground stateenergies of the first row atoms (from Li to Ne) are reported. The authors use trial wave functions of four types: single-determinant Slater-Jastrow wave functions, multideterminant Slater-Jastrow wave functions, single-determinant Slater-Jastrow wave functions with backflow transformations, and multideterminant Slater-Jastrow wave functions with backflow transformations. At the diffusionquantum Monte Carlo level and using their multideterminant Slater-Jastrow wave functions with backflow transformations, they recover 99% or more of the correlationenergies for Li, Be, B, C, N, and Ne, 97% for O, and 98% for F.
- Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry
126(2007); http://dx.doi.org/10.1063/1.2739524View Description Hide Description
High level ab initio methods have been used to calculate values of the quadrupole moment of the ground state of on a dense radial mesh spanning the interval of Detailed convergence tests indicate that the resulting equilibrium values of the quadrupole moment and its first radial derivative have absolute uncertainties of 0.3% and 0.8%, respectively, and are more accurate than the best experimental values of these quantities. The calculated quadrupole moment function, together with a recently reported accurate analytic empirical potential energy function [Le Roy et al., J. Chem. Phys.125, 164310 (2006)], is used to generate values of the radial matrix elements determining the absolute intensities of infrared vibration-rotation transitions of ground-state , which take full account of vibration-rotation interactions. These results should improve the reliability of the interpretations of contributions to infrared atmospheric spectra.
126(2007); http://dx.doi.org/10.1063/1.2738945View Description Hide Description
Photofragmentation of mass-selected (, ) clusters is investigated over photonenergies ranging from by linear tandem time-of-flight mass spectrometry. The aniline ring turns out to survive irradiation of photons, and most of the absorbed photonenergy flows to the hydrogen-bonding networks to be used up for liberation of water molecules. The average number of ejected water molecules measured as a function of photonenergy reveals that the loss of water molecules is a photoevaporation process. The distributions of internal energies for parent ions and binding energies of water molecules are estimated from the plots of photofragment branching ratio versus photonenergy, which give nice Gaussian fits. Also, density functional theory calculations are performed to obtain optimized structures of isomers for clusters and binding energies. The authors find that the cluster has a highly symmetric structure and its binding energy in stands out. This is in line with the experimental results showing that is a magic number in the mass distribution and is relatively stable in metastable decay.
126(2007); http://dx.doi.org/10.1063/1.2743433View Description Hide Description
The authors find even-odd variations as functions of for multiple ionization of van der Waals dimers in slow electron-transfer collisions. This even-odd behavior is in sharp contrast to the smooth one for fullerenemonomers and may be related to even-odd effects in dimer ionizationenergies in agreement with results from an electrostatic model. The kinetic energy releases for dimer dissociations [predominantly yielding intact fullerenes in the same or nearby charge states] are found to be low in comparison with the corresponding model results indicating that internal excitations of the separating (intact) fullerenes are important. Experimental appearance sizes for the heavier clusters of fullerenes ( and ) compare well with predictions from a new nearest-neighbor model assuming that unit charges in are localized to molecules such that the Coulomb energy of the system is minimized. The system is then taken to be stable if (i) two (singly) charged are not nearest neighbors and (ii) the molecules have binding energies to their neutral nearest neighbors which are larger than the repulsive energies for the pairs. Essential ingredients in the nearest-neighbor model are cluster geometries and the present results on dimer stabilities.
Real or artifactual symmetry breaking in the BNB radical: A multireference coupled cluster viewpoint126(2007); http://dx.doi.org/10.1063/1.2746027View Description Hide Description
The ground state of the linear BNB radical has been examined via the recently developed reduced multireference coupled cluster method with singles and doubles that is perturbatively corrected for triples [RMR CCSD(T)] using the correlation consistent basis sets (, , T, and Q). Similar to earlier results that were based on the single reference CCSD(T) and BD(T) approaches, the RMR CCSD(T) method also predicts an asymmetric structure with two BN bonds of unequal length, even though the MR effects significantly reduce the barrier height. The computed frequencies for the symmetric and antisymmetric stretching modes agree reasonably well with the experimental data.
126(2007); http://dx.doi.org/10.1063/1.2743015View Description Hide Description
The potential energy curves of the low-lying electronic states of yttriumcarbide (YC) and its cation are calculated at the complete active space self-consistent field and the multireference single and double excitation configuration interaction (MRSDCI) levels of theory. Fifteen low-lying electronic states of YC with different spin and spatial symmetries were identified. The state prevails as the ground state of YC, and a low-lying excited state is found to be higher at the MRSDCI level. The computations of the authors support the assignment of the observed spectra to a transition with a reinterpretation that the state is appreciably populated under the experimental conditions as it is less than of the ground state, and the previously suggested ground state is reassigned to the first low-lying excited state of YC. The potential energy curves of confirm a previous prediction by Seivers et al. [J. Chem. Phys.105, 6322 (1996)] that the ground state of is formed through a second pathway at higher energies. The calculated ionizationenergy of YC is , while the adiabatic electron affinity is at the MRSDCI level. The computed ionizationenergy of YC and dissociation energy of confirm the revised experimental estimates provided by Seivers et al. although direct experimental measurements yielded results with greater errors due to uncertainty in collisional cross sections for formation.
126(2007); http://dx.doi.org/10.1063/1.2737455View Description Hide Description
A recently proposed phenomenon of charge division in a molecular cation [K. T. Lee et al., J. Am. Chem. Soc.129, 2588 (2007)] was examined in a number of molecules by experiment and theory. We investigated the spatial distribution of electrostatic charge in the cation of the following benzene derivatives: -propylbenzene (PB), 3-phenylpropionic acid (PPA), 2-phenylethyl alcohol (PEAL), and 2-phenylethylamine (PEA). A density functional theory calculation indicated that the positive charge was divided into two cationic charge cores in both conformers of , while it is localized mainly on the phenyl group in , , and . This finding was experimentally verified by the characteristic range of electronic transition of these species reflected in the fragmentation pattern of the mass spectra. The degree of charge division in was slightly less than in the cationic conformers of L-phenylalanine in its subgroup II. The charge distribution in a phenyl-containing cation is suggested to depend on whether there exists a functional group that can act as a competing charge core against the phenyl ring.
Anharmonicity and tunneling effects in revisited vibrational photoelectron spectrum of water gas phase126(2007); http://dx.doi.org/10.1063/1.2736700View Description Hide Description
The authors have revisited the description of the core-hole ionization dynamics of the oxygen atom in water by re-exploiting the high-resolution, vibrationally resolved, XPS photoelectron spectrum of gas phase at the edge. The agreement between theory and experiments is mainly controlled by (i) the description of the tunneling behavior near the barrier top (linear H–O–H conformation) of wave functions with high vibrational quanta, and (ii) the relative displacement of the potential-energy minimum of the final state with respect to the ground state one. Accurate change in bond angle between the neutral and core-ionized states is essential to account for the Franck-Condon factors. The photoelectron spectrum of water is well reproduced by the molecular ab initio calculations based on density functional theory and Franck-Condon factors calculations in a double-well simulation of the bending motion.
Rotationally resolved electronic spectra of 9,10-dihydrophenanthrene. A “floppy” molecule in the gas phase126(2007); http://dx.doi.org/10.1063/1.2732753View Description Hide Description
Rotationally resolved fluorescence excitation spectra of several bands in the electronic spectrum of 9,10-dihydrophenanthrene (DHPH) have been observed and assigned. Each band was fit using rigid rotor Hamiltonians in both electronic states. Analyses of these data reveal that DHPH has a nonplanar configuration in its state with a dihedral angle between the aromatic rings of . The data also show that excitation of DHPH with UV light results in a more planar structure of the molecule in the electronically excited state, with . Three prominent Franck-Condon progressions appear in the low resolution spectrum, all with fundamental frequencies lying below . Estimates of the potential energy surfaces along each of these coordinates have been obtained from analyses of the high resolution spectra. The remaining barrier to planarity in the state is estimated to be along the bridge deformation mode and is substantially reduced by excitation of the molecule along the (orthogonal) ring twisting coordinate.
Ab initio design of picosecond infrared laser pulses for controlling vibrational-rotational excitation of CO molecules126(2007); http://dx.doi.org/10.1063/1.2738469View Description Hide Description
Optimal control of rovibrational excitations of the CO molecule using picosecond infrared laser pulses is described in the framework of the electric-nuclear Born-Oppenheimer approximation [G. G. Balint-Kurti et al., J. Chem. Phys.122, 084110 (2005)]. The potential energy surface of the CO molecule in the presence of an electric field is calculated using coupled cluster theory with a large orbital basis set. The quantum dynamics of the process is treated using a full three dimensional treatment of the molecule in the laser field. The detailed mechanisms leading to efficient control of the selected excitation processes are discussed.
- Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation
Transition between collapsed state phases and the critical swelling of a hydrogen bonding gel: Poly(methacrylic acid-co-dimethyl acrylamide)126(2007); http://dx.doi.org/10.1063/1.2743960View Description Hide Description
Transition between collapsed state phases and discontinuous volume phase transition for a hydrogen bondinggel, poly(methacrylic acid-co-dimethyl acrylamide), were observed by using both the volume measurements and fluorescence intensity of the pyranine fluoroprobe (8-hydroxypyrene-1,3,6-trisulfonic acid trisodium salt) bonded to the gel by means of electrostatic interactions. In the collapsed state, while there is no appreciable change in the volume of the gel, a considerable variation in the fluorescence intensity occurred around signaling a second order phase transition between collapsed state phases, from relatively frozen to a fluctuating phase. Our analysis of the data around indicates that the critical point of gel volume transition belongs to the so-called mean-field universality class, as predicted in Onuki [Phys. Rev. A38, 2192 (1988)] and by Golubovic and Lubensky [Phys. Rev. Lett.63, 1082 (1989)]. The relaxation time for the equilibrium swelling critically depends on the temperature and diverges near , where both fluorescence intensity and the volume of the gel change drastically and indicate the discontinuous volume phase transition. The swelling kinetics of the critical gel during the discontinuous volume phase transition can be modeled best with the first term in the expansion of the Li-Tanaka equation for a long initial period of the swelling time.