Molecular Electronic Structure Theory Research Articles

Many-orbital probabilities and their entropy/information descriptors in orbital communication theory of the chemical bond

The joint/conditional “probability” measures of simultaneous many-orbital events in chemical bonds, which involve several basis functions, are derived within standard SCF LCAO MO description of molecular systems. These generalized projection/overlap quantities satisfy the symmetry properties and sum rules of the ordinary probabilities, but can exhibit negative values. The associated information-theoretic descriptors of chemical bonds for a general case of several (dependent) orbital probability schemes are examined. The many-orbital theory extends the range of applications of the orbital communication theory to many classical issues in the theory of molecular electronic structure and chemical reactivity. Such probabilities are required in several molecular scenarios, e.g., bimolecular and catalytic reactivity, directing influence of ligands/substituents, the three-centre bonds, etc., which are also identified. Such an approach implies the effect of the IT-ionic activation of the chemisorbed reactants in catalytic systems.

Multicenter distribution of molecular integrals and energy components

A central problem in both semiempirical and ab initio molecular electronic structure theory is treatment of the three- and four-center interactions. A systematic evaluation of multicenter contributions and a search for invariants has been carried out by computing frequency distribution functions for one-, two- versus three-, four-center two-electron integrals and by separating one-, two-center from three-, four-center terms in the one-electron energies of molecular-orbital theory. Data have been obtained for a considerable number of polyatomic molecules and representative results are presented for NH−2, NH3, CH4, H3O+, C2N2, C3H+3, N4, and C6H6.

Multiscale modeling of polymer materials using field-theoretic methodologies: a survey about recent developments

Understanding the chemistry and physics of polymer systems challenges scientists from a wide spectrum of research areas, ranging from polymer science to molecular electronic structure theory. One of the characteristic features of polymer systems is that their physics involve a multitude of different length and time scales, which generally render the determination of their structure and physical properties on a detailed level computationally exhaustive. To overcome this difficulty, novel field-theoretic methodologies based on the mean field approximation have emerged recently and have proven to deliver useful results in the calculation of mesoscopic polymer models in the regime of high monomer concentrations. In this review we demonstrate that the field-theoretic approach is not only an useful formalism for treating highly concentrated polymer systems on the mesoscopic level of description, but that it is also a promising theoretical tool, to solve the multiscale problems arising in the calculation of physical properties of a wide variety of neutral and charged polymer materials. To this end, we show that the field-theoretic approach possesses the advantageous property to enable the treatment of all levels of description, spanning from the quantum to the continuum scale, within an unified theoretical framework. On the example of the coupling of the mesoscopic and continuum scale, we show that this specific feature constitutes a crucial advantage of field-theoretic approaches with regard to current state-of-the-art particle-based simulation methodologies for connecting different levels of description. Another major benefit relates to their favorable approximation characteristics, which permit to devise efficient approximation strategies for evaluating sophisticated polymer solution models in the low to moderate regime of monomer concentrations in a reliable way. To show this, we present novel low-cost approximation strategies beyond the mean field level of approximation using effective renormalization concepts, originating from the domain of quantum field theory, and demonstrate their usefulness in the calculation of structure and physical properties of several polymer models, described at various levels of description.

High-order entropy measures and spin-free quantum entanglement for molecular problems

A new entropy measure is proposed for the molecular electronic structure theory. The corresponding many-electron, Shannon-like measure reflects quantum entanglement between electronic subsystems with different spins. The related Renyi entropy is introduced, and its connection with the previously considered collectivity analysis is discussed. Investigation of the second-order reduced density matrix (2-RDM) allows one to define an irreducible, size-consistent component of the 2-RDM entropy and to find the irreducible component of the 2-RDM squared norm. Specific computations on several small molecules are carried out at the full configuration interaction level, providing new insights into non-classical, long-range electron correlations and quantum entanglement in these systems. The local spin analysis and the spin-correlator analysis reveal nontrivial spin structure underlying the entangled states.

Theoretical investigation of the potential energy surface for the N( 4S) + C 2H 3 reaction via density functional theory and ab initio molecular electronic structure theory

The potential energy surface for the N( 4S) + C 2H 3 reaction has been theoretically investigated using various quantum chemical methods, including G3, G3B3 and CBS-APNO. Both singlet and triplet potential energy surfaces have been constructed. The reaction mechanism on the singlet surface is simple. However, the reaction mechanism on the triplet surface is more complicated. It is revealed that the formation of CH 2CN + H is the dominant channel on the triplet surface. The minimum-energy crossing point (MECP) connecting the triplet and singlet surfaces has been characterized at the B3LYP/6-311++G(3df,2p) level. The calculational results suggest the possibility of the production of CH 2CN + H on the singlet surface. The conclusions are in agreement with the experimental results.

Challenging scaling laws of flexible polyelectrolyte solutions with effective renormalization concepts

Recasting a many-particle problem in a field-theoretic formalism is nowadays a well-established theoretical tool used by scientists across a wide spectrum of research areas, ranging from polymer physics to molecular electronic structure theory. It has shown to provide useful results in many complex situations, where the physics of the system involves many degrees of freedom and a multitude of different length scales, generally rendering its numerical treatment on a detailed level computationally intractable. To reduce the computational burden, field-theoretic methodologies usually take advantage of the mean-field approximation. This approximation technique is known to give reliable information about the system in the high concentration regime, where the interactions are highly screened. However, it is well established that the ranges of physical interest in most biological and technological applications lie in the intermediate to low concentration regimes, where fluctuations beyond the mean-field level of approximation become important and dominate the overall physical behavior. In this work we introduce a new self-consistent field theory for flexible polyelectrolyte chains, in which the monomers interact via a pair potential of screened Coulomb type, and derive suitable thermodynamic expressions for all concentration regimes. Our approach combines the renormalization concepts of tadpole renormalization, which has recently been successfully employed in calculations of prototypical neutral polymer and polyelectrolyte solutions, with the Hartree renormalization procedure. By comparing our approach to experimental measurements as well as alternative theoretical approaches, we demonstrate that it provides useful osmotic pressure results for polyelectrolyte systems composed of sodium poly(styrene-sulfonate) without and with added salt over the whole range of monomer concentrations.

σ- and π-Bond Strengths in Main Group 3−5 Compounds

The sigma- and pi-bond strengths for the molecules BH2NH2, BH2PH2, AlH2NH2, and AlH2PH2 have been calculated by using ab initio molecular electronic structure theory at the CCSD(T)/CBS level. The adiabatic pi-bond energy is defined as the rotation barrier between the equilibrium ground-state configuration and the C(s)symmetry transition state for torsion about the A-X bond. We also report intrinsic pi-bond energies corresponding to the adiabatic rotation barrier corrected for the inversion barrier at N or P. The adiabatic sigma-bond energy is defined as the dissociation energy of AH2XH2 to AH2 + XH2 in their ground states minus the adiabatic pi-bond energy. The adiabatic sigma-bond strengths for the molecules BH2NH2, BH2PH2, AlH2NH2, and AlH2PH2 are 109.8, 98.8, 77.6, and 68.3 kcal/mol, respectively, and the corresponding adiabatic pi-bond strengths are 29.9, 10.5, 9.2, and 2.7 kcal/mol, respectively.

Characterization of singlet ground and low-lying electronic excited states of phosphaethyne and isophosphaethyne

The singlet ground ((approximate)X(1)Sigma1+) and excited (1Sigma-,1Delta) states of HCP and HPC have been systematically investigated using ab initio molecular electronic structure theory. For the ground state, geometries of the two linear stationary points have been optimized and physical properties have been predicted utilizing restricted self-consistent field theory, coupled cluster theory with single and double excitations (CCSD), CCSD with perturbative triple corrections [CCSD(T)], and CCSD with partial iterative triple excitations (CCSDT-3 and CC3). Physical properties computed for the global minimum ((approximate)X(1)Sigma+HCP) include harmonic vibrational frequencies with the cc-pV5Z CCSD(T) method of omega1=3344 cm(-1), omega2=689 cm(-1), and omega3=1298 cm(-1). Linear HPC, a stationary point of Hessian index 2, is predicted to lie 75.2 kcal mol(-1) above the global minimum HCP. The dissociation energy D0[HCP((approximate)X(1)Sigma+)-->H(2S)+CP(X2Sigma+)] of HCP is predicted to be 119.0 kcal mol(-1), which is very close to the experimental lower limit of 119.1 kcal mol(-1). Eight singlet excited states were examined and their physical properties were determined employing three equation-of-motion coupled cluster methods (EOM-CCSD, EOM-CCSDT-3, and EOM-CC3). Four stationary points were located on the lowest-lying excited state potential energy surface, 1Sigma- -->1A", with excitation energies Te of 101.4 kcal mol(-1) (1A"HCP), 104.6 kcal mol(-1)(1Sigma-HCP), 122.3 kcal mol(-1)(1A" HPC), and 171.6 kcal mol(-1)(1Sigma-HPC) at the cc-pVQZ EOM-CCSDT-3 level of theory. The physical properties of the 1A" state with a predicted bond angle of 129.5 degrees compare well with the experimentally reported first singlet state ((approximate)A1A"). The excitation energy predicted for this excitation is T0=99.4 kcal mol(-1) (34 800 cm(-1),4.31 eV), in essentially perfect agreement with the experimental value of T0=99.3 kcal mol(-1)(34 746 cm(-1),4.308 eV). For the second lowest-lying excited singlet surface, 1Delta-->1A', four stationary points were found with Te values of 111.2 kcal mol(-1) (2(1)A' HCP), 112.4 kcal mol(-1) (1Delta HPC), 125.6 kcal mol(-1)(2(1)A' HCP), and 177.8 kcal mol(-1)(1Delta HPC). The predicted CP bond length and frequencies of the 2(1)A' state with a bond angle of 89.8 degrees (1.707 A, 666 and 979 cm(-1)) compare reasonably well with those for the experimentally reported (approximate)C(1)A' state (1.69 A, 615 and 969 cm(-1)). However, the excitation energy and bond angle do not agree well: theoretical values of 108.7 kcal mol(-1) and 89.8 degrees versus experimental values of 115.1 kcal mol(-1) and 113 degrees. of 115.1 kcal mol(-1) and 113 degrees.

R12 methods in explicitly correlated molecular electronic structure theory

The past few years have seen a particularly rich period in the development of the explicitly correlated R12 theories of electron correlation. These theories bypass the slow convergence of conventional methods, by augmenting the traditional orbital expansions with a small number of terms that depend explicitly on the interelectronic distance r 12. Amongst the very numerous discoveries and developments that we will review here, two stand out as being of particular interest. First, the fundamental numerical approximations of the R12 methods withstand the closest scrutiny: Kutzelnigg's use of the resolution of the identity and the generalized Brillouin condition to avoid many-electronic integrals remains sound. Second, it transpires that great gains in accuracy can be made by changing the dependence on the interelectronic coordinate from linear (r 12) to some suitably chosen short-range form (e.g., exp(−αr 12)). Modern R12 (or F12) methods can deliver MP2 energies (and beyond) that are converged to chemical accuracy (1 kcal/mol) in triple- or even double-zeta basis sets. Using a range of approximations, applications to large molecules become possible. Here, the major developments in the field are reviewed, and recommendations for future directions are presented. By comparing with commonly used extrapolation techniques, it is shown that modern R12 methods can deliver high accuracy dramatically faster than by using conventional methods. Contents PAGE 1. Introduction 429 1.1. The origin of the problem 429 1.2. Two-electron systems 430 1.3. Explicitly correlated MP2 methods 430 1.4. Gaussian geminals 431 1.5. Exponentially correlated Gaussians 432 1.6. The transcorrelated method 433 2. R12 wavefunctions 433 2.1. Definition 434 2.2. Correlation factors 435 2.3. Projection operators 437 2.4. Levels of theory 439 2.5. Methods for open shells 440 3. Approximations of many-electron integrals 441 3.1. Exact evaluation 442 3.2. Approximations: GBC, EBC and 443 3.3. Resolution of the identity 445 3.4. Numerical quadrature 447 3.5. Density fitting 449 3.6. DF combined with RI 451 4. Examples from second-order perturbation theory 452 4.1. Technical details 453 4.2. R12 results in comparison with extrapolated values 454 4.3. Comparison between R12 and F12 results 458 5. Perspectives 461 5.1. Higher level methods 461 5.2. Local approximations 461 5.3. Conclusions 462 5.3.1. Correlation factor 462 5.3.2. Projection operator 462 5.3.3. Formulation of intermediate B 463 5.3.4. Approximating integrals 463 5.3.5. Efficiency improvements 463 Acknowledgements 463 References 464

Bonding analysis using localized relativistic orbitals: Water, the ultrarelativistic case and the heavy homologues H2X (X=Te, Po, eka-Po)

We report the implementation of Pipek-Mezey [J. Chem. Phys. 90, 4916 (1989)] localization of molecular orbitals in the framework of a four-component relativistic molecular electronic structure theory. We have used an exponential parametrization of orbital rotations which allows the use of unconstrained optimization techniques. We demonstrate the strong basis set dependence of the Pipek-Mezey localization criterion and how it can be eliminated. We have employed localization in conjunction with projection analysis to study the bonding in the water molecule and its heavy homologues. We demonstrate that in localized orbitals the repulsion between hydrogens in the water molecule is dominated by electrostatic rather than exchange interactions and that freezing the oxygen 2s orbital blocks polarization of this orbital rather than hybridization. We also point out that the bond angle of the water molecule cannot be rationalized from the potential energy alone due to the force term of the molecular virial theorem that comes into play at nonequilibrium geometries and which turns out to be crucial in order to correctly reproduce the minimum of the total energy surface. In order to rapidly assess the possible relativistic effects we have carried out the geometry optimizations of the water molecule at various reduced speed of light with and without spin-orbit interaction. At intermediate speeds, the bond angle is reduced to around 90 degrees , as is known experimentally for H(2)S and heavier homologues, although our model of ultrarelativistic water by construction does not allow any contribution from d orbitals to bonding. At low speeds of light the water molecule becomes linear which is in apparent agreement with the valence shell electron pair repulsion (VSEPR) model since the oxygen 2s12 and 2p12 orbitals both become chemically inert. However, we show that linearity is brought about by the relativistic stabilization of the (n + 1)s orbital, the same mechanism that leads to an electron affinity for eka-radon. Actual calculations on the series H2X (X = Te, Po, eka-Po) show the spin-orbit effects for the heavier species that can be rationalized by the interplay between SO-induced bond lengthening and charge transfer. Finally, we demonstrate that although both the VSEPR and the more recent ligand close packing model are presented as orbital-free models, they are sensitive to orbital input. For the series H2X (X = O, S, Se, Te) the ligand radius of the hydrogen can be obtained from the covalent radius of the central atom by the simple relation r(lig)(H) = 0.67r(cov)(X) + 27 (in picometers).

Molecular quantum mechanics to biodynamics: Essential connections

Computational tools and the underlying theoretical framework for direct simulation of complex molecular behavior have become extremely sophisticated. Nevertheless, further improvements in speed, accuracy, and usability can be expected. The future application of these tools to chemical, biochemical, and materials problems needs to be critically considered in any new developmental work, for it is important to understand the role of detailed information all the way down to the quantum mechanical level. To what extent information from the most fundamental treatments, particularly molecular electronic structure theory, needs to be incorporated should be assessed. This report offers several perspectives on the connections and developments that exist now and that may be ahead.

Some late-term thoughts of a density-functional theorist

Fourteen problems are stated within the density-functional theory of molecular electronic structure. Their alleviation will bring the subject closer to maturity.

Some late-term thoughts of a density-functional theorist

Fourteen problems are stated within the density-functional theory of molecular electronic structure. Their alleviation will bring the subject closer to maturity.

Vibrational Analysis of the Inelastic Neutron Scattering Spectrum of Tetramethylammonium Borohydride by Molecular Dynamics Simulations and Electronic Structure Calculations

The vibrational spectra of three isotopomers of tetramethylammonium borohydride (TMAB) as well as of tetramethylammonium borofluoride were measured at 15 K by inelastic neutron scattering (INS). Direct analysis of the measured spectra was accomplished using classical molecular dynamics (MD) simulations and ab initio electronic structure theory for the crystalline solid. Comparison of observed and computed INS spectra revealed that the periodic electronic structure calculations for the crystalline solid provide a good description of the experimental INS spectrum and clearly demonstrates the power of this combined experimental/theoretical approach.

Theoretical Study of Glass Systems Using ab Initio Molecular Electronic Structure Theory. 1. Lithium Metaphosphate Glass

A methodology for the theoretical study of glass systems using ab initio molecular electronic structure theory is discussed. Lithium metaphosphate glass of the formula Li2O·P2O5 is considered, and the choice of models and methods is discussed. The presence and significance of multiple minima on the potential energy surface is also discussed. Four lowest energy structures for the model (Li2O·P2O5)4 are given, and vibrational spectra are predicted and compared to experimental data. A structure that would indicate preference for the formation of P−O−P chains in the lithium metaphosphate glass is found to be the most stable energetically in the model. Good overall agreement with experimental infrared and Raman spectra is achieved.

Macroconfigurations in molecular electronic structure theory

AbstractBased on the well‐known idea of dividing a molecular orbital set into groups, and imposing restrictions on allowed group occupancies, a more general formalism, which we refer to as the macroconfiguration approach, is developed. The approach is shown to be useful in four complementary contexts: First, as with previous uses of orbital groupings, physical considerations can actively be taken into account in constructing configuration spaces; second, the approach is demonstrated to enable the screening of a vast number of noninteracting electron configuration pairs in a computationally efficient manner; third, all advantages of the Table–configuration interaction (CI) technique can be used effectively for evaluating Hamiltonian matrix elements between interacting configurations; finally, the macroconfiguration technique provides an efficient way of regenerating excited configurations as needed in a calculation. These characteristics indicate that the suggested approach is promising for improving the computational efficiency of methods describing electron dynamic correlation and, in particular, for CI calculations involving highly (e.g., triply and quadruply) excited configurations and for methods of effective Hamiltonian theory. The advantages of the suggested technique are illustrated by the results of calculations on the ground and excited states of the difluorodioxirane (CF2O2) molecule at the second‐order generalized Van Vleck perturbation theory (GVVPT2) level. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Alternatives to multireference methods for the molecular electronic structure problem

AbstractThe development of robust many‐body methods for the molecular electronic structure problem with respect to multireference functions has attracted much attention over the past two decades. In recent years, multireference methods based on the Brillouin–Wigner expansion have been shown to overcome the intruder state problems which have plagued similar approaches based on the Rayleigh–Schrödinger series. However, there are some problems in molecular electronic structure theory, which may be handled by means of multireference methods, but can be treated by methods that avoid the use of multireference functions. We consider two examples of alternatives to multireference methods for the molecular electronic structure problem. The study of excited states having the same symmetry as the ground state or some lower lying excited state often involves the use of a multireference function. We describe an alternative procedure based on the generalized Rayleigh–Ritz variation principle. Gidopoulos, Glushkov, and Wilson have termed this the optimized trace method. The generalized Rayleigh–Ritz principle for the relativistic formulation of the molecular electronic structure problem is briefly also considered. Molecular dissociative processes are frequently described by quantum chemical methods based on multireference functions. Single‐reference Hartree–Fock methods usually provide a qualitatively incorrect description of such processes even in the simplest of molecules, H2. However, approximate single configuration wave functions constructed from nonorthogonal orbitals can often afford a useful approximation to bond‐breaking processes. Each occupied nonorthogonal orbital is then an eigenfunction of a different Fock‐like operator. Each of these Fock‐like operators supports a spectrum of M single particle states, where M is the size of the basis set, and only the lowest of these is occupied. We briefly consider the relativistic formulation of the molecular electronic structure problem based on approximations involving products of nonorthogonal functions within the Furry bound state interaction picture of quantum electrodynamics. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Accurate molecular integrals and energies using combined plane wave and Gaussian basis sets in molecular electronic structure theory

This paper introduces two developments for the application of plane wave basis sets for accurate molecular calculations. (1) An analytical formula is introduced for the momentum space representation of a Coulomb operator truncated to a finite range. Using this operator, interactions between the molecule and its periodic replicas can be exactly eliminated. Examples demonstrating the accuracy of our scheme are given. Calculations using a good-quality plane wave basis yield variational total SCF energies which are lower than those obtained with the cc-pvQZ basis for simple two-electron systems. (2) A new mixed-basis augmented plane wave all-electron method, the plane wave core Gaussian method has been developed which expands the valence part of the molecular orbitals in plane waves, and the corelike part in nonoverlapping compact Gaussians. Analytic equations have been derived for the necessary mixed Gaussian/plane wave electron repulsion integrals. Using such augmented basis set, we were able to reproduce the Gaussian-basis Hartree energies of small molecules to within a few μEh.

First-principles based matrix Green's function approach to molecular electronic devices: general formalism

Transport in molecular electronic devices is different from that in semiconductor mesoscopic devices in two important aspects: (1) the effect of the electronic structure and (2) the effect of the interface to the external contact. A rigorous treatment of molecular electronic devices will require the inclusion of these effects in the context of an open system exchanging particle and energy with the external environment. This calls for combining the theory of quantum transport with the theory of electronic structure starting from the first-principles. We present a self-consistent yet tractable matrix Green's function (MGF) approach for studying transport in molecular electronic devices, based on the non-equilibrium Green's function formalism of quantum transport and the density functional theory (DFT) of electronic structure using local orbital basis sets. By separating the device rigorously (within an effective single-particle theory) into the molecular region and the contact region, we can take full advantage of the natural spatial locality associated with the metallic screening in the electrodes and focus on the physical processes in the finite molecular region. This not only opens up the possibility of using the existing well-established technique of molecular electronic structure theory in transport calculations with little change, but also allows us to use the language of qualitative molecular orbital theory to interpret and rationalize the results of the computation. We emphasize the importance of the self-consistent charge transfer and voltage drop on the transport characteristics and describe the self-consistent formulation for both device at equilibrium and device out of equilibrium. For the device at equilibrium, our method provides an alternative approach for solving the molecular chemisorption problem. For the device out of equilibrium, we show that the calculation of elastic current transport through molecules, both conceptually and computationally, is no more difficult than solving the chemisorption problem.

On the use of many-body perturbation theory and quantum-electrodynamics in molecular electronic structure theory

Many-body perturbation theory is firmly established in molecular electronic structure studies both as a method of calculation in its own right and in underpinning other approaches to the electron correlation problem, such as coupled electron pair approximations and various cluster expansions. The central pillar of the many-body perturbation theory is the linked diagram theorem obtained by Goldstone using the method of Feynman graphs to enumerate the terms of the perturbation series. Feynman had introduced his graphs in his formulation of quantum electrodynamics. Goldstone restricted his analysis to the non-relativistic many-body problem, so that interactions were taken to be instantaneous and the effects of relativity were ignored. In recent years, the growing interest in the treatment of relativistic and quantum electrodynamic effects in atoms and molecules has necessitated the re-introduction of physics that has been known for over forty years. A key to this development for molecular systems is a rigorous and robust implementation of the algebraic approximation for Dirac and Dirac-like equations. The algebraic approximation provides a representation of both the positive-energy and the negative-energy branches of the Dirac spectrum. Relativistic many-body perturbation theory, relativistic coupled pair approximations and relativistic coupled cluster theories can be formulated within the ‘no-virtual-pair’ approximation. Such formulations are restricted to the positive energy branch of the spectrum. However, the negative energy states make an essential contribution to the description of atomic and molecular electronic structure. The investigation of this contribution is facilitated by proper implementation of the algebraic approximation using formulations which are amenable to systematic refinement.